Yeah I would have to agree! Considering that I used to teach Maths and Physics to college students, I felt compelled to understand each and every topic that I had to teach them, so that I could help THEM understand it! Because some of us don't have robot like minds, simply absorbing information that flies right over your head, in order to pass exams at some point in the future, or perform some monotonous task! Look! Of course I don't understand Quantum Mechanics! No body does! But one CAN get to grips with the abstract mathematics involved in order to at least get a handle on the workings of Quantum Mechanics, in order to do useful work! Of course I don't understand the imaginary number *i* ! But one can get to grips with Complex Mathematics, to carry out whatever computation that they need to do, because the mathematics of Complex Numbers is sound! What I'm trying to say is, sure! There are PLENTY of abstract ideas out there! Not just in Physics but in Mathematics too! Ideas sooo abstract, that they truly bend the mind! But so long as you can get to grips with, and understand the Mathematics behind these concepts, then you can at least get a working idea behind them, even if you do not fully understand the abstract ideas themselves! There is a dichotomy between an abstract idea... And the Mathematics used to describe that idea! Fully understanding the abstract idea might be impossible! But fully understanding the Mathematics used to describe that idea is imperative!!!
@@sdwoneI'm just a pupil, but I really get obsessed with such abstract ideas like number i or trigonometry, but I'm only trying to understand and more often at the end I just don't understand.
@@AGguyy-j9n Remember... Ultimately Mathematics is just a set of abstract ideas bound by the rules of Logic! Sure, that's a HUGE over simplification, but a valid one. And as for imaginary *i* ??? LOL! Honestly... This is one of the Biggest Mysteries out there! Right up there with PI, Euler's number *e* and the Golden Ratio etc... Trying to understand these concepts leads you into philosophical territory... But nonetheless, these concepts are also bound by Mathematical Logic. And so long as your grip on the fundamental logic is sound, then you can confidently work with them... Even if you don't fully understand them! And to be honest... Nobody does! So don't sweat it! As one famous Physicist once quipped: "Shut up and calculate!" And oftentimes, that's the best we can do...
"The important thing isnt can you read music, its can you hear it". Let me tell you dude, I was having a full on awakening during my last college class
Wow , what a great moment it must be.. I am struggling and struggling With understanding and solving the problems.. Some People are just blessed with a brain ...
I think the video is talking about a different way of learning and it involves more of the unconscious brain (female brain), where you just expose yourself to it but you don't make much effort, you just watch it, absorb what you can absorb without worrying about anything and let it (your unconscious brain) do the work for you. Learning this way is much more sufficient and so much less work needed, you'll just find yourself knowing. This is how babies learn language. This is how I learned English starting 4 years ago. In school I would have never been able to make more than a very simple sentence. Look it up. Its a real thing
@@violetlup8652 Your comment seems important, even though I did not comprehend it entirely. I've read it three times already ans took some notes. I'm putting it all in on cracking this nut!
This did not interfere with your self-education. This was self-education! If you don't understand something, then you haven't learned it. Dot. If you use multiplication without understanding what the hell multiplication is, then you don't know multiplication.
The video is right. Don't slow yourself down because your mind might not be ready yet. So roll with the process, learn the skill, and at the very minimum you can at least solve the problems and at best going through the motions many times may help things click.
@@olegrooo713 this isn't what he meant though, you have to understand what you need to understand, an idea bothering you at the time doesn't mean you can't make progress unless you understand its in and outs, we all have objectives, its not a straight path where every concept has to be crystal clear or else your knowledge is incomplete, if that was the case nobody would have time to develop meaningful skills
I failed algebra 2 times before I had a math teacher say this to me. Stop trying to understand, memorize the steps, do the steps, and eventually it will start to make sense. Math for me is a field where you have to run before you can walk.
I think understanding first IS genuinely a better way of teaching. Its just having a teacher who can effectively teach that way is really rare. I thought what you did before I had the best teacher I ever had for algebra 2 who made me enjoy math for the first time in my life.
the weird thing is all things are memorization. Some people memorize calculations. More advanced people memorize processes and formulas. Even more advanced people memorize themes and algorithms and problem solving strategies. At that 3rd stage we usually just call it "understanding the material deeply and conceptually". Even more advanced people solely focus on memorizing "how to focus" and making a habit of "focusing".
One way I encourage myself not to get hung up on things is by internalizing the mantra: "trust your brain". The idea is, your brain uses much more than just the information you have in your working memory to solve problems; it recognizes patterns, it remembers things, it keeps important ideas more accessible than less important ideas, etc. The road to conscious understanding is often paved with improvements in all these metrics; it's not all or nothing. If you're improving, you are learning, even if you can't yet fit the general pattern of the problem into your working memory. Trust that the other parts of your brain matter also.
In my experience jumping around from doing the steps/memorizing and understanding is what works best. Also look for multiple sources and related topics. It all starts to fall in together like a puzzle
The most surprising part about math is how it'll suddenly teach you practical lessons for life. One of my biggest problems was solving too quickly and making extremely minor mistakes. It became such a problem that it made me dispise math. It wasn't until I decided what the problem was because I knew I wasn't stupid, and I knew I was capable of doing hard things. I eventually deduced that all I needed to do was to simply slow down. There is no shame in being painstakingly considerate of every single stroke of the process in solving hard problems. Then, I started to relate it to everything in my life with logic. Math has made me appreciate the process, and to love the process. I've developed a deeper appreciation for life, and I have a deep joy in the hard things.
Understanding the explanations in math is like understanding poetry: you need experience, especially with relevant problems, so that the words have more meaning for you and resonate better.
Is that not what the students are seeking out though? He's giving them an idea void of any meaning, and they're seeking out the context from which it arose, or seeking to create and explore context for themselves to grasp it, and he's suggesting that they just don't, and you're suggesting that 'it'll come'. It kind of reminds me of _the parable of the drowning man_. It feels like what you're both really saying is that to 'mesh' better with the education system you've just got to give up on understanding things and trust things blindly, which I'd be inclined to agree with, but which I also despise.
@@callumscott5107 Ah, sorry, that's not what I'm trying to imply. I'm saying that if a student isn't understanding an idea, then the student should do more practice problems -- perhaps a mix of problems from earlier sections and from the current section -- so that the explanations will make more sense. It's not about blind faith, but delayed gratification, because real world problem-solving often involves a humbling period of mystery where we're feeling our way around in the dark, until we find a candle, and can use it to light other candles. Another way to put it is that sometimes our ideas are waiting for not another revision, but just a few more glimpses of the sun before they can blossom. 🌻 I'm not a fan of our education system. It puts too much pressure on students to learn more than they're ready for, too quickly. These things take time, and everyone's clock is different, especially at different periods of their development.
@@callumscott5107 your mistake is thinking this only applies to the education system. this applies to every problem in the world. if we had to understand everything before doing something, we wouldn't have time to do anything. in the case of college, if i had stayed trying to understand every single concept i came across because i enjoyed it, i wouldn't have the job i have now, not because i wouldn't have a title but because of the actual meaningful things i learned, and in fact, now i have a broader perception of things and i can understand the things that were once complicated. plus, wanting to "understand" maths or science isn't totally possible, you're always learning at your own pace, whether its advanced or low level stuff and you have to follow this philosophy to truly make it work
@b_delta9725 I don't like the premise of intensely studying and learning lists of concepts, defined by others as useful, precisely because I don't think that's how people really learn best. I advocate a more holistic and self-directed, curiosity driven learning. So yes I think we agree that that's a waste of time, that's not what I stand for. But the problem with trying to master every topic on the course isn't that they're too curious, it's that their curiosity is too narrowed to something defined by an authority, as opposed to something more broad and open to life in general. I was more-so saying that if people are legitimately curious about this, in a healthy and eclectic way, then denying them answers to the questions they're asking, under the guise of 'you don't need those answers' is a pretty disturbing thing to righteously do to someone. It's like there's anxious questions and legitimately curious questions, and I'm talking about respecting the latter whilst I get the sense you're talking about disregarding the former.
@SpoiledViking I'm not making a case for brute forcing lists of problems to learn, in fact I'm making the opposite case. I think we've read very different things from the video. What I've been disturbed by is the possibility that someone might approach him with a genuinely curious question, emanating from their heart and soul, and this guy just goes "stop trying to understand this stuff, sacrifice that curiosity in favour of continuing with the course material". To me, it's as though curiosity extends these hooks from us that get caught on the most unpredictable of things, and there's tremendous beauty in trying to delicately untangle ourselves from what captures us, then this guy's just advocating for you to snip at their base and get on with life. What kind of an education system punishes those who are caught by curiosity?
This is helpful advice for any arena of life I feel. As a filmmaker (and TH-camr) I get so worked up, frustrated, anxiety-ridden over every little video that I make, overanalyzing whether it's funny, watchable, entertaining, why it didn't get more views/likes/subscribers, worrying that it sucks horribly and I should've never made it.... when I could just finish the video/film, put it out there, let it exist, and move onto the next film project. Thankyou, time to finish watching the video lol.
I'm early in my career of learning college math 20 years after highschool and emotionally this is the biggest change for me, when I start to think "But why???" I replace it with "ok textbook I believe you" and I move on. I've also found that for some of these concepts as you say later it is clicking. Before I could not move on and would also give up as these frustrations built and my foundation weakened.
Same thing I've been going thru with computer programming... I'm better at just moving on and trusting it will all fall into place at some point, but it used to bother me quite a bit not understanding the "why?" of some topics or concepts.
@@gregorio87 Good rule of thumb for me with CompSci is "Why?; usually because its either better use of time/space computationally or saves time &/or headspace for you & your co-workers later on" a better question is "how". "Why is 5v representative of 'True' on this bus but 0v or 3.3v is T on this other bus"; "because we said so".. "How is this presumption incorporated into the rest of the system" is far more important because axioms can be arbitrary, whereas the build up of arbitrary selections (made simply because somehere eventually required A decision to be made) result in interfaces that must be implemented particularly such to enable interoperability between distinct sets of arbitrary selections. Also technical debt & sunk cost fallacy is a far broader socio-economic phenomenon than many will like to admit. If you just need your "feet to touch the bottom of the pool" to get over your ~"thalassophobia" I recommend constructing an ALU in TTL or just write out a truth table for a 'full adder' & meditate on what's going on with ASM. This may come across as condescending or daunting depending on where you are but I feel its a fairly solid place to start gathering the "long pieces" to clear up those longer standing "tetris rows" by grounding with physical representations.
Hey man this is I believe the second video I’ve watched of yours and I just want to say as a 19 year old struggling to figure out the equation of living a good life I can’t put into words how thankful I am of the person you are and the teachings you give, I love these videos you’re awesome man
When I was a Paramedic student in 2000-01, I asked an ER Doctor how he remembered everything. He said,” Don’t study to memorize. Study to recognize this way when you see it, you know what to do.” I carry that with me every day, and always told my students the same.
@@binayrawat1866I just saw you comment the same thing under someone else's comment and you did it twice under this guy's comment. I just meant that ask one person and wait for a response. If you don't get one, ask someone else and wait.
@@dynaspinner64 yeah you're right, but I really need this as soon as possible. And asking help to every person at the same time is not a wrong thing I guess. I just want to know the people's opinion.
I know what he means. Here's an analogy: imagine you're asked to explore and memorize a forest, so you can lead a group safely through it. So you go into the forest to start exploring, and you come across a strange tree that looks like it's important. So, you spend time memorizing this single tree's location in the forest to later tell the group about. Then, you move on, and come across another strange tree. You once again spend time memorizing the location of a singular tree. You try to continue, but you find yourself stopping at every single bizarre tree and memorizing each position. "Here's tree number 46, tree number 47..." and so on. Soon, the sun sets, so you return to to the group. They ask if you found a source of water. You tell them where you found a tree. They ask you what the safest route is. You tell them where you found a tree. They ask you where they can find food. You tell them where you found a tree. In the end, your efforts were unproductive! You spent so much time looking at the trees instead of the forest, that you're just as clueless now as you went in. In other words, you need to see the bigger picture before small things make sense. It's okay to walk past a strange looking tree without memorizing it (it's okay to be confused and not fully [emphasis on fully] understand something), later once you've explored the entire forest (learned the full scope of something), it'll be easier to remember where that tree is (understanding something becomes easier with more context)
Thanks for your insightful comment; it's a nice thought provoker. I sometimes struggle with looking too far into one task at a time, and I think sometimes it's okay to just do the best you can and move on even if it doesn't pan out instead of trying too hard to fully solve a difficult problem. Though, maybe that struggle is beneficial to future problem solving.
This is such an important message. I suffer from same. The intense need to UNDERSTAND a particular point before moving on. Its a bit like the social media FOMO, the 'Fear Of Missing Out'. The fear of not understanding something that could seriously impact you later. Understanding is all about context. If you dont understand something at a particular point then your brain isn't READY to understand, it doesnt have the necessary context. But thats OK, that context will come. I think if more lecturers gave this pep talk right at the beginning, I think more students would spend less time fretting and more time enjoying studying.
It’s similar to our social media addiction. It started off as a little bit of entertainment, but because of the unlimited content, we’re constantly scrolling trying to enjoy as much of it as possible, which is bad for our mental health. In the same way, when we’re learning something there so much information freely available and because of this freedom, were tempted to get through it all at once, but learning is meant to be a natural process, that like u said, is best done in context and overtime. So even though the information is there in as much detail as u could ask, we should focus on absorbing it naturally comes to us.
"understanding always comes in retrospect" only when you have all the pieces of the puzzle will you be able to see the full picture. One of my professors told me this and it has stuck with me until now. Amazing video.
I always write down every single confusion I have when I learn a topic. It relieves my anxiety since I know I am not going to forget about these details and I will eventually understand them tomorrow or day after.
Agreed. The better you are managing your stress and anxiety, the more successful you’ll usually be in all areas of life. So many of us want to know everything in order to have a greater impact/image on our respective disciplines, and forget the role of community, peers, teams etc.
I'm in computer science, and I think this is probably one of the best pieces of advice any student learning anything needs. I looked too far ahead at where I'm headed, but I realize it doesn't matter. I might think it does, but time is evolving, nonstop, forever. Every one of us lives with only a decent understanding of anything around us, and we keep moving forward and get to live anyway. Maybe I will get that job in the end. Maybe I'll learn neetcode and algorithms at some point. Or maybe I'll get a job in IT and be run-of-the-mill, but maybe I'll get to work on music as well like I wanted. But this video helped me see the infinitesimal-crunching numbers down closer to nothing, to no possible chance. And then I didn't adapt; I got hung up on my ego, my pride as a student, when that wasn't a luxury. The luxury was learning what I could do today and adapting again tomorrow. I'll always do that because I get to live and revisit things later.
The message of the video is clear. The title is a bit misleading. You shouldn't stop trying to understand ever again. Instead, you should stop trying to understand immediately. Thank you for your video!
The truth is you need to selectively accept truth, otherwise you are too easy to bias. Just using something you don't understand, leads to poor ability to optimize and create new solutions. I had a lot of bad teachers tell me it was okay not to understand, but those are the teachers I learned to ignore, and I would work on my own and just come in for the exams, and then get 95% - 100% in the course. The only thing I agree with is taking a break and moving on to something else for a bit, refueling yourself, but then get back to it.
I actually agree. If your goal is just to solve the problem, then you don't necessarily need to understand it. But if your goal is to learn, then it doesn't matter how many problems you get done if you don't learn anything from them.
It depends on how interdisciplinary your discipline is. If your a math phd student that makes sense. But if your an HVAC engineer or an industrial engineer selecting what type of conveyor to use your probably going to use a lot of equations and charts that really just situationally dependent approximations of complex math. And the math and reasoning to develop those simple equations can be hard to remember if you never use it. It’s important to know the general first principles of your field, but no one can solve every problem from scratch or understand everything that goes into a complex project. So in engineering it is often necessary to trust the situationally dependent simple linear approximated algebra equation vs trying to analytically solve the same problem with complex differential equation model yourself. This is one of the main reasons why espionage is so powerful. It take a super intelligent entity like a large tech company to create an F35 or an iPhone. No one person knows how every component works. The Soviets had good engineers working on there own bomb design that would have made there first bomb a little better than the first U.S. bomb. But they ended up using the design they stole from the Americans. Now assuming they didn’t have the expertise to have done there own design they still would have had to know how to run there own enrichment plant that requires all kinds of engineering to execute. They would not have needed to know why or how the Americans selected the dimensions of various components they did. That required punch card computers and lots of brilliant people to have already figured out. They would not want to take a risk in changing anything but rather just use what works until they had time to learn the first principles later. Then they could build there own mathematical models for next generation bomb design. But most importantly it requires a very high IQ to understand every single equation and problem in a technical discipline undergraduate program. But there are a lot of jobs that require an aptitude that lies in between a technician and a 4.0 engineering graduate. If we expected everyone to understand all the complex differential equations in there textbooks to graduate we would not have nearly as many engineers as we do.
It took me a long time to realize this as well. Sometimes you just have to focus on the task at hand and try to “black box” certain important results and focus on what you can apply with them
Always that one guy in every one of these types of videos. "Oh I already learned that and I'm gonna leave my tidbit here to let everyone know I'm ahead of this chapter" lmao. Every single video, ALWAYS that guy.
Elementary mathematics (as in High-school, or in college Engineering courses), mathematics are a tool. There is almost nothing to understand. With a math degree, you can understand PROOFS of theorems.... But to feel that you understand what it really means and why, you have to develop mathematical intuition. When someone asks WHY in math: the answer is always: "Because someone invented it that way and we can show that it is logically consistent and that it works".
Eh you can do better with physical intuition with elementary math due to the fact that a lot of it was developed alongside physics. Introducing that to students can often be a game-changer. I know it was for me.
Its hard to argue with your logic. But for people who learn such topics for fun, it doesn't matter how long it will take. The only thing that matters is overcoming barriers. This type of thinking "just go on, no need to ask more questions or trying to understand" is what ruined my enthusiasm for learning math and sciences at an early age. I remember being very interested in maths and performing on the top of my class in primary school. The moment middle school came and they started rushing sophisticated (for a middle schooler) concepts on us, which I wanted to analyse thoroughly before going forward but was denied the time and chance to do so, was the moment I started loathing everything about school and math. It became a sad chore, memorising formulas, regurgitating that mess onto the exam paper, rinse and repeat for years. I hate that, hate everything about such approach. Feeling like a parrot copying and pasting things and acting like a mindless calculator, being told this is what will make me better. It kills all creativity and joy of learning. I do not recommend such approach to anyone who is enthusiastic about maths. It took me nearly a decade to recover from this sorry state.
@labirintocomplesso1273because they have no choice but to do that . If you go deep into the concepts you will lose all the students including the good one .
I had a similar experience. I hate decontextualized information more than anything else in the world. No learner should ever be denied the why behind a method.
It's what you get when you run schools like kennels. Student computers are how they teach, yet there's no real use for something like this anymore. Formula memorization doesn't help any more than actually doing problems does. To really take advantage of better learning techniques, the whole thing needs a revamp.
@@algorithme1950 Not true. There's a certain level of depth that is acceptable to students. I don't need to explain how axiomatic set theory works to explain to a kindergarten student why 2+2=4. Same thing with students jn much higher levels. You don't need to invoke some obscure detail to answer students' questions about algebra or geometry. Most of the time, the intuitive answer is good enough.
@@GaussianEntity We can only hope that the upcoming next technological revolution will liberate people to do the things that they like, in a time that they like and schools will change as well. But I feel like a fool writing that when I know people expected the same thing to happen after the first Industrial Revolution. Ultimately, I feel like schools are controlled by the state and the state wants to kill all creativity and passion, as it doesn't need critical thinkers, it needs obedient fools.
Wow so true. Noticed this for a long time. A lot of the time we spend so much time trying to understand some part , section , paragraph or a section of a particular equation or so. But fail to understand that something moving forward. Everything becomes clearer and understandable as we study more about the subject. Some people literally stop, give up or put the entire topic away for days, weeks, months just because they find it so difficult to conceptualize that particular section of it. Write it down, Move on, pay more attention and focus deep on every information coming afterwards. You’d be surprised just how clearer everything eventually turn out to be. You’ve saved time . And you’ve learnt even more. It’s hard. But studying with pain usually is the best method of studying.
I purchased his calculus 3 course on Udamy like a month ago. It is really good. Mainly examples and the chapters/sections are clearly labeled and organized so you can select what specific topic you want to cover. So far, each chapter or section is around 30-60 minutes. I am really into it. I watch them before I even bother looking at my instructors lectures. I plan to keep getting more of his course as I take more math classes. It is really cheap tbh. It cost less thn bills, textbooks, groceries and maybe even eating out, depending on where you go. I still need linear algebra and diffy q so hopefully those classes are available in his store soon. His Udamy stuff is similar to his online lectures but he is not distracted by students in his Udamy stuff so its all steamline and quick material. 10/10. Dude is alpha.
This is great advice, not only for maths but, honestly, in life in general. I've caught myself so many times getting hung up on something while so many other areas of my life were screaming for attention. Thanks for the reflection!
For me, it stems from this pithy statement drilled as a child "Half knowledge is dangerous." However, in the real world there are degrees of complexity and conclusion are always in gray zone, which means there is a constant refinement of our mental models and a lot depends on case to case analysis and the context that particular case is derived from. Thankfully, the process of genuine effort is what makes life an enjoyable ride.
I think half knowledge is only dangerous when you believe it's complete. If you know it isn't everything, then it's okay to accept it for some time. Time is the crucial missing factor.
If you were a public speaker on the cutting edge of math. Then this half knowledge is dangerous. If you're just trying to solve problems in your text book this is all you need.
I totally agree with this guy. I’ve always been someone who got all As in math, but I wouldn’t call myself someone who excels at math. I’ve always understood probably about 70-80% of the material on a fundamental level, one where I actually understand what is going on and why the method I’m using finds the solution, but the other 20-30% of the time I just have to teach myself to be able to identify what information is given and what method finds whatever I need to find from that information. Sometimes it just comes down to blindly trusting and memorizing the process the teacher or the book has shown you, without actually having a fundamental understanding of the subject at hand.
Lately, I've been writing any math problems I can't solve on the last page of my notebooks. It's easier to move on when you know you can come back to it on a rainy day or something.
Math aside… applying this philosophy toward anything else in life seems game changing! Don’t get hung up perfection be completely understanding things and just move on!
Very fortuitous this video was recommended to me. I did my undergrad and a year of a PhD program in math, then left for a career in music. In the meantime, I got married, had two kids, and became a lot more patient with myself. I decided to go back for a master's in math around the time I turned 40, and specifically tried to avoid some of the self-destructive habits that had plagued me when I studied math 20 years ago. I was successful in part (stayed up til 3 AM on the first week of the program, then never again), but I still see ways to improve. I'm starting a PhD program again in the fall and I'm excited to keep refining a healthier relationship with mathematics.
To fully understand modern mathematics requires an if not more than a lifetime of effort, because you are compressing centuries of exporation and research into a time frame of roughly 100 years. This is definitely great advice for learning mathematics or anything in general, especially at an advanced level.
So why is learning another language easier than me learning simple math? English is like 300 years of complex knowledge compressed into 20 years. Same goes with French and Khmer.
Perfect timing. At the moment I am trying my hardest to understand a topic in calc 3. As I was doing my homework, I noticed I was taking forever to understand the third problem. Sometimes I get very upset because I feel like I will never get it. I tried looking up videos, reading the class textbook, but for some reason I still have no clue what's going on. Really nice to hear this advice.
As an Aerospace engineering stu, I can say this is exactly the reason why I got depressed at a certain stage of my studies, so basically I used to try to understand the concept of everything and the reasons behind every conclusion, like every single thing, which ended me up wasting too much time on all of that and not practicing very well and not going through all of the ideas. At the first of my journey, it was working cause I had a bunch of time to do all of these back then, but as I moved forward; things started to get harder and harder to the point there was like no time to even cry, like working while crying, so my technique was no longer beneficial to get good grades and that's ended me up feeling like I become stupid! so I got depressed and now I changed my way to a completely more effective one that allows me to understand as much as possible while maintaining progress and that literally reflected positively on my grades!
This is what I say to my classmates who I help a day before the exam. They start asking me “why” certain things are the way they are, I just say, “this isn’t the time to learn why, you just need to know that this is how it is cause there’s an exam tomorrow.” 😂
It's also referred to as 'accepting things on their own terms', which is closely related to 'trusting the process'... Your videos on mindset are far more important than any other you've created. I found that in learning math, following the process and using good bookkeeping will eventually lead to understanding after much practice - especially when coupled with learning other maths. It takes time and you have to 'move the pencil'.
Mathematics has the extraordinary power to reduce complicated problems to simple rules and procedures. Therein lies the danger in teaching mathematics: it is possible to teach the subject as nothing but the rules and procedures-thereby losing sight of both the mathematics and its practical value. Fluency-the ability to carry out procedures such as expanding, factoring, and solving equations-is important, but too often students do not see the purpose or structure of the procedures. Strategic competence and conceptual understanding in math mean being able to read math expressions and equations in real-life contexts, not just manipulate them, and being able to make choices of which form or which operation will best suit the context. They also mean being able to translate back and forth between symbolic representations and graphical, numerical, and verbal ones.
Your "Stop Trying To Understand" message was a crucial realisation to me. To "break free" and start to progress in and make maths work. My more specific cases, as they mattered in chronological order: * Get to know maths equations for what they do. Play with them. See them progress things from input to output. I nearly broke myself thinking I needed to "understand" them before I could use them. Maths - it works the other way around - "crank it". use it and get familiar with it for what it does, first and foremost. Later you might understand where I comes from. * If you have to learn a new topic and you have a big thick book, do do a once-through and feeling the retention is negligible. Suffer having your hair spiked-backward horizontally and being pushed into a "doomed" depression. Thing is, no-one can construct a linear narrative (text as an expression has this limitation it is linear-sequential) which is hermetically-sealed all-there. You'll see what you need earlier further down-the-line. Doing your secondn pass you have a better idea what things are, where they come from and where they are going. * It is abundant experience that if you "park" any idea of understanding something now, it is likely that many other things learned along the path made possible by "cranking" equations will provide context to later "understand" the mathematics anyway In every other aspect of my world of machines, metals, making structures, etc. you must understand. Working in a workshop or on a construction site, you must be able to visualise problems, which could be lethal, along the path of the plan you are looking to implement. Maths - the "rules" of learning are so different. In line with what you say.
Thank you for this advice. I waste so much time being upset about not understanding and a lot of times I remain stuck in one problem for so much time because I can't deal with the guilt of not understanding or the fear of missing out on any detail.
This mostly has to do with grades. You can get As without understanding anything. You can just memorize the algorithms, practice, get the A. There's no actual requirement to understand any of it. You don't NEED understanding if you just care about grades. However, if you value understanding intrinsically, and want to be a great mathematician, then understand everything you can.
Very refreshing. Feynman said something similar and I tell my students also. Just accept things and build on them and trust they make sense. Its hard to explain. I teach computers and sometimes i just tell people to use a 'formula' first and understand later.
@@MatthewTaylor86 yes I did. I agree with the video, but some of the comments here telling people to just completely give up on understanding for good, I disagree with.
My brain clogs the second it has to actually memorise stuff, unless that something simply "makes sense" Everything makes sense but i mean unless i see the method, even if i don't understand it, i won't be satisfied
I am 41 and just started understanding some concepts. Always hated trigonometry. Now I have no issues with it. It takes time for the brain to form certain structures to deal with math.
As soon as I read the title I knew exactly what this video was going to be about, and the words initially spoken just hit the nail for me. This was something I needed to hear so badly and immensely, I was hoping to understand the same through the hard way(By dissecting each and every section of the question for better understanding) but this video reinforced that belief much more clearly and concisely for me. Thanks a lot for the effort and knowledge.
Exactly, but it should be specifically emphasized that even the top experts don't 'fully understand,' yet we still fall victim to the illusion of their high status, and think they do. Whether it's Einstein or Terrence Tao.
Math is understanding! It means exactly THAT. The calculation itself is nothing, that can be done by computers/calculators. But to UNDERSTAND what is going on is the Most important thing. But OK, you should not try to solve problems you have not divided in smaller parts (enough) yet.
People understanding is the most important value in the world. Truth is not accepting a frame or a perspective. I would dare say that 100% of the problems in the world come from a lack of understanding.
The issue is you cannot understand everything all at once. You need to value your time and understand what you can and use the properties of math ad leverage for the stuff you do not have time to understand. It makes more sense if you consider your understanding as organizing books in a bookshelf and retrieving them as actions such as finding that book and opening it. There's only so many books you can put in the shelf. There's only so much retrieval you can do. Accept your limitations, and you shall find ways around them.
As someone who loves understanding things and often does better when I do, I was almost ready to brush this off as something that doesn't apply to me. And then I realized that every single new mathematical concept I learned in high school didn't always come easy to me. I looked at it, scratched my head, then half-moved on, only having fully understood it after a day or two (or even a week). In a way, this comment is just me thanking you for posing an important piece of advice that's helped me self-reflect.
Great timing. I spend so much time trying to understand so-called "trivial" things... things that do not effect my ability to solve math problems. (Because I hate memorizing things, I would much rather forget everything and then retrace my steps to get back to where I was )
So true! This is how I work with formulas, but sometimes u just have to bite the bullet and actually memorise them instead of logicing your way out lol, especially at a level or higher
I am exactly the same way. I have been spending hours trying to just understand a FUNCTION. I know it is stupid to keep ruminating on it because I have been able to use it.
@@dosomestuff1949 I disagree. It's about learning "why" or "how" over just learning the "what". it's about getting a deeper level of understanding. The problem with this is the time efficiency. It's not always worth it to dig into everything. FYI: I got an A in the class I was referring to when I made this comment.
Man I love your videos. So wholesome, guiding, relaxing and comforting all at the same time for people who are stressed out about their math education. This one hits home in particular because I used to be an extreme perfectionist as an ex-engineering student, to the point I had to drop out. There were also health problems at play, but the perfectionism played a significant role as well. Engineering is all about pragmatism; using what’s there from math and the sciences to use for building things, yet I was so focused on where all these results came from that the course, professor and textbooks didn’t go into because it was “too advanced”, to the point that I lost track of the main idea; using that knowledge to actually make stuff. I’d have to simply accept why Stokes’ theorem, a highly nontrivial, useful and not very intuitive result, was true in order to formulate the Maxwell equations in their differential version. Or how to interpret the seemingly “infinitesimal” energy and heat transfers in classical thermodynamics. I didn’t like this at all so I put most of my time really trying to figure out every step of the way building up from formal logic to set theory, both of which I had to learn by myself, to the definition of the number systems in the setting of set theory and building up from there to the actual material I had to study. Now that I’m older, I notice that with becoming an adult comes a more pragmatic mentality, which is a good antidote against perfectionism. I’m sure I’d do better now with this new mindset.
There are parallels here with language learning. We can easily waste time staring at grammar rules early on - but for any of it to make “sense” you first must accept the weirdness and bulk-learn, phrases and vocabulary. Once you have loads of examples safely held in your memory - the reasons and rules you didn’t understand earlier will start to make sense.
I think this is also bad advice. Learning grammar first would have helped me immensely when I was attempting to learn Spanish. It's difficult because it's a process of logic. But once you do it it's like a superpower. You can make valid sentences by deriving them in your head without having an intuition of the language. There is so much value in rules and grammar
I'm not mathematician and I get this advice not literally but as "Don't torture yourself by not understanding something", otherwise trying to understand things is what make us humans and reason of humans development.
This is the type of wisdom I pay my internet for! Thank you SO MUCH for sharing it. Funnily enough, I probably wouldn't have listened to this if I found it sooner, so I am glad I got lucky on the timing.
You can turn many courses into patern recognition. That is how i got through calc and organic chemistry . But now I am retired and going back to study cal on my own so grades dont mean much. Understanding is more important as it is just for it's own sake. The future of higher math,like the future of many things is in transition. It may be that the ability to ask the right question will be more important than the mechanics of calculating the answer. Think of how calculators changed math fifty years ago. Understanding may go from an intelectual achievement to a necessity. My experience with calculus was that while i was able to recognize paterns in equations recognizing paterns in real problems was harder as there were just too many paterns to memorize. I think that a deeper understanding would have helped.
Im about to take my geometry graduation test to graduate 7 years late in life as I had to drop out to work. The class I had no problem with but its been a few months since Ive been in the class and Ive forgotten so much. Ive spent the last week sun up to sun down researching and trying to understand everything again. This is giving me the courage I need to believe in myself and feel that i have done enough to prepare myself. I needed this more than I would ever know before I watched it. Thank you so much for this
Just spent two hours on a proof with mathematical induction. How timely a video! I suffer from the need to understand as well so thanks for the reminder! On to the next chapter!
There’s also so much to this approach because of subconscious processes as well. I cannot count how many things I saw in undergrad that I never fully grasped or had a deep understanding of, and then when I saw them again in later work, it all came together without extra work and pain. Your brain processes and takes time to work on things in ways that we really do not understand. I love this video.
I love this video. Learning and teaching is such a "human" effort, even with something as abstract as maths. The beauty of it is that it's scaffolded by definition; each theorem works because the theorems it's based on work. It's liberating to finally break through and realise it's not like other topics; doing comes before understanding.
“Forest for the trees” I have slowed my progress immensely due to my need to know and understand things deeply to the lowest possible level. This is great advice you’re giving here. Sometimes your understanding will improve simply by exposure to more material elsewhere or by trying something different.
This is so true!! I’m in calculus 3 and if I tried to truly understand not just learn the concepts, material, and patterns, I would a lot more clueless than I am now.
This is an extremely beautiful and important piece of advice. I struggled with mathematics in high school. In college, I took statistics and had a C in first semester by a stroke of luck. In second semester, my luck ran out and I failed. I had 14/100. I had to resit the exam, but I was justifiably scared. I knew I wouldn't be able to pass it if I wrote the exam again. Fast forward to when exam was coming, I started getting tutored by a friend. Everything I learned flew away from my head when I entered exam hall and couldn't remember a thing. I picked answers randomly. When result came out, I was lucky to have 52/100. Then, something interesting happened last year. I decided to have a career in data science-a maths-heavy discipline. For someone who flunked his way through high school and scared of writing any exam that has anything to do with numbers, it was a crazy idea. But I believed my deficiency wasn't a functional of my capacity. It's more about psychological. It had nothing to do with my cognitive capability. So I walked into ring and started learning statistics again. There were times, I wouldn't understand some things, but I would keep banging my head on it, trying to understand everything, instead of moving to another topic. But this piece came in handy. It will help me on my journey and as I continue the journey of becoming an outstanding data scientist and machine learning engineer. Thank you so much for this, sir.
In the past I was nervous to move on from problems I didn't understand because I believed if I didn't tackle it head on, the ideas would be gone forever. I wouldn't think about or internalize the solution, therefore I'd forget. However, I did have to move on in a series of books and that was Knuth's "Art of Computer Programming" series. Six years later, I encountered a problem at work and I remembered that Knuth had written about this and I picked up right where I left off. I didn't expect that the process of giving up on something, made me actually remember it at the very least.
I was stuck in a quantum mechanics problem and feeling really disappointed for not being able to understand it when I found this video by chance. Thanks for this relieving message I really needed to hear it now.
You're definitely right. It's hard to find the right balance between basic understanding, sufficient practice and constant progression. It's definitely wise to have a basic understanding of a topic before moving on. And yet it is sometimes the case that you may not understand where every rule comes from or why something works that way, but if you keep going, dive into other topics and have accumulated knowledge, you look back on the tasks you didn't understand and think to yourself, ahh, now I get it. And yet you can also get lost if you jump to a new topic too quickly. Well, as I said, it's not so easy to find the right
Just recently have I begun to take managing my time seriously. Part of that deal with myself is that I have some time to reward myself for time well spent. One of such rewards is that I can watch youtube videos without that nagging guilt feeling that I could be doing something productive. What I'm trying to say is that, today my reward got me stumbling upon your video and I have never felt so strongly the urge to comment on a video (something I rarely ever do) as I do this one. This was just exactly what I needed. This isn't maths, this is philosophy. Wisdom. I have just taken up a new skill, all in the direction of being a better person and this has been immensely insightful as well as validating the thoughts I have had to myself about "just moving forward". There's only so much time we have. One ought to jealously guide attention and focus, channelling energy for high-priority tasks that move one toward their goals. So, thank you, sir. For me, you smashed this one. Subscribed!
No never! but yeah I agree the more you try to understand, the more the math gets deeper and deeper. But I find trying to understand in the summer is pretty good.
I'm so glad someone as high profile as you is saying this. It took me half way through college until I understood this was necessary. I still am slightly unclear on when you can dig deeper for more understanding and have it be a net positive. Some combination of always being slightly alert for patterns, maybe when you're combining multiple areas you should also look for patterns anew, and only when you have built up lots of experience and patterns you can try to understand more deeply with that context subconsciously helping you dig through to find deeper patterns so you "understand".
This is very true and I think definitely applies to much more than just mathematics. I notice a lot of people do this in language learning especially. People spend a lot of time pondering and trying to make sense of something than just practicing more, reviewing more and letting the intuition naturally be formed through practice. I've never personally found sitting and staring at something for periods of time to ever be productive, and since realizing this I save a lot of time by just moving on, learning more and coming back later. Developing an intuition for math or physics, whatever is never about how much time you spend pondering about it but more about how much time you actively spend engaging with it in a variety of ways, seeing how things actually work.
Thank you, Math Sorcerer. You gave this advice a long time ago, and I have followed it since. It has been very helpful. I like writing down what I get and what I don't about a formula or whatever, so at least I can define that.
Sometimes forgetting things for some time helps understanding it when you come across it again. I've come across things after years and they were clear after that. It's weird feeling. Maybe memory works little bit like a computer, but it takes time to move them from short memory to long term memory. Something you will remember always.
Keep moving forward! When you dive into other subjects and gain more experience, you'll look back and see things from a new perspective. For instance, before I took Linear Algebra, I was grappling with a Differential Equations course. I kept asking myself, "Why do we even need to find particular solutions and complementary solutions? What’s the point?" At the time, I didn’t really grasp the concepts; I just crunched the numbers and powered through exams. But a year later, after learning Linear Algebra, it all clicked. Finding complementary solutions is like finding bases to span the entire solution space. So, my advice? Keep those puzzling questions in the back of your mind, but don’t let them bog you down. You’ll get it when you're ready.
True! Thank you very much! Now when I revisit the maths I couldn't understand eight years ago, WITHOUT EVER HAVING SEEN ANY OF THAT MATHS SINCE, I feel like laughing at myself. It was maths at the MSc level and was supposedly very hard, but it looks like a walk in the park now. Our brains are very powerful. The brain analyses and studies stuff when you're not focused on it. So, if you ever don't understand anything, leave it and come back to it much later. Your brain will process the information it couldn't understand, and the next time you see it, you will have understood something, if not everything.
This is great advice. I never had natural aptitude at math and had to work really hard to do just okay in middle and high school. Through stubbornness I got a bachelors and Phd in physics and ended up with a few publications on theory-heavy topics. I attribute avoiding getting hung up on understanding every step and just building the muscle memory of solving problems to get me out of a rut. Just accept some amount of mysteriousness and solve the problems you can - eventually the understanding will come! Revisiting entry level material after you've completed higher level material is a truly eye-opening moment.
The author Barbara Oakley explains this proccess very well. I recommend her books, start with "A mind for numbers". They're mainly introduction of STEM for people who are afraid to even consider it, so yeah, not technical heavy calliber stuff for pleasing Einsteins. Just a simple and good book that would generate a ton of short videos for you to tip people with.
Been in so many math classes where the lecture keeps getting derailed by some students saying “I don’t understand”. As if the expectation is that you have to understand everything right away. It takes time! Glad someone with a high profile is making the point…
Але повністю згоден що зависнути на чомусь, чи зрозуміти на половину і рухатист далі важливіше ніж впертись у щось незрозуміле і "захглохнути" на цьому. Хочу вивчати математику і все що з нею пов'язане англійською. Дякую що ділитесь. Фізика, математика, геометрія та географія, так само як і юриспруденція є послідовними цікавими і логічними науками ❤❤❤❤
This is how I passed calc and physics in college. In school, I was able to understand the concepts so well, that I could not study at all and do well. But at a certain point, there's so much you need to remember and hold in your head at the same time that it's best to just trust the process and maybe with enough repetition, it'll start sticking intuitively.
thank you , I needed that because as an engineering student for the past couple of months I have been stuck on why of things and not focusing on my grades. You are right sometimes we need to move on to understand it better in the future with more knowledge. :)
Such great advice sir. I'm a Physics student and I have a habit of making a clear diagram to connect everything I just learned after class. I will feel really uneasy even when I solve the problem because I am just doing it instinctively and not clearly understanding what I am doing. So sometimes, I would spend the whole week trying to write a whole 20-page note of the theory before actually doing some experiment with it. However, I wasted so much time on it, and sometimes when I think I have composed a great document about the subject, the experiment proves otherwise. It was not until a very long time ago that I concluded that sometimes, it's good to just learn something instinctively, don't need to fully understand WHY and HOW, and instead just move on with your other current goals.
This is exactly what I need at the moment! I have been trying to understand a paper for weeks, almost 2 months. I read so many other papers trying to work around it and tried to figure out top down/ bottom up. I feel so dumb because I can't imagine that I cant figure out such a simple equation. But you are right I should move on.
This is excellent advice. Sometimes you learn a thing and live with it without understanding. Then one day, you understand it completely. When a problem stymies me, I leave it and do something else. Come back later; suddenly it is clear. You reach the point where you realize understanding is a construction in your own mind. Just keep doing the math.
Thank you for this, great advice! This week I sent 4 hours trying to solve problems for an exercise class. I spent all my time on the first problem, and could not figure it out! We had been told that we could be called up to solve the problems infront of the class, so you can probably understand why I was so motivated not to mention stressed out. Turns out they had forgot to include some crucial slides during the lectures...
![[MV] A leap of faith...ความเชื่อใจครั้งสุดท้าย (From "Petrichor the series")](http://i.ytimg.com/vi/U1piZH2CNXA/mqdefault.jpg)
As someone who ALWAYS needs to know WHY something works. This is some insane advice.
Yeah I would have to agree! Considering that I used to teach Maths and Physics to college students, I felt compelled to understand each and every topic that I had to teach them, so that I could help THEM understand it! Because some of us don't have robot like minds, simply absorbing information that flies right over your head, in order to pass exams at some point in the future, or perform some monotonous task!
Look! Of course I don't understand Quantum Mechanics! No body does! But one CAN get to grips with the abstract mathematics involved in order to at least get a handle on the workings of Quantum Mechanics, in order to do useful work!
Of course I don't understand the imaginary number *i* ! But one can get to grips with Complex Mathematics, to carry out whatever computation that they need to do, because the mathematics of Complex Numbers is sound!
What I'm trying to say is, sure! There are PLENTY of abstract ideas out there! Not just in Physics but in Mathematics too! Ideas sooo abstract, that they truly bend the mind! But so long as you can get to grips with, and understand the Mathematics behind these concepts, then you can at least get a working idea behind them, even if you do not fully understand the abstract ideas themselves!
There is a dichotomy between an abstract idea... And the Mathematics used to describe that idea! Fully understanding the abstract idea might be impossible! But fully understanding the Mathematics used to describe that idea is imperative!!!
@@sdwoneI'm just a pupil, but I really get obsessed with such abstract ideas like number i or trigonometry, but I'm only trying to understand and more often at the end I just don't understand.
@@AGguyy-j9n Remember... Ultimately Mathematics is just a set of abstract ideas bound by the rules of Logic! Sure, that's a HUGE over simplification, but a valid one.
And as for imaginary *i* ??? LOL! Honestly... This is one of the Biggest Mysteries out there! Right up there with PI, Euler's number *e* and the Golden Ratio etc...
Trying to understand these concepts leads you into philosophical territory... But nonetheless, these concepts are also bound by Mathematical Logic. And so long as your grip on the fundamental logic is sound, then you can confidently work with them... Even if you don't fully understand them! And to be honest... Nobody does!
So don't sweat it! As one famous Physicist once quipped:
"Shut up and calculate!"
And oftentimes, that's the best we can do...
@@sdwone"Shut up and calculate",
This Mathe-Mathecian is my destiny,
He says oh-oh-oh,
"Shut up and calculate",
The whole point of this video is that this is not an inherent virtue.
"The important thing isnt can you read music, its can you hear it". Let me tell you dude, I was having a full on awakening during my last college class
Bro is the honoured one 😭
Wow , what a great moment it must be.. I am struggling and struggling With understanding and solving the problems..
Some People are just blessed with a brain ...
It’ll happen eventually. Just keep trying
I always took that quote to mean that a physical intuition is more important than the mathematical mastery
“Young man, in mathematics you don't understand things. You just get used to them.”
― John von Neumann
That describes The Axiom of Choice perfectly.
It's the abstract thinking.
😂
Nice
lmao was about comment that comment aswell
I'd say those are the same things
I'm not sure I understood the message here. Guess I'll rewatch this video 10 more times until I get it!
😂😂
Move on
👊🤣
I think the video is talking about a different way of learning and it involves more of the unconscious brain (female brain), where you just expose yourself to it but you don't make much effort, you just watch it, absorb what you can absorb without worrying about anything and let it (your unconscious brain) do the work for you. Learning this way is much more sufficient and so much less work needed, you'll just find yourself knowing. This is how babies learn language. This is how I learned English starting 4 years ago. In school I would have never been able to make more than a very simple sentence. Look it up. Its a real thing
@@violetlup8652 Your comment seems important, even though I did not comprehend it entirely. I've read it three times already ans took some notes. I'm putting it all in on cracking this nut!
This is profound. My self-study has been hindered by my insistence on fully understanding each and every concept, and formula before moving on.
This did not interfere with your self-education. This was self-education! If you don't understand something, then you haven't learned it. Dot. If you use multiplication without understanding what the hell multiplication is, then you don't know multiplication.
The video is right. Don't slow yourself down because your mind might not be ready yet. So roll with the process, learn the skill, and at the very minimum you can at least solve the problems and at best going through the motions many times may help things click.
@@olegrooo713 isn't multiplication fundamentally iterations of addition?
Yep! I go down rabbit holes just trying to understand one little thing. It really slows down my forward progress.
@@olegrooo713 this isn't what he meant though, you have to understand what you need to understand, an idea bothering you at the time doesn't mean you can't make progress unless you understand its in and outs, we all have objectives, its not a straight path where every concept has to be crystal clear or else your knowledge is incomplete, if that was the case nobody would have time to develop meaningful skills
I failed algebra 2 times before I had a math teacher say this to me. Stop trying to understand, memorize the steps, do the steps, and eventually it will start to make sense. Math for me is a field where you have to run before you can walk.
I think understanding first IS genuinely a better way of teaching. Its just having a teacher who can effectively teach that way is really rare. I thought what you did before I had the best teacher I ever had for algebra 2 who made me enjoy math for the first time in my life.
the weird thing is all things are memorization. Some people memorize calculations. More advanced people memorize processes and formulas. Even more advanced people memorize themes and algorithms and problem solving strategies. At that 3rd stage we usually just call it "understanding the material deeply and conceptually". Even more advanced people solely focus on memorizing "how to focus" and making a habit of "focusing".
One way I encourage myself not to get hung up on things is by internalizing the mantra: "trust your brain". The idea is, your brain uses much more than just the information you have in your working memory to solve problems; it recognizes patterns, it remembers things, it keeps important ideas more accessible than less important ideas, etc. The road to conscious understanding is often paved with improvements in all these metrics; it's not all or nothing. If you're improving, you are learning, even if you can't yet fit the general pattern of the problem into your working memory. Trust that the other parts of your brain matter also.
In my experience jumping around from doing the steps/memorizing and understanding is what works best.
Also look for multiple sources and related topics.
It all starts to fall in together like a puzzle
If your teacher couldn’t make you understand algebra TWICE that’s just a bad teacher 💀
The most surprising part about math is how it'll suddenly teach you practical lessons for life.
One of my biggest problems was solving too quickly and making extremely minor mistakes. It became such a problem that it made me dispise math.
It wasn't until I decided what the problem was because I knew I wasn't stupid, and I knew I was capable of doing hard things. I eventually deduced that all I needed to do was to simply slow down. There is no shame in being painstakingly considerate of every single stroke of the process in solving hard problems.
Then, I started to relate it to everything in my life with logic. Math has made me appreciate the process, and to love the process. I've developed a deeper appreciation for life, and I have a deep joy in the hard things.
This feels like life advice more than it does just mathematics
That is his gimmick.
mathematics is philosophy of life my dude
Advice tends to surpass its intended fields
@@Raod14Reference good advice*
I am going to apply this to programming, i suck at this, yeap, i fixate alot on a problem
Understanding the explanations in math is like understanding poetry: you need experience, especially with relevant problems, so that the words have more meaning for you and resonate better.
Is that not what the students are seeking out though? He's giving them an idea void of any meaning, and they're seeking out the context from which it arose, or seeking to create and explore context for themselves to grasp it, and he's suggesting that they just don't, and you're suggesting that 'it'll come'. It kind of reminds me of _the parable of the drowning man_.
It feels like what you're both really saying is that to 'mesh' better with the education system you've just got to give up on understanding things and trust things blindly, which I'd be inclined to agree with, but which I also despise.
@@callumscott5107 Ah, sorry, that's not what I'm trying to imply. I'm saying that if a student isn't understanding an idea, then the student should do more practice problems -- perhaps a mix of problems from earlier sections and from the current section -- so that the explanations will make more sense.
It's not about blind faith, but delayed gratification, because real world problem-solving often involves a humbling period of mystery where we're feeling our way around in the dark, until we find a candle, and can use it to light other candles.
Another way to put it is that sometimes our ideas are waiting for not another revision, but just a few more glimpses of the sun before they can blossom. 🌻
I'm not a fan of our education system. It puts too much pressure on students to learn more than they're ready for, too quickly. These things take time, and everyone's clock is different, especially at different periods of their development.
@@callumscott5107 your mistake is thinking this only applies to the education system. this applies to every problem in the world. if we had to understand everything before doing something, we wouldn't have time to do anything. in the case of college, if i had stayed trying to understand every single concept i came across because i enjoyed it, i wouldn't have the job i have now, not because i wouldn't have a title but because of the actual meaningful things i learned, and in fact, now i have a broader perception of things and i can understand the things that were once complicated.
plus, wanting to "understand" maths or science isn't totally possible, you're always learning at your own pace, whether its advanced or low level stuff and you have to follow this philosophy to truly make it work
@b_delta9725 I don't like the premise of intensely studying and learning lists of concepts, defined by others as useful, precisely because I don't think that's how people really learn best. I advocate a more holistic and self-directed, curiosity driven learning. So yes I think we agree that that's a waste of time, that's not what I stand for. But the problem with trying to master every topic on the course isn't that they're too curious, it's that their curiosity is too narrowed to something defined by an authority, as opposed to something more broad and open to life in general.
I was more-so saying that if people are legitimately curious about this, in a healthy and eclectic way, then denying them answers to the questions they're asking, under the guise of 'you don't need those answers' is a pretty disturbing thing to righteously do to someone.
It's like there's anxious questions and legitimately curious questions, and I'm talking about respecting the latter whilst I get the sense you're talking about disregarding the former.
@SpoiledViking I'm not making a case for brute forcing lists of problems to learn, in fact I'm making the opposite case. I think we've read very different things from the video. What I've been disturbed by is the possibility that someone might approach him with a genuinely curious question, emanating from their heart and soul, and this guy just goes "stop trying to understand this stuff, sacrifice that curiosity in favour of continuing with the course material". To me, it's as though curiosity extends these hooks from us that get caught on the most unpredictable of things, and there's tremendous beauty in trying to delicately untangle ourselves from what captures us, then this guy's just advocating for you to snip at their base and get on with life. What kind of an education system punishes those who are caught by curiosity?
This is helpful advice for any arena of life I feel. As a filmmaker (and TH-camr) I get so worked up, frustrated, anxiety-ridden over every little video that I make, overanalyzing whether it's funny, watchable, entertaining, why it didn't get more views/likes/subscribers, worrying that it sucks horribly and I should've never made it.... when I could just finish the video/film, put it out there, let it exist, and move onto the next film project.
Thankyou, time to finish watching the video lol.
:)
I'm early in my career of learning college math 20 years after highschool and emotionally this is the biggest change for me, when I start to think "But why???" I replace it with "ok textbook I believe you" and I move on. I've also found that for some of these concepts as you say later it is clicking. Before I could not move on and would also give up as these frustrations built and my foundation weakened.
我要像您学习。
当初学习数学是为考试，却没认真理解其用意。
Same thing I've been going thru with computer programming... I'm better at just moving on and trusting it will all fall into place at some point, but it used to bother me quite a bit not understanding the "why?" of some topics or concepts.
Can you please help me sir please🙏🙏🙏🙏🙏🙏
@@gregorio87 Good rule of thumb for me with CompSci is "Why?; usually because its either better use of time/space computationally or saves time &/or headspace for you & your co-workers later on" a better question is "how". "Why is 5v representative of 'True' on this bus but 0v or 3.3v is T on this other bus"; "because we said so".. "How is this presumption incorporated into the rest of the system" is far more important because axioms can be arbitrary, whereas the build up of arbitrary selections (made simply because somehere eventually required A decision to be made) result in interfaces that must be implemented particularly such to enable interoperability between distinct sets of arbitrary selections. Also technical debt & sunk cost fallacy is a far broader socio-economic phenomenon than many will like to admit.
If you just need your "feet to touch the bottom of the pool" to get over your ~"thalassophobia" I recommend constructing an ALU in TTL or just write out a truth table for a 'full adder' & meditate on what's going on with ASM. This may come across as condescending or daunting depending on where you are but I feel its a fairly solid place to start gathering the "long pieces" to clear up those longer standing "tetris rows" by grounding with physical representations.
314 likes as of now, now where have i seen this number🤔🤔🧐?
Hey man this is I believe the second video I’ve watched of yours and I just want to say as a 19 year old struggling to figure out the equation of living a good life I can’t put into words how thankful I am of the person you are and the teachings you give, I love these videos you’re awesome man
Thank you my friend!!
When I was a Paramedic student in 2000-01, I asked an ER Doctor how he remembered everything. He said,” Don’t study to memorize. Study to recognize this way when you see it, you know what to do.”
I carry that with me every day, and always told my students the same.
@@binayrawat1866Hey, you can ask for help but please don't spam this under every comment.
@@dynaspinner64 Sorry I don't get your point
@@dynaspinner64 Can you pls explain me
@@binayrawat1866I just saw you comment the same thing under someone else's comment and you did it twice under this guy's comment. I just meant that ask one person and wait for a response. If you don't get one, ask someone else and wait.
@@dynaspinner64 yeah you're right, but I really need this as soon as possible. And asking help to every person at the same time is not a wrong thing I guess. I just want to know the people's opinion.
I know what he means. Here's an analogy: imagine you're asked to explore and memorize a forest, so you can lead a group safely through it. So you go into the forest to start exploring, and you come across a strange tree that looks like it's important. So, you spend time memorizing this single tree's location in the forest to later tell the group about. Then, you move on, and come across another strange tree. You once again spend time memorizing the location of a singular tree. You try to continue, but you find yourself stopping at every single bizarre tree and memorizing each position.
"Here's tree number 46, tree number 47..." and so on.
Soon, the sun sets, so you return to to the group. They ask if you found a source of water. You tell them where you found a tree. They ask you what the safest route is. You tell them where you found a tree. They ask you where they can find food. You tell them where you found a tree.
In the end, your efforts were unproductive! You spent so much time looking at the trees instead of the forest, that you're just as clueless now as you went in.
In other words, you need to see the bigger picture before small things make sense. It's okay to walk past a strange looking tree without memorizing it (it's okay to be confused and not fully [emphasis on fully] understand something), later once you've explored the entire forest (learned the full scope of something), it'll be easier to remember where that tree is (understanding something becomes easier with more context)
Wow!
How simply you conveyed the msg ❤
Excellent metaphor excellently expressed with excellent execution of parenthetical thoughts.
Great comment
Thanks for your insightful comment; it's a nice thought provoker. I sometimes struggle with looking too far into one task at a time, and I think sometimes it's okay to just do the best you can and move on even if it doesn't pan out instead of trying too hard to fully solve a difficult problem. Though, maybe that struggle is beneficial to future problem solving.
This is such an important message. I suffer from same. The intense need to UNDERSTAND a particular point before moving on. Its a bit like the social media FOMO, the 'Fear Of Missing Out'. The fear of not understanding something that could seriously impact you later. Understanding is all about context. If you dont understand something at a particular point then your brain isn't READY to understand, it doesnt have the necessary context. But thats OK, that context will come. I think if more lecturers gave this pep talk right at the beginning, I think more students would spend less time fretting and more time enjoying studying.
i have had the fomo before this stupid thing called social media.
It’s sooooo truuuue. That makes so much sense! Thank u for speaking ur mind 🙏🏾
It’s similar to our social media addiction. It started off as a little bit of entertainment, but because of the unlimited content, we’re constantly scrolling trying to enjoy as much of it as possible, which is bad for our mental health. In the same way, when we’re learning something there so much information freely available and because of this freedom, were tempted to get through it all at once, but learning is meant to be a natural process, that like u said, is best done in context and overtime. So even though the information is there in as much detail as u could ask, we should focus on absorbing it naturally comes to us.
100%agreed
Love this comment. I relate so hard to this
"understanding always comes in retrospect" only when you have all the pieces of the puzzle will you be able to see the full picture. One of my professors told me this and it has stuck with me until now. Amazing video.
Glad it’s not just me! 😭 sometimes it just feels like I’m trying to understand everything in my engineering classes.
I'm in the same spot as you. I'm a sophomore in computer engineering. You're not the only one
Well if it is engineering....
Same. I dont understand anything
Same❤
@@AutoFirePad Lmao I had the same reaction
I always write down every single confusion I have when I learn a topic. It relieves my anxiety since I know I am not going to forget about these details and I will eventually understand them tomorrow or day after.
Agreed. The better you are managing your stress and anxiety, the more successful you’ll usually be in all areas of life. So many of us want to know everything in order to have a greater impact/image on our respective disciplines, and forget the role of community, peers, teams etc.
I'm in computer science, and I think this is probably one of the best pieces of advice any student learning anything needs. I looked too far ahead at where I'm headed, but I realize it doesn't matter. I might think it does, but time is evolving, nonstop, forever. Every one of us lives with only a decent understanding of anything around us, and we keep moving forward and get to live anyway. Maybe I will get that job in the end. Maybe I'll learn neetcode and algorithms at some point. Or maybe I'll get a job in IT and be run-of-the-mill, but maybe I'll get to work on music as well like I wanted.
But this video helped me see the infinitesimal-crunching numbers down closer to nothing, to no possible chance. And then I didn't adapt; I got hung up on my ego, my pride as a student, when that wasn't a luxury. The luxury was learning what I could do today and adapting again tomorrow. I'll always do that because I get to live and revisit things later.
The message of the video is clear. The title is a bit misleading. You shouldn't stop trying to understand ever again. Instead, you should stop trying to understand immediately. Thank you for your video!
Thanks for this comment i was in doubt about it
A very insightful comment, I agree !
The truth is, you should not EXPECT to understand right away, but never cease to TRY to understand.
Let’s be real though. We all clicked on the video because of the title. It draws you in even if it’s a bit misleading.
@@MRM.98 exactly what I was thinking lol
The truth is you need to selectively accept truth, otherwise you are too easy to bias. Just using something you don't understand, leads to poor ability to optimize and create new solutions. I had a lot of bad teachers tell me it was okay not to understand, but those are the teachers I learned to ignore, and I would work on my own and just come in for the exams, and then get 95% - 100% in the course. The only thing I agree with is taking a break and moving on to something else for a bit, refueling yourself, but then get back to it.
I actually agree. If your goal is just to solve the problem, then you don't necessarily need to understand it. But if your goal is to learn, then it doesn't matter how many problems you get done if you don't learn anything from them.
It depends on how interdisciplinary your discipline is. If your a math phd student that makes sense. But if your an HVAC engineer or an industrial engineer selecting what type of conveyor to use your probably going to use a lot of equations and charts that really just situationally dependent approximations of complex math. And the math and reasoning to develop those simple equations can be hard to remember if you never use it.
It’s important to know the general first principles of your field, but no one can solve every problem from scratch or understand everything that goes into a complex project. So in engineering it is often necessary to trust the situationally dependent simple linear approximated algebra equation vs trying to analytically solve the same problem with complex differential equation model yourself.
This is one of the main reasons why espionage is so powerful. It take a super intelligent entity like a large tech company to create an F35 or an iPhone. No one person knows how every component works.
The Soviets had good engineers working on there own bomb design that would have made there first bomb a little better than the first U.S. bomb. But they ended up using the design they stole from the Americans. Now assuming they didn’t have the expertise to have done there own design they still would have had to know how to run there own enrichment plant that requires all kinds of engineering to execute. They would not have needed to know why or how the Americans selected the dimensions of various components they did. That required punch card computers and lots of brilliant people to have already figured out. They would not want to take a risk in changing anything but rather just use what works until they had time to learn the first principles later. Then they could build there own mathematical models for next generation bomb design.
But most importantly it requires a very high IQ to understand every single equation and problem in a technical discipline undergraduate program. But there are a lot of jobs that require an aptitude that lies in between a technician and a 4.0 engineering graduate. If we expected everyone to understand all the complex differential equations in there textbooks to graduate we would not have nearly as many engineers as we do.
It took me a long time to realize this as well. Sometimes you just have to focus on the task at hand and try to “black box” certain important results and focus on what you can apply with them
I did not do it. Because I could not let it go. This was one of main reasons my grades were that bad at physics major.
Please give an example with laprase
Always that one guy in every one of these types of videos. "Oh I already learned that and I'm gonna leave my tidbit here to let everyone know I'm ahead of this chapter" lmao. Every single video, ALWAYS that guy.
Sameeeeee. It did took a long time ngl
@@wingnutmcspazatron3957 how does this help?
Elementary mathematics (as in High-school, or in college Engineering courses), mathematics are a tool. There is almost nothing to understand. With a math degree, you can understand PROOFS of theorems.... But to feel that you understand what it really means and why, you have to develop mathematical intuition.
When someone asks WHY in math: the answer is always: "Because someone invented it that way and we can show that it is logically consistent and that it works".
Eh you can do better with physical intuition with elementary math due to the fact that a lot of it was developed alongside physics. Introducing that to students can often be a game-changer. I know it was for me.
Its hard to argue with your logic.
But for people who learn such topics for fun, it doesn't matter how long it will take. The only thing that matters is overcoming barriers.
This type of thinking "just go on, no need to ask more questions or trying to understand" is what ruined my enthusiasm for learning math and sciences at an early age. I remember being very interested in maths and performing on the top of my class in primary school. The moment middle school came and they started rushing sophisticated (for a middle schooler) concepts on us, which I wanted to analyse thoroughly before going forward but was denied the time and chance to do so, was the moment I started loathing everything about school and math. It became a sad chore, memorising formulas, regurgitating that mess onto the exam paper, rinse and repeat for years. I hate that, hate everything about such approach. Feeling like a parrot copying and pasting things and acting like a mindless calculator, being told this is what will make me better. It kills all creativity and joy of learning. I do not recommend such approach to anyone who is enthusiastic about maths. It took me nearly a decade to recover from this sorry state.
@labirintocomplesso1273because they have no choice but to do that . If you go deep into the concepts you will lose all the students including the good one .
I had a similar experience.
I hate decontextualized information more than anything else in the world.
No learner should ever be denied the why behind a method.
It's what you get when you run schools like kennels. Student computers are how they teach, yet there's no real use for something like this anymore. Formula memorization doesn't help any more than actually doing problems does. To really take advantage of better learning techniques, the whole thing needs a revamp.
@@algorithme1950 Not true. There's a certain level of depth that is acceptable to students. I don't need to explain how axiomatic set theory works to explain to a kindergarten student why 2+2=4. Same thing with students jn much higher levels. You don't need to invoke some obscure detail to answer students' questions about algebra or geometry. Most of the time, the intuitive answer is good enough.
@@GaussianEntity We can only hope that the upcoming next technological revolution will liberate people to do the things that they like, in a time that they like and schools will change as well. But I feel like a fool writing that when I know people expected the same thing to happen after the first Industrial Revolution.
Ultimately, I feel like schools are controlled by the state and the state wants to kill all creativity and passion, as it doesn't need critical thinkers, it needs obedient fools.
Wow so true. Noticed this for a long time. A lot of the time we spend so much time trying to understand some part , section , paragraph or a section of a particular equation or so. But fail to understand that something moving forward. Everything becomes clearer and understandable as we study more about the subject. Some people literally stop, give up or put the entire topic away for days, weeks, months just because they find it so difficult to conceptualize that particular section of it. Write it down, Move on, pay more attention and focus deep on every information coming afterwards. You’d be surprised just how clearer everything eventually turn out to be. You’ve saved time . And you’ve learnt even more. It’s hard. But studying with pain usually is the best method of studying.
I purchased his calculus 3 course on Udamy like a month ago. It is really good. Mainly examples and the chapters/sections are clearly labeled and organized so you can select what specific topic you want to cover. So far, each chapter or section is around 30-60 minutes. I am really into it. I watch them before I even bother looking at my instructors lectures. I plan to keep getting more of his course as I take more math classes. It is really cheap tbh. It cost less thn bills, textbooks, groceries and maybe even eating out, depending on where you go. I still need linear algebra and diffy q so hopefully those classes are available in his store soon. His Udamy stuff is similar to his online lectures but he is not distracted by students in his Udamy stuff so its all steamline and quick material. 10/10. Dude is alpha.
Omg I didn’t know he was on Udemy! Thank you for this info
This is great advice, not only for maths but, honestly, in life in general. I've caught myself so many times getting hung up on something while so many other areas of my life were screaming for attention. Thanks for the reflection!
For me, it stems from this pithy statement drilled as a child "Half knowledge is dangerous." However, in the real world there are degrees of complexity and conclusion are always in gray zone, which means there is a constant refinement of our mental models and a lot depends on case to case analysis and the context that particular case is derived from. Thankfully, the process of genuine effort is what makes life an enjoyable ride.
I think half knowledge is only dangerous when you believe it's complete. If you know it isn't everything, then it's okay to accept it for some time. Time is the crucial missing factor.
If you were a public speaker on the cutting edge of math. Then this half knowledge is dangerous. If you're just trying to solve problems in your text book this is all you need.
@@awesomedavid2012W pfp
@@awesomedavid2012very well said 👍🏼
I totally agree with this guy. I’ve always been someone who got all As in math, but I wouldn’t call myself someone who excels at math. I’ve always understood probably about 70-80% of the material on a fundamental level, one where I actually understand what is going on and why the method I’m using finds the solution, but the other 20-30% of the time I just have to teach myself to be able to identify what information is given and what method finds whatever I need to find from that information. Sometimes it just comes down to blindly trusting and memorizing the process the teacher or the book has shown you, without actually having a fundamental understanding of the subject at hand.
Lately, I've been writing any math problems I can't solve on the last page of my notebooks. It's easier to move on when you know you can come back to it on a rainy day or something.
that is good advice
Nice application of the Z transform in a way .
Fast forward 3 months and every single problem is in the back of the notebook. Just joking, good advice I should do this!
Why is this in my recommended?😂
Math aside… applying this philosophy toward anything else in life seems game changing! Don’t get hung up perfection be completely understanding things and just move on!
Very fortuitous this video was recommended to me. I did my undergrad and a year of a PhD program in math, then left for a career in music. In the meantime, I got married, had two kids, and became a lot more patient with myself. I decided to go back for a master's in math around the time I turned 40, and specifically tried to avoid some of the self-destructive habits that had plagued me when I studied math 20 years ago. I was successful in part (stayed up til 3 AM on the first week of the program, then never again), but I still see ways to improve. I'm starting a PhD program again in the fall and I'm excited to keep refining a healthier relationship with mathematics.
You don't know how much I needed to hear this advice at this point in time
To fully understand modern mathematics requires an if not more than a lifetime of effort, because you are compressing centuries of exporation and research into a time frame of roughly 100 years.
This is definitely great advice for learning mathematics or anything in general, especially at an advanced level.
So why is learning another language easier than me learning simple math? English is like 300 years of complex knowledge compressed into 20 years. Same goes with French and Khmer.
Change that to like 600 years plus
Perfect timing. At the moment I am trying my hardest to understand a topic in calc 3. As I was doing my homework, I noticed I was taking forever to understand the third problem. Sometimes I get very upset because I feel like I will never get it. I tried looking up videos, reading the class textbook, but for some reason I still have no clue what's going on. Really nice to hear this advice.
Having finished it last semester, this is painfully relatable and I loved the class. Love some content or hate it, that is def. relatable.
I'm in Further Math Year 10 ( 9th Grade ) and same applies lol
As an Aerospace engineering stu, I can say this is exactly the reason why I got depressed at a certain stage of my studies, so basically I used to try to understand the concept of everything and the reasons behind every conclusion, like every single thing, which ended me up wasting too much time on all of that and not practicing very well and not going through all of the ideas. At the first of my journey, it was working cause I had a bunch of time to do all of these back then, but as I moved forward; things started to get harder and harder to the point there was like no time to even cry, like working while crying, so my technique was no longer beneficial to get good grades and that's ended me up feeling like I become stupid! so I got depressed and now I changed my way to a completely more effective one that allows me to understand as much as possible while maintaining progress and that literally reflected positively on my grades!
This is what I say to my classmates who I help a day before the exam. They start asking me “why” certain things are the way they are, I just say, “this isn’t the time to learn why, you just need to know that this is how it is cause there’s an exam tomorrow.” 😂
Stop trying to understand, this piece of advice has taken me a very long time to understand.
It's also referred to as 'accepting things on their own terms', which is closely related to 'trusting the process'... Your videos on mindset are far more important than any other you've created.
I found that in learning math, following the process and using good bookkeeping will eventually lead to understanding after much practice - especially when coupled with learning other maths. It takes time and you have to 'move the pencil'.
My guy! I'm 47 and taking pre-cal for the first time. My grades are good but struggling to understand everything. I needed to hear this. Thank you!
Mathematics has the extraordinary power to reduce complicated problems to simple rules and procedures. Therein lies the danger in teaching mathematics: it is possible to teach the subject as nothing but the rules and procedures-thereby losing sight of both the mathematics and its practical value.
Fluency-the ability to carry out procedures such as expanding, factoring, and solving equations-is important, but too often students do not see the purpose or structure of the procedures. Strategic competence and conceptual understanding in math mean being able to read math expressions and equations in real-life contexts, not just manipulate them, and being able to make choices of which form or which operation will best suit the context. They also mean being able to translate back and forth between symbolic representations and graphical, numerical, and verbal ones.
Your "Stop Trying To Understand" message was a crucial realisation to me. To "break free" and start to progress in and make maths work.
My more specific cases, as they mattered in chronological order:
*
Get to know maths equations for what they do.
Play with them. See them progress things from input to output.
I nearly broke myself thinking I needed to "understand" them before I could use them. Maths - it works the other way around - "crank it". use it and get familiar with it for what it does, first and foremost.
Later you might understand where I comes from.
*
If you have to learn a new topic and you have a big thick book, do do a once-through and feeling the retention is negligible. Suffer having your hair spiked-backward horizontally and being pushed into a "doomed" depression.
Thing is, no-one can construct a linear narrative (text as an expression has this limitation it is linear-sequential) which is hermetically-sealed all-there. You'll see what you need earlier further down-the-line. Doing your secondn pass you have a better idea what things are, where they come from and where they are going.
*
It is abundant experience that if you "park" any idea of understanding something now, it is likely that many other things learned along the path made possible by "cranking" equations will provide context to later "understand" the mathematics anyway
In every other aspect of my world of machines, metals, making structures, etc. you must understand. Working in a workshop or on a construction site, you must be able to visualise problems, which could be lethal, along the path of the plan you are looking to implement.
Maths - the "rules" of learning are so different. In line with what you say.
Thank you for this advice. I waste so much time being upset about not understanding and a lot of times I remain stuck in one problem for so much time because I can't deal with the guilt of not understanding or the fear of missing out on any detail.
This mostly has to do with grades. You can get As without understanding anything. You can just memorize the algorithms, practice, get the A. There's no actual requirement to understand any of it. You don't NEED understanding if you just care about grades. However, if you value understanding intrinsically, and want to be a great mathematician, then understand everything you can.
Very refreshing. Feynman said something similar and I tell my students also. Just accept things and build on them and trust they make sense. Its hard to explain. I teach computers and sometimes i just tell people to use a 'formula' first and understand later.
If I just accept it, then I don’t feel like I’ve actually learned anything new
@@dosomestuff1949yeah that's the point, you haven't. You'll get it the next time round. Or the time after that! Did you even watch the video?!
@@MatthewTaylor86 yes I did. I agree with the video, but some of the comments here telling people to just completely give up on understanding for good, I disagree with.
I doubt Feynman said that. Source?
@@But_Whyyyy corpusles of light lecture
For philosophical inquiry, sometimes the "why" can be the most important bit of the problem.
"Stop trying to understand." That's how I do it. That's how dad did it. And it's worked out pretty well so far.
Yea it’s the numpty way
My brain clogs the second it has to actually memorise stuff, unless that something simply "makes sense"
Everything makes sense but i mean unless i see the method, even if i don't understand it, i won't be satisfied
We should apply this to life as well, not only math. Great video :)
I am 41 and just started understanding some concepts. Always hated trigonometry. Now I have no issues with it. It takes time for the brain to form certain structures to deal with math.
Indeed it does, I can say the same at 19, I too was late to learn trig, doing the how before the why with it allowed me to understand later.
As soon as I read the title I knew exactly what this video was going to be about, and the words initially spoken just hit the nail for me. This was something I needed to hear so badly and immensely, I was hoping to understand the same through the hard way(By dissecting each and every section of the question for better understanding) but this video reinforced that belief much more clearly and concisely for me. Thanks a lot for the effort and knowledge.
It’s over for mathcels. You can’t even understand.
underrated comment
Exactly, but it should be specifically emphasized that even the top experts don't 'fully understand,' yet we still fall victim to the illusion of their high status, and think they do. Whether it's Einstein or Terrence Tao.
Haha!
They are so cooked 🍳
its ovER
Math is understanding! It means exactly THAT. The calculation itself is nothing, that can be done by computers/calculators. But to UNDERSTAND what is going on is the Most important thing. But OK, you should not try to solve problems you have not divided in smaller parts (enough) yet.
People understanding is the most important value in the world. Truth is not accepting a frame or a perspective. I would dare say that 100% of the problems in the world come from a lack of understanding.
In some areas, understanding is very important. Math is not one of those areas.
The issue is you cannot understand everything all at once. You need to value your time and understand what you can and use the properties of math ad leverage for the stuff you do not have time to understand.
It makes more sense if you consider your understanding as organizing books in a bookshelf and retrieving them as actions such as finding that book and opening it. There's only so many books you can put in the shelf. There's only so much retrieval you can do. Accept your limitations, and you shall find ways around them.
As someone who loves understanding things and often does better when I do, I was almost ready to brush this off as something that doesn't apply to me. And then I realized that every single new mathematical concept I learned in high school didn't always come easy to me. I looked at it, scratched my head, then half-moved on, only having fully understood it after a day or two (or even a week). In a way, this comment is just me thanking you for posing an important piece of advice that's helped me self-reflect.
Great timing. I spend so much time trying to understand so-called "trivial" things... things that do not effect my ability to solve math problems. (Because I hate memorizing things, I would much rather forget everything and then retrace my steps to get back to where I was )
So true! This is how I work with formulas, but sometimes u just have to bite the bullet and actually memorise them instead of logicing your way out lol, especially at a level or higher
I am exactly the same way. I have been spending hours trying to just understand a FUNCTION. I know it is stupid to keep ruminating on it because I have been able to use it.
Dude what the actuall hell? Then at that point your not learning anything
@@dosomestuff1949 I disagree.
It's about learning "why" or "how" over just learning the "what". it's about getting a deeper level of understanding. The problem with this is the time efficiency. It's not always worth it to dig into everything.
FYI: I got an A in the class I was referring to when I made this comment.
@@brandoncrenshaw6813 what if you get a question on your test that requires deep thinking, more than just plugging in numbers into a formula?
Man I love your videos. So wholesome, guiding, relaxing and comforting all at the same time for people who are stressed out about their math education.
This one hits home in particular because I used to be an extreme perfectionist as an ex-engineering student, to the point I had to drop out. There were also health problems at play, but the perfectionism played a significant role as well.
Engineering is all about pragmatism; using what’s there from math and the sciences to use for building things, yet I was so focused on where all these results came from that the course, professor and textbooks didn’t go into because it was “too advanced”, to the point that I lost track of the main idea; using that knowledge to actually make stuff. I’d have to simply accept why Stokes’ theorem, a highly nontrivial, useful and not very intuitive result, was true in order to formulate the Maxwell equations in their differential version. Or how to interpret the seemingly “infinitesimal” energy and heat transfers in classical thermodynamics. I didn’t like this at all so I put most of my time really trying to figure out every step of the way building up from formal logic to set theory, both of which I had to learn by myself, to the definition of the number systems in the setting of set theory and building up from there to the actual material I had to study. Now that I’m older, I notice that with becoming an adult comes a more pragmatic mentality, which is a good antidote against perfectionism. I’m sure I’d do better now with this new mindset.
There are parallels here with language learning. We can easily waste time staring at grammar rules early on - but for any of it to make “sense” you first must accept the weirdness and bulk-learn, phrases and vocabulary.
Once you have loads of examples safely held in your memory - the reasons and rules you didn’t understand earlier will start to make sense.
Also the fact that none of it really makes sense and you just eventually get used to it lol
Its completely different with math...
I think this is also bad advice. Learning grammar first would have helped me immensely when I was attempting to learn Spanish. It's difficult because it's a process of logic. But once you do it it's like a superpower. You can make valid sentences by deriving them in your head without having an intuition of the language. There is so much value in rules and grammar
Eh, i would say if the people who discovered it discovered it then it isn't impossible for me to understand it
As someone who's always stuck with the "why"s this is invaluable advice for me. Thank you...
I'm not mathematician and I get this advice not literally but as "Don't torture yourself by not understanding something", otherwise trying to understand things is what make us humans and reason of humans development.
This is the type of wisdom I pay my internet for! Thank you SO MUCH for sharing it. Funnily enough, I probably wouldn't have listened to this if I found it sooner, so I am glad I got lucky on the timing.
You can turn many courses into patern recognition. That is how i got through calc and organic chemistry . But now I am retired and going back to study cal on my own so grades dont mean much. Understanding is more important as it is just for it's own sake. The future of higher math,like the future of many things is in transition. It may be that the ability to ask the right question will be more important than the mechanics of calculating the answer. Think of how calculators changed math fifty years ago. Understanding may go from an intelectual achievement to a necessity. My experience with calculus was that while i was able to recognize paterns in equations recognizing paterns in real problems was harder as there were just too many paterns to memorize. I think that a deeper understanding would have helped.
Im about to take my geometry graduation test to graduate 7 years late in life as I had to drop out to work. The class I had no problem with but its been a few months since Ive been in the class and Ive forgotten so much. Ive spent the last week sun up to sun down researching and trying to understand everything again. This is giving me the courage I need to believe in myself and feel that i have done enough to prepare myself. I needed this more than I would ever know before I watched it. Thank you so much for this
Just spent two hours on a proof with mathematical induction. How timely a video! I suffer from the need to understand as well so thanks for the reminder! On to the next chapter!
There’s also so much to this approach because of subconscious processes as well. I cannot count how many things I saw in undergrad that I never fully grasped or had a deep understanding of, and then when I saw them again in later work, it all came together without extra work and pain. Your brain processes and takes time to work on things in ways that we really do not understand. I love this video.
I love this video. Learning and teaching is such a "human" effort, even with something as abstract as maths. The beauty of it is that it's scaffolded by definition; each theorem works because the theorems it's based on work. It's liberating to finally break through and realise it's not like other topics; doing comes before understanding.
“Forest for the trees”
I have slowed my progress immensely due to my need to know and understand things deeply to the lowest possible level. This is great advice you’re giving here. Sometimes your understanding will improve simply by exposure to more material elsewhere or by trying something different.
This is so true!! I’m in calculus 3 and if I tried to truly understand not just learn the concepts, material, and patterns, I would a lot more clueless than I am now.
This is an extremely beautiful and important piece of advice. I struggled with mathematics in high school. In college, I took statistics and had a C in first semester by a stroke of luck. In second semester, my luck ran out and I failed. I had 14/100. I had to resit the exam, but I was justifiably scared. I knew I wouldn't be able to pass it if I wrote the exam again. Fast forward to when exam was coming, I started getting tutored by a friend. Everything I learned flew away from my head when I entered exam hall and couldn't remember a thing. I picked answers randomly. When result came out, I was lucky to have 52/100. Then, something interesting happened last year. I decided to have a career in data science-a maths-heavy discipline. For someone who flunked his way through high school and scared of writing any exam that has anything to do with numbers, it was a crazy idea. But I believed my deficiency wasn't a functional of my capacity. It's more about psychological. It had nothing to do with my cognitive capability. So I walked into ring and started learning statistics again. There were times, I wouldn't understand some things, but I would keep banging my head on it, trying to understand everything, instead of moving to another topic. But this piece came in handy. It will help me on my journey and as I continue the journey of becoming an outstanding data scientist and machine learning engineer. Thank you so much for this, sir.
In the past I was nervous to move on from problems I didn't understand because I believed if I didn't tackle it head on, the ideas would be gone forever. I wouldn't think about or internalize the solution, therefore I'd forget. However, I did have to move on in a series of books and that was Knuth's "Art of Computer Programming" series. Six years later, I encountered a problem at work and I remembered that Knuth had written about this and I picked up right where I left off. I didn't expect that the process of giving up on something, made me actually remember it at the very least.
Thanks for this message. Maybe I needed this now.
Man, this is just good life advice beyond mathematics.
I was stuck in a quantum mechanics problem and feeling really disappointed for not being able to understand it when I found this video by chance.
Thanks for this relieving message I really needed to hear it now.
You're definitely right.
It's hard to find the right balance between basic understanding, sufficient practice and constant progression.
It's definitely wise to have a basic understanding of a topic before moving on.
And yet it is sometimes the case that you may not understand where every rule comes from or why something works that way, but if you keep going, dive into other topics and have accumulated knowledge, you look back on the tasks you didn't understand and think to yourself, ahh, now I get it.
And yet you can also get lost if you jump to a new topic too quickly.
Well, as I said, it's not so easy to find the right
I think this is the first time I have heard someone say I should not expect to understand everything in the class. So liberating. Thank you.
Good advice as always. Thanks for posting and thanks for all you do.
Just recently have I begun to take managing my time seriously. Part of that deal with myself is that I have some time to reward myself for time well spent. One of such rewards is that I can watch youtube videos without that nagging guilt feeling that I could be doing something productive.
What I'm trying to say is that, today my reward got me stumbling upon your video and I have never felt so strongly the urge to comment on a video (something I rarely ever do) as I do this one. This was just exactly what I needed. This isn't maths, this is philosophy. Wisdom. I have just taken up a new skill, all in the direction of being a better person and this has been immensely insightful as well as validating the thoughts I have had to myself about "just moving forward". There's only so much time we have. One ought to jealously guide attention and focus, channelling energy for high-priority tasks that move one toward their goals.
So, thank you, sir. For me, you smashed this one. Subscribed!
No never! but yeah I agree the more you try to understand, the more the math gets deeper and deeper. But I find trying to understand in the summer is pretty good.
Yeah. But if it's not summer, I'm still impatient to understand.
I'm so glad someone as high profile as you is saying this. It took me half way through college until I understood this was necessary. I still am slightly unclear on when you can dig deeper for more understanding and have it be a net positive. Some combination of always being slightly alert for patterns, maybe when you're combining multiple areas you should also look for patterns anew, and only when you have built up lots of experience and patterns you can try to understand more deeply with that context subconsciously helping you dig through to find deeper patterns so you "understand".
This is very true and I think definitely applies to much more than just mathematics. I notice a lot of people do this in language learning especially. People spend a lot of time pondering and trying to make sense of something than just practicing more, reviewing more and letting the intuition naturally be formed through practice. I've never personally found sitting and staring at something for periods of time to ever be productive, and since realizing this I save a lot of time by just moving on, learning more and coming back later. Developing an intuition for math or physics, whatever is never about how much time you spend pondering about it but more about how much time you actively spend engaging with it in a variety of ways, seeing how things actually work.
As someone who is learning another language that is difficult, I barely encounter this problem, but with Math, I ALWAYS encounter this problem.
I don't think it applies to mathematics solely. This video is best general life advice that I have ever been told ❤
Thank you, Math Sorcerer. You gave this advice a long time ago, and I have followed it since. It has been very helpful. I like writing down what I get and what I don't about a formula or whatever, so at least I can define that.
I hope u r happy with your grimoire
Sometimes forgetting things for some time helps understanding it when you come across it again. I've come across things after years and they were clear after that. It's weird feeling. Maybe memory works little bit like a computer, but it takes time to move them from short memory to long term memory. Something you will remember always.
Bro looks llike an ancient mathematician/Scientist.
Keep moving forward! When you dive into other subjects and gain more experience, you'll look back and see things from a new perspective. For instance, before I took Linear Algebra, I was grappling with a Differential Equations course. I kept asking myself, "Why do we even need to find particular solutions and complementary solutions? What’s the point?" At the time, I didn’t really grasp the concepts; I just crunched the numbers and powered through exams. But a year later, after learning Linear Algebra, it all clicked. Finding complementary solutions is like finding bases to span the entire solution space. So, my advice? Keep those puzzling questions in the back of your mind, but don’t let them bog you down. You’ll get it when you're ready.
True! Thank you very much!
Now when I revisit the maths I couldn't understand eight years ago, WITHOUT EVER HAVING SEEN ANY OF THAT MATHS SINCE, I feel like laughing at myself. It was maths at the MSc level and was supposedly very hard, but it looks like a walk in the park now. Our brains are very powerful. The brain analyses and studies stuff when you're not focused on it. So, if you ever don't understand anything, leave it and come back to it much later. Your brain will process the information it couldn't understand, and the next time you see it, you will have understood something, if not everything.
This is great advice. I never had natural aptitude at math and had to work really hard to do just okay in middle and high school. Through stubbornness I got a bachelors and Phd in physics and ended up with a few publications on theory-heavy topics. I attribute avoiding getting hung up on understanding every step and just building the muscle memory of solving problems to get me out of a rut. Just accept some amount of mysteriousness and solve the problems you can - eventually the understanding will come! Revisiting entry level material after you've completed higher level material is a truly eye-opening moment.
The author Barbara Oakley explains this proccess very well. I recommend her books, start with "A mind for numbers". They're mainly introduction of STEM for people who are afraid to even consider it, so yeah, not technical heavy calliber stuff for pleasing Einsteins. Just a simple and good book that would generate a ton of short videos for you to tip people with.
There is also an online course.
Thanks for the suggestion
Been in so many math classes where the lecture keeps getting derailed by some students saying “I don’t understand”. As if the expectation is that you have to understand everything right away. It takes time! Glad someone with a high profile is making the point…
Але повністю згоден що зависнути на чомусь, чи зрозуміти на половину і рухатист далі важливіше ніж впертись у щось незрозуміле і "захглохнути" на цьому. Хочу вивчати математику і все що з нею пов'язане англійською. Дякую що ділитесь. Фізика, математика, геометрія та географія, так само як і юриспруденція є послідовними цікавими і логічними науками ❤❤❤❤
This is how I passed calc and physics in college. In school, I was able to understand the concepts so well, that I could not study at all and do well. But at a certain point, there's so much you need to remember and hold in your head at the same time that it's best to just trust the process and maybe with enough repetition, it'll start sticking intuitively.
You are an excellent philosopher who happens to be good at math ❤
thank you , I needed that because as an engineering student for the past couple of months I have been stuck on why of things and not focusing on my grades. You are right sometimes we need to move on to understand it better in the future with more knowledge. :)
Thank you, Sorcerer
Such great advice sir. I'm a Physics student and I have a habit of making a clear diagram to connect everything I just learned after class. I will feel really uneasy even when I solve the problem because I am just doing it instinctively and not clearly understanding what I am doing. So sometimes, I would spend the whole week trying to write a whole 20-page note of the theory before actually doing some experiment with it. However, I wasted so much time on it, and sometimes when I think I have composed a great document about the subject, the experiment proves otherwise.
It was not until a very long time ago that I concluded that sometimes, it's good to just learn something instinctively, don't need to fully understand WHY and HOW, and instead just move on with your other current goals.
Thank you for this video. ❤
You are so welcome!
This is exactly what I need at the moment! I have been trying to understand a paper for weeks, almost 2 months. I read so many other papers trying to work around it and tried to figure out top down/ bottom up. I feel so dumb because I can't imagine that I cant figure out such a simple equation. But you are right I should move on.
Thank you
You are so correct.
This is excellent advice. Sometimes you learn a thing and live with it without understanding. Then one day, you understand it completely. When a problem stymies me, I leave it and do something else. Come back later; suddenly it is clear.
You reach the point where you realize understanding is a construction in your own mind. Just keep doing the math.
No, understanding is good.
Thank you for this, great advice!
This week I sent 4 hours trying to solve problems for an exercise class. I spent all my time on the first problem, and could not figure it out! We had been told that we could be called up to solve the problems infront of the class, so you can probably understand why I was so motivated not to mention stressed out.
Turns out they had forgot to include some crucial slides during the lectures...