@@WebDevAnjali You are going for the good way. In the first year of walking, you will begin to perceive how mathematical knowledge rains down on you from nowhere.
that's very candid of you! at good engineering schools, engineers often have more math requirements than some Math majors, and for a reason--we actually have to use it in the real world! glad that you overcame your struggles, & maybe you're just being modest, but either way great model for other aspiring engineers to look up to
That is so awesome, since you have a PhD and I love engineering, I would love to read some of your peer-reviewed papers. What is your name sir and how can we find your work?
The "why" was my issue with math. It drove me crazy and made me falsely believe that I was bad at math. Then something I never could have imagined happened. I was in a low level college algebra class that I needed for my bachelor of science degree, and I was _struggling_ hard. My mom had a friend who was a high school math teacher who offered to tutor me. I went to her, but without much hope. Two hours later I walked out of her home understanding algebra like I never had before. From that point on I made A's and B's in math and never needed another tutor session. My moms friend didn't perform magic. What she did was teach me WHY by using analogies. That is how my brain processes apparently, and once I understood the larger concept (in analogous terms) behind what I was being asked to do, it all clicked. From this experience my suspicion is that people who say they are bad at math, but who are otherwise above average in intelligence, are not being taught math the way that their brain processes information. If more math professors were taught to offer simple analogies and even a few storylines to teach math concepts, we would have many more people excelling at least to the undergraduate college algebra level.
same problem i have like if teacher solving the question i always be like WHY ..why will we do this particular thing in this question ...and sadly i hv still stuck between this WHY everytime.
I think it's fair to say that the experience of confusion is a sign that your brain is actually working and learning. I try to remind myself that the sensation of "not getting it" is a good thing; it means my mind is being challenged with something new. If your mind is comfortable it's probably not learning anything new.
Awwww he is giving up, in the end, what is math used for if it just numbers in your face thinking about how the real way it works but there is no meaning for math is there, we will never know until someone else gets it and we the people who look like the failure trying to decypher math since countries ago
I'm not sure if he was referring to not getting how to solve a problem, or not getting WHY you solve it that way. The latter is always my problem. I can follow instructions, we all can. But I NEED to get it!! I need to intuitively, on some level, understand why I'm using a certain approach, what it means, what it implies geometrically or analytically. You know? I guess we're all that way? I feel like I can't possibly move forward in the course if I don't understand every concept along the way.
John von Neumann once was approached by a student after class who said "Professor, I don't understand the math you're using". Von Neumann answered: "Young man, one doesn't understand mathematics. One only gets used to it".
Good one! That implies that a significant portion of becoming good at math is to practice a lot, and not spend too much time on theory. Of course, one cannot practice if one doesn't know the theory. But, one shouldn't let theory to slow one down.
Math has broken me down to tears in school. I’ve struggle with it my whole life. I needed to hear this. Maybe it will help me get the confidence back to get some degrees.
You can do it. learn what you can and keep learning. Try and realise that learning is fun. It won’t be easy but you’ll grow as a person and so will your knowledge and you might surprise yourself for how far you have come. Things may be harder for you to understand compared to others or the other way around. But why should that stop you or anyone. What makes someone great isn’t never falling, it’s how they recover from a fall. Don’t just lie on the dirt after a fall, get up, get up and show the world and yourself what you can do. Because we can all achieve great things.
It was terrible advice. People stop trying to understand math and then we get a society with conspiracy theorists, flatearthers and people with imaginary friends. You want to understand math not because you want to do Lorentz transformations in your free time, but because you want to have critical thinking.
Neil deGrasse Tyson said in an interview about calculus: "If you don't understand something immediately, it doesn't mean you're not good at it". This quote has given me sooo much motivation in my mathematics journey.
Well, especially when taking a test -- "I'll come back for this one later". Really, it once really saved my ass during a Calculus I midterm, that I didn't even know what Question Two was asking, but then the second to last problem was almost the same thing but set up differently, but in a way it EXPLAINED what I was to do for Problem Two. Heck, examples can go back years.... remember back in Algebra when you still couldn't see Dif Squares and Complete Square Identities a mile away.... just Come Back To It Later is just the thing for coming back and Seeing What You Missed Before.
This guy is so passionate! It's so inspiring Summary: don't spend too much time on a problem refresh ur mind interleave, do something different realise it's okay to be stuck
i love how this comment is right under the one it was stolen from (for me right now). cmon man, don’t repost a comment for likes, they’re just worthless numbers
Literally the advise my prof told me today when we asked him how to come up with that approach to solve a specific integral he just showed us. Told us we will get used to integrals, though we probably would never have come up with that solution on our own as it took a long time to be discovered xD
I'm studying mathematics at a relatively prestigious university and the workload is TOUGH man, both in terms of volume and difficulty. I just wanted to say that your videos are so wholesome and they are a big source of motivation for me to keep going, keep studying, keep being curious.
I am studying mathematics with an interest in physics. However, the math is presently beyond my understanding. I have been hitting a road block with derivatives of trigonometric functions and identities. But inconsistent study habits and back tracking to review math concepts slowed me down. Your advice to just move on is valuable. After looking at more advanced material, I can see the relevance of what I was trying to learn and it started to make sense. Persistence is the key. You have not failed until you stop trying. By the way, I am 73 years of age with over 40 years in the computer field.
I've never been good at math in high school and I never got the help I needed at the time. 6 years later I'm really fighting to accept that I am just 'bad' at math. And I am looking to get a degree in my current field of software development because a diploma is not enough for me. And getting a degree is another thing that I really feel I need to achieve. I started with math again as its part of the admission requirements for any comp sci field, I really hope I can do this 🥺
@@Haniefatries_ focus on linear algebra (matrices and vectors) thats what compsci needs most. and if you are doing 3d graphics linear algebra is pretty much compulsory.
I remember I used to spend hours (3 or 4 sometimes even more) trying to prove some induction problems, every day I tried so hard but I wasn't able to solve them, I didn't want to give up but eventually I did, and I started to wonder what is wrong and so on, I realized my algebra background wasn't good so I spend winter holidays to get better at algebra something like 1 o 2 months, when I got back at those problems everything was so clear now, I was able to solve them in less than 30 minutes. The lesson was, learn to when give up, you cannot fight all your battles.
Yeah, I've learned not to fight the idea that I need to do some review. If I'm blocked for more than a few seconds, I get up and get the old book and flip to the section and go through the examples. the more you review, the less you need to review.
i thought it's just me that have a really2 long time to prove induction problems,and it's not bcs im dull,like i can understand concepts quickly than my friends,but yes maybe i need to move on
this brought me to tears. after an incredibly frustrating relationship with math this is what i needed to hear. i was going to drop my class and change my major because i'm feeling so beat down and stupid trying to learn calc. thank you.
I felt the same but it was because the class was tanking my grades. Not because I physically couldn't understand it but because I did not see the point in memorizing Taylor series
I am abysmal at maths! I am a brilliant speller, and an excellent writer. I aspire to be a novelist. I score highly on everything else. Find out what works best for you.
I believe the key to learn math (specially abstract topics) is to accept that you ain't gonna understand anything but, you'll get used to it. The more you practice, the more you get used to a concept and thus you will develop "your own" understanding/intuition of a topic.
My struggle is that I can't practice without understanding it though unless it's very basic just fill in the formula type of math. If I go to a lecture, work through the material (which is practically impossible if you don't understand it) and start with the assignment... well, what then? Unless it is a math problem that we have done already the exact same way in the lecture, I just blank. I can google for hours but still nothing. "Just practice" worked super well for me in school, I ended up as the best student in math with a straight A on my final exam but advanced math/comp science at the university just destroys me at the moment. Sorry for the vent, just casually breaking down here.
So true. I know for me there were times, particularly in my various physics classes, where I got caught up in trying to understand the why, finally just learned the math with understanding why the math worked. And then found that as I trusted the math I just got used to the physics concept to where it made sense.
@@GeoRedtickI am sucker for trying to understand it too much and not accepting it as true. Do you feel that you find those concepts that you let yourself practice actually make sense now? Could you answer those questions that you had prior?
I legitimately hate it when a professor states that a problem is “easy” or “straightforward” and I’m on the other side struggling to figure out what’s going on. I think it would help a lot of math teachers/professors to get through to their students if they put things into perspective from the majority that truly struggle with understanding the concepts. That’s why I appreciate your videos, Math Sorcerer. You’re constantly letting the audience know that math is hard and it takes a lot of time and practice. It reminds people like myself that it is okay to struggle on this topic and just as long as you keep at it, you will improve, and that is ultimately what it is all about. Are you better today than you were yesterday? When I assess my math skills today relative to a year ago, I could honestly say yes. It’s important not to lose site of that measurement when times get tough and you’re struggling trying to learn a new mathematical concept.
Empathy is the single most important skill a math teacher must possess. the absolute worst teachers of math are the people who were naturally gifted at it. They cannot understand, appreciate, or empathize with the struggles of others. They should not be the ones teaching math at all. In my opinion, mathematicians should be barred from teaching math below the level of Differential Equations. Engineers and others should be hired as math teachers instead, people with practical understanding of its applications, who have struggled themselves, and who possess empathy.
@@thewryneckarchivist no, that's not it. They lack empathy to begin with. Empathy tends to grow with knowledge, not diminish. Those who become mathematicians, tend to be those who never struggled with math growing up. They never struggled as their students do/will. They can't understand why students don't understand things, because they never struggled with it. To them concepts came easily, and too often they only know one right way to solve problems, their way. The Way that came so easy to them, even if that way is a more complicated way to solve things. Teachers who also learned math through struggle make better teachers. They can see how a student is stumbling, recognize the struggle with a given concept, as they once experienced it as well. They can explain the problem in different ways, to help the student understand.
the problem is that in the classroom, especially during that traumatic time known as high-school years, math and other sciences are taught like something more similar to military training with live ammunition. there is no room for mistakes under fire, and especially when failiure in math and science is often viewed as a sign of failiure in life, there is a huge difference between this relaxed attitude and the pressure put on students in real time. to some extent, you can say the same about any field of study in the classroom, that there is no time for any deep engagement with the subject, if the top priority is getting good grades and pleasing others with them. from parents and teachers to future employers.
this is largely a symptom of grade inflation. That itself is largely because companies are way too selective of their employees for things that do not require such selectivity.
I'm in my senior year of high school now, and have always been a straight A student. The kind that studies the night before and still gets A grade. And due to this,usually maths is the subject that I have lowest marks compared to others.But it was always above average/good marks. This exam,I put in some effort and studied math. Even the exam itself was kinda easy for me. And somehow.. I failed. For the first time in my life I got a taste of failure in my life. All my classmates were shocked when the professor announced my grade. That I failed. I've checked the paper several times and I can't figure out where and why I went wrong. I'm stumped rn.. I have my finals in 2 months. What should I do?? I'm m worried. I'm worried of facing my parents rn.
I needed this. I just failed calculus2. I’m a single mom, have to get through these math classes to get a good career t support my munchkin and I. I am so bad about planting myself and forcing myself into attempting to understand before moving on. And then I have spent hours on one problem out of 50. I definitely need to spend more time doing problems and less trying to understand. That is such a hard mind shift for me. I’m going to do it! Lol!
Hello, much love to you and your child, I'm happy for you, you're doing great, I wish you the best on your journey, joyful learning and living fully. Have a splendid time ahead🌻❤️🍀
Beeing a single mum must put a lot of pressure on top of studying. Doing a lot of problems and choosing the right problem so you are still challenged but don't get stuck is hard. Personally i like to learn in groups. Solving and explaining your solution gives you a deeper understanding for principles, so you are less likely to get stuck. 😅 also a good portion of exams is just to get things up to speed because you don't have the time to think twice, something only practice can do.
1. Manage your Time 2. Pivot(Go for a walk just try to focus on any thing else) 3. step back and do something else 4.Its okay to Get stuck (My insight: It's okay to get stuck but its not okay to remain stuck) 5.(My advice: generally clear your concept the problems generally their solutions are simple but not easy they take sheer amount of how much did your understood your concept then that is applied inside of an question)
Stoic X, I'm honestly not trying to be a jerk, believe me. But in your #5, I got the sense that you were saying something very useful for all of us. But for the life of me, I couldn't comprehend it. Could punctuation clear it up? I'm not sure. But could you give it a second crack? I'm all ears! (Btw, #1 - #4 were quite useful...thank you).
@stoicx. Thanks for the summary 😃. I would be also very grateful if you could rephrase the fifth point. It seems there is a good idea behind an accidentally misformulated sentence.
🧡 Super helpful advice! Thank you. I'm a math major and these are things that I wish I had done. Right on! I just want to add: The more you immerse yourself in math, the more you get it. The more you get it, the more you love it. The more you love it, the more you want to learn. This is such an amazing cycle!!! 🧡
This reminds me the famous Feynman quote: “You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!” I found myself practicing that for whatever I study and for many study subjects in parallel. Never give up any - but take a break and continue with another one from which you effectively just took a break. Often understanding more about another problem gives you inspiration or even a hint for another one in the back of your mind. This way you are always busy with what is important to you and you are never even tempted to give up any of them. It’s very productive, efficient and satisfying 🤓
This is great advice. I used to feel bad that I wanted to learn so many different things, thinking I *had to* choose one and stick to it. It helps to realize that they are all related in some way and even if they're not immediately applicable to one another there is still a connection. Also whenever I go back to a subject I always come in with more information than before, and because I can't help but want to learn more about it, I keep coming back to it.
I agree. Just give it time. Knowledge acquisition is not a discrete event, it's not a step function. You rarely go from "not knowing" to "knowing" just like that. Just give it time for hard mathematical concepts or ideas to grow inside your brain.
I was identified as a gifted child early on, and the bad side of that is that everything comes easily for quite awhile. This advice is particularly good for people like me, because we all reach a point where things no longer come naturally. For me it was AP Calculus my senior year of high school (which I failed for this very reason even though I got an A in every single math class before it). When you are trained as a child that things shouldn't be frustrating or hard to understand, it can be extremely difficult to unlearn that pattern of behavior. As good as this advice is, I anticipate that I will still have a very hard time putting it into practice. My life is not so good now and I attribute a lot of this to never developing any sort of frustration tolerance as a child.
Also, I'm going back to college for a computer science degree at the young age of 36, so I made sure to subscribe to your channel. Something tells me that your advice and teachings will prove invaluable as I tackle math that is very difficult. :)
Yeah, apparently your parents didn't challenge you enough as a kid and wanted the easiest route so you keep quiet and they don't deal with your screaming or crying for not getting the shiny thing you are after and they have more free time to themselves instead of raising a kid right. That's why you can quit without consequences. Most people HAVE TO get it right. Their lives depend on getting it right. There's no mom and dad to enable them or sugarcoat things for them. The conclusion is: Privilege makes people lazy and unaccomplished.
I’m studying math on my own right now and I realize that for my entire academic life I have been placed in a box and not allowed to see the true beauty of math because of standardization.
@@nigelcardoso7653 Standardized education in math is studying for tests to get the grade, and if you get a passing grade it’s good, but you really don’t get to know math this way.
@Tech Maybe you should pick up a dictionary and become well aquatinted with the definition of two words ‘example’ and ‘obtuse’. I’m sorry you’re having such a hard time with this.
@Tech obviously this is the hill you want to die on, which is sad, but I’ll give you the much needed ego boost that you’re seeking since it’s in short supply for so many nowadays. Being placed in a box means that in a math course there are boundaries set on how in-depth a student can go in their study of math. Those boundaries are time constraints as a result of students having to meet very specific metrics. Once those boundaries are lifted and math students are able to really take the time to explore mathematics in-depth. I hope this helps.
This is what I did to get a 95 percentile on the GMAT and a 99 percentile on the Indian version of the gmat, called the CAT. Go through a chapter 3 times on 3 different occasions during the week. On every attempt you’ll see yourself noticing previously overlooked concepts. Used to do this during my school days. That’s how my basics became crystal clear. But I know lotsa students doing the same before their entrance tests. Secondly, trust yourself, some folks are naturally gifted and pick up stuff on their first attempt while you may do the same on your third. Doesn’t really matter, because at whatever level of school you’re in, the quantity of chapter’s to study will always be finite. And once you’ve gone through the entire syllabus, no one will be able to tell the difference. Best of luck for you’re exams. Cheers 🍻
That's not even maths. It's just a set of mindless simple calculations in a short time... Perhaps your achievement is important for you, but it is irrelevant for the current discussion where we are talking about "understanding maths" not "being better than 99% students to get a lucrative job".
Thanks! I always doubt my own intelligence whenever I don't get something and I'm too embarrassed to ask questions. I wish more math professors and teachers had your mindset
I can 100% vouch for walking. I've come back to programming and math after a long long while (a decade) and as usually happens you find yourself banging your head against a wall, trying to wrestle solutions out that just won't come. For whatever reason, going for a walk for an hour or so, even with some music on (without vocals) just helps the mind to flow and organise itself. I refer to walking as 'defragging for the mind'. It doesn't just help with math but any kind of problem you have, personal, logistical. I come home from a walk peaceful, optimistic and usually with an action plan for solving my problem.
I agree with you on that. Let me add another piece to it. A source from HackTheBox said that you should take a break when you feel frustrated that you don't understand a topic or can't solve a problem, because doing so let's your subconscious mind try to solve the problem instead of you actively focusing on it. From my experience this worked plenty of times.
Dr. Andrew Huberman (neuroscientist who focuses on neuroplasticity, search him) talked about this: during intense focus your brain marks synapses for change and the change only occurs when those synapses are not in use, basicly to learn you need to have intense focus on the thing you're learning and then the least amount of focus on that thing (sleep, taking a break and doing something else, etc.).
I agree, it is ok to allow yourself to not understand something for this moment in time. I realized, I often understood some concept or something in math when I was not feverishly chasing it. I give up today but only to fight another day. Writing questions down in a book helps too. It allows you to move on and work on other important stuff too without being overly obsessed/concerned with the stuff you dont understand YET. Also as we learn and grow it allows us to attack the problem from different intellectual/mathematical directions. So instead of telling myself: you are too stupid to understand this, I say and believe I am not just ready yet, I will continue working and growing and at some point I will be ready :) Thanks for the video upload
Thank you for really pushing the point that it's ok to not understand or not get it. I think there is this misconception that if you're good at math, it comes easy to you and if it doesn't you shouldn't be doing it. Thank you so much for that.
"Self study is so wonderful because you can pick any book, no one's forcing you" In the time of pandemic, "Self study" meant totally different for us students or possibly just me. Here in my country where modular distance learning is a custom for education during this time, made self study really really hard.. not only did it change the definition of self study from studying what you want on your own to studying what is needed for school on your own.. and it really hit me hard specially on math, physics and biology
@@ReiiRussWentMissing haha life is hard men, bruh my previous comment got deleted so this was my short response haha, I hope we will understand the meaning of life one day =)
Especially then you'd want to spend your time most efficiently. But boring over a problem for too long isn't the most efficient way to solve it, according to this video.
I think the point here is that banging your head against the desk isn't going to work. When I don't understand something, I try to identify gaps in knowledge and fill those gaps, even if it's something basic or fundamental.
when i get stuck solving anything, math engineering solution, etc, I just stop, get up, walk away. Even at work as an ME, I just stop and take a break. go for a walk, talk to someone else, go run an errand in town. Clear my head, try to prepare to come at it with a fresh perspective. Collaboration with others improves problem solving too. Some of the best solutions were achieved by working with 1 or 2 other people to solve it.
This is what I needed. I always thought about it. The more I stop caring, the more I do better at applying math. It occurred to me after I started taking treatment for my ADHD, where I would focus WAY too much on trying to understand. Thanks for this, I feel very confident moving forward to my Uni Grad and future personal studies.
This is great advice. I tend to want to understand everything from first principles. When I was in college, I would get stuck thinking about what the prof just said when I should have just accepted it and moved on. That caused me to not catch what followed and then it just snowballs. I think it's best to just accept what is presented at the moment, don't panic, then move on. That's one piece of advice I wish I could go back and tell my younger self. A good example is the use of imaginary numbers to represent AC circuits. I racked my brain trying to understand how imaginary numbers related to anything "real" or "physical". It just blew my mind. Many years later I learned that it was just a mathematical convenience that made phase rotation easier through multiplication. That's it, nothing magic, just a "tool" that makes the math easier. And you always end up with "real" quantities because the "i" (or "j" as it's used in EE to distinguish from "i" which is already used to represent current) ultimately disappear from the result. So what used to puzzle me, now seems "beautifully clever". :)
Going for a walk or doing some kind of exercise in general always helps. Your brain keeps working on the problem even if you're not actively thinking about it, and when I return to my work 2-3 hours later I almost always see the path to the solution or the solution itself.
I remember crying every night before my math exams as a kid. It intimidated me so much. It still does to this day. But here I am, willing to try again because it is one of the main subjects in an exam that'll get me into my dream career. Thank you for this video ❤
The way he describes this makes me realize that programming and maths are not so different. The way the connections grow exponentially with the size of the problem. And the way this forces you to decide how to use your time.
@@leovolont Yes and actually anything that takes you through a door will help a bit. When people pass through a doorway there's a context refresh that happens as you no longer need information about the room you were in and suddenly need information about the room that you're entering. It's why when people go to the kitchen they often forget what they were going there for. The upshot is that if you're stuck doing the wrong things on a problem, sometimes you can just leave the room for a couple minutes and you get unstuck. It's a bit like rebooting a computer that's acting up.
@Artificial Hobos Yes, so can lowering the temperature in the room a few degrees or looking at something green. All 3 of these things often times happen when you go outside. (Obviously assuming it's not blazing hot middle of summer)
@@SmallSpoonBrigade Hi Chris. HOLY SHIT! That makes all the Sense In The World. the idea ISN'T to take a break, no, when stuck, YOU HAVE TO WALK OUT OF THE ROOM. Heck, I see that with my Cats... if a Cat is pissed off about something, well, I learned to just pick them up and walk them about 20 feet away and put them down someplace "fresh". Works every time. Who would have thought it works for Humans and Monkeys too. THANKS Chris!
This is the exact thing I’ve needed to hear my whole life. Have devoted 2024 to learning to LOVE math, it is a beautiful subject of study and I have always felt drawn and inspired by mathematics and those who are passionate about it. The concept of learning math in a non linear direction has been monumental for my belief in my own capabilities. I’m working now on filling the cracks and resettling my foundation and will build from there. I heard recently “brick walls are only there to prove to yourself that you want it bad enough”.
The professor is speaking a universal truism. Trust him. Move on. If it is important then keep coming back, try new perspectives. Discuss the topic with others. Always share your difficulties. Don't be so foolish as to believe you can solve everything by yourself. Find out what works for you. Then again, I am not a mathematician, just an old retired ChemE that still enjoys the beauty of math and science. Especially, when applying maths in the real world.
Hey. I’m a senior at college and I’ve been having a hard time with mathematics. I’m so glad that I stumbled upon this video. For the past year, I’ve been telling myself that if I don’t understand something, that’s my temperament. But it’s not. I will always use this video to remind me that it’s ok. This will really help me.
Thank you Sir. I'm learning computer science and it is so frustrating sometimes when I don't understand the theories. Most of the times I feel like everyone is ahead of me and I'm standing alone going nowhere but this video gave me a big advice, a mental relief and a breath of fresh air ❤️🍃
This is a very good point that I still struggle with. I kinda thought of an analogy that might go with this: It's like trying to defeat a boss in a video game, instead of going on side quests and increasing your arsenal, it might very well be possible that giving up and moving on to other things will give you the inventory you need to defeat that boss. It also might not, but I'm just being optimistic.
This advice is pure gold. I'm a late bloomer, I'm the guy that couldn't add simple fractions or do long division in school, but always had an amateur passion for physics and science. I believed the lie that some people just "didn't have it", or that I just wasn't a "maths person". Years later, after knowing that I could never enter those fields properly without tackling the math issue, I spent hours each afternoon and evening after work, starting from the bottom up, teaching myself from books and online Udemy courses, prealgebra, algebra, trig etc. With a lot of hard work, I'm now a mature age student in the middle of university calculus and loving every minute of this beautiful subject, despite its challenges and stresses. Thank you for your channel and everything you do, your videos have been incredibly reassuring and inspiring to me.
You're really a math sorcerer, thanks for making me realize it's okay, once I was depressed that I couldn't understand maths but now I know it's okay and that I shouldn't be stuck in one place
A great message. I remember being in grade school and having a tougher time with my multiplication tables than other kids. We'd play a flash card game, and I never won. I thought I'd never learn them. Then later, after the pressure was off a bit, all of a sudden, seemingly, I just knew my times tables. They just appeared in my head and made sense. Better a little bit late than never. This message, by the way, applies to everything. Take a break, do something else. If you're writing poetry or working on a piece of music, step away from it, distract yourself. There's a good reason why so many eureka moments happen on the toilet or in the shower. :)
Thank you so much for this, letting go off the things you don't get right away is okay. I came back 10 years to math and was the best decision ever. The funny is that now I understand topics much better than I did a decade ago.
Best advice ever. Me also as engineer student tried to understand every single point of the matter, losing a lot of time . It's way better to just accept some assertions without challenge them. The deep understanding will often come with years.
Beautiful advice! Still remember my uni days solving a Maths problem for days and not moving ahead, telling myself the story that I won't leave any weak material in my foundation. At the end of the day, it was pure intellectual ego, which harmed me more than it benefited me. There were times when I was able to come up with some unique solutions, but there were other times when my obsession for "solving" everything, led me to even depression where I thought I wasn't good enough because I couldn't solve a problem! It would take just one unsolved problem for weeks to make me forget all the other times when I came up with something good. I would suddenly sink into the blackhole of believing that I was stupid. Once I lost a complete year chasing the dream of being a perfect Mathematician! Beautiful advice from you here. The most important words in one's life if you are suffering because you can't get something- LET GO! I think walking is a wonderful way of practising letting go of things. Meditation is another beautiful thing. May all be free from suffering.
This guy speaks the truth - his words resonate so much, they always make me laugh. I'm the sort of person that wastes hours trying to understand something and can't move on until I get it - it's genuinely tiring.
I am just a high schooler who came across this video of yours...I scored 45/80 in my pre finals and my score has never been so low...my finals are on 21 march....I aim for 80/80. You motivated me lott. thnk you so so much..! ill update my results after they are out🤞 edit: i scored 75 / 80..i kinda feel proud of myself but i expected more
Take every math problem as a challenge... And develop an attitude of not giving up... Let it take time.... Frequently go through basics... Try to understand and relate concepts asked in a problem... Make friends with same attitude and who are open to discuss on the ideas to solve the sum....
You are absolutely correct!I am a grade 9 student, but your channel is a source through which I found very good recommend books, which helped me guiding/understanding mathematics, the whole credit goes to you!
This video should be clipped at 1 minute, concluding with: "(When you don't get something in math) you have to be able to prioritize your time and give up strategically." (The whole clip is a great watch, but that first 60 seconds is brilliant.)
Good advice! Also, my suggestion is that if there's a gap in your proof that you just can't fill, just write "I think it follows that " and leave out the justification. After all, it's much better to get 4/5 because your proof had a gap, than to get 0/5 because you just gave up.
I can attest to the effectiveness of this advice. I'm a software and electronic engineer, and when I'm stuck on a problem, breaking away and taking a walk, soaking in a bath*, or just switching to something else, has on hundreds (maybe thousands?) of occasions brought the solution to me. In fact it is just about guaranteed to open up, if not _the_ solution, an approach to get to the solution. This has worked over 90% of the time. I posit that during those times the brain is able to rest and allow the creative side to flow freely, unconsciously. It took a long time for me to get this, as I used to naturally be very choleric and tenacious and would want to just pummel my way through it. By accident I started observing that breaking away from it was much more productive. *I now call this "going to the think tank".
The advice I give to others working on coding problems is, “if you ever ask yourself whether you should keep working on this problem or go to bed, the correct is always to go to bed. The number of times I have solved a problem in a few minutes the next morning after hours of fruitless work the night before ….
This is exactly how I feel, I’m currently struggling massively with the Binomial Theorem (I’m at advanced higher in Scotland which is the highest level before university) and this is just what I needed to hear.
I try to imagine it not understand it. As an engineer i see a decade after my degrees that there are things i thought I understood. Things i definitely understood. Things i understood better than others with others thinking im dumb for not understanding something trivial which they didnt get in the first place. Shift focus is true. I get glimpses or strokes of clarity when i go to sleep or shower on things i did 10 years ago knowing that i never understood just did.
This remember me when the internet spent months trying to solve the last question of the mensa norway test, reddit and you tubers coming up with all kinds of crazy theories about how to solve the puzzle. Eventually someone emailed Mensa and got in contact with the creator of the puzzle and ... ups... the instructions were actually typed wrongly, it wasnt possible to be solved, so the question was removed and all internet theories from the geniuses were all just completely wrong. All time spent for nothing.
Yes, I agree. In studying electronics, I’ve come across some things that I just can’t grasp, and it is easy to get discouraged and think that maybe I’m not made for this endeavor. But then I remember that there are SO many things to learn in electronics, there’s no point in banging my head over just one thing, when I could branch in a different direction and then circle back around some other time.
I really needed this. I’ve been teaching myself algebra (trying to catch up where public school failed me) and I’ve been really stuck on the “why” on certain things. I’m an analytical person, I love figuring out the reasons behind what’s done, but as long as I can get the how I can let that go. Thank you💕
Thank you so much. I am currently taking an asynchronous course in Multivariable Calculus and I find myself spending hours on just one problem or topic. Last week I was stuck on a few problems from my textbook and couldn't see why my answers were wrong. I spent so much time on these problems, only to find out later that the answers in the textbook had typos :(. I will try to apply what you talked about to avoid this happening again in the future.
Thank you! I needed to hear this. I have been self studying differential equations for the last month. I’m preparing for that class this upcoming semester. I’ve heard some… questionable things about the teachers teaching style. But, I have been stuck on this second order homogeneous differential for 2 days and I finally moved on. I was woken up this morning at 5 am for some reason and then it clicked! I knew the answer! I went to my chalk board and immediately solved the problem! Long story short I needed a break. The brain is a muscle and needs rest just like every other muscle after extensive use! Thank you for your content, your advice is sound and gives me hope every time!
Thank you sir, i'm a physics major taking math courses and i find myself trying to micromanage every part of math and getting frustrated. Taking a break is a definite must, it stops you from burning out or getting as frustrated
Another thing about learning math, esp. up to the undergraduate level, is that there are two aspects to it -- 1. mechanical and symbolic fluency, and 2. conceptual and theoretical understanding. It is very common (at least, in my experience) for one aspect to outpace the other at various times. This is completely normal. So sometimes when you feel "stuck", it might be that the other aspect needs more work. For example, maybe you're not getting the theory or abstract definitions of a topic. Rather than hitting your head against a wall reading the same theory over and over, try to work some problems, and don't worry if you can't justify all the steps. Just try to complete them. Working many problems mechanically will help you understand the theory. On the other hand, maybe you feel overwhelmed and exhausted by the homework problems. You're trying to just memorize all the mechanical steps, but there are too many cases and no two problems are ever exactly the same. Rather than spending all your time memorizing steps that don't mean anything to you, try to see the bigger picture. Read the definitions and the theorems. Look for general conceptual patterns. You might begin to see that all those unrelated steps you were trying to memorize have some structure to them.
This is a skill I really need to pick up but I absolutely get so sucked in to certain problems and concepts and can’t make myself move on and I end up getting behind on other things. There has definitely been times when I have found just moving on or coming back to it has helped a lot. I’m terrible with procrastinating so that’s another thing I need to work on: to allow myself time to not understand something and let that be okay. Thank you for this video!
Thank you for this message, I have been struggling with math 099 and its hard for me doing graphing problens and when I get fraustered with someone my performance on testing can be horrible. Recently, I didn't do so well on my first test, I felt crummy and total unprepared. So when I saw your video, I feel like the weight has been lifted.
What sometimes helped me was when im stuck at a perticular question for hours, then i simply move on to another similar question. This way you might solve a different question correctly and you develop new ideas for calculating the previous question you were struggling with
I'm 33 haven't touched math since highschool. Well I decided to finally go to school for computer science and I have to take calc 1 and linear algebra. So before I start my journey I'm going to do a couple of your Udemy courses and hopefully have a decent foundation to start on 🤞
My man just said:
"Stop trying to understand math, go outside"
And I like it
touch grass and stop worrying about Hilbert spaces
Lmao, I'm about to throw hands with Linear Algebra with 1 & 2variables, Hilbert spaces better back up
Long live procastination
i've been on walk for months still cant understand lol. going for a walk again. see ya later thanks
@@WebDevAnjali You are going for the good way. In the first year of walking, you will begin to perceive how mathematical knowledge rains down on you from nowhere.
I was never particularly good at math my whole life. But I focused on what I could do and today I am PhD in engineering. You can do it guys.
Hell yeah
that's very candid of you! at good engineering schools, engineers often have more math requirements than some Math majors, and for a reason--we actually have to use it in the real world! glad that you overcame your struggles, & maybe you're just being modest, but either way great model for other aspiring engineers to look up to
That is so awesome, since you have a PhD and I love engineering, I would love to read some of your peer-reviewed papers. What is your name sir and how can we find your work?
@@consig1iere294 nice call out lol
@@consig1iere294 Hahaha, amazing. He’s not gonna reply.
The "why" was my issue with math. It drove me crazy and made me falsely believe that I was bad at math. Then something I never could have imagined happened. I was in a low level college algebra class that I needed for my bachelor of science degree, and I was _struggling_ hard. My mom had a friend who was a high school math teacher who offered to tutor me. I went to her, but without much hope. Two hours later I walked out of her home understanding algebra like I never had before. From that point on I made A's and B's in math and never needed another tutor session.
My moms friend didn't perform magic. What she did was teach me WHY by using analogies. That is how my brain processes apparently, and once I understood the larger concept (in analogous terms) behind what I was being asked to do, it all clicked. From this experience my suspicion is that people who say they are bad at math, but who are otherwise above average in intelligence, are not being taught math the way that their brain processes information. If more math professors were taught to offer simple analogies and even a few storylines to teach math concepts, we would have many more people excelling at least to the undergraduate college algebra level.
most people are bad at math because the teachers are trash.
WHAT WAS THE ANALOGY? I DONT GET IT
Please share the analogies you learned I have a D in my algebra class with a quiz coming up and I don’t understand anything🙏🏾
same problem i have like if teacher solving the question i always be like WHY ..why will we do this particular thing in this question ...and sadly i hv still stuck between this WHY everytime.
Tell us, please
I think it's fair to say that the experience of confusion is a sign that your brain is actually working and learning. I try to remind myself that the sensation of "not getting it" is a good thing; it means my mind is being challenged with something new. If your mind is comfortable it's probably not learning anything new.
What a great comment, I totally agree. Thank you for posting this:)
I loved this comment
Awwww he is giving up, in the end, what is math used for if it just numbers in your face thinking about how the real way it works but there is no meaning for math is there, we will never know until someone else gets it and we the people who look like the failure trying to decypher math since countries ago
I'm not sure if he was referring to not getting how to solve a problem, or not getting WHY you solve it that way. The latter is always my problem. I can follow instructions, we all can. But I NEED to get it!! I need to intuitively, on some level, understand why I'm using a certain approach, what it means, what it implies geometrically or analytically. You know?
I guess we're all that way? I feel like I can't possibly move forward in the course if I don't understand every concept along the way.
If it's not learning anything "new" Then it already a genius!!!!!
John von Neumann once was approached by a student after class who said "Professor, I don't understand the math you're using". Von Neumann answered: "Young man, one doesn't understand mathematics. One only gets used to it".
Haha love that
It's so true
th-cam.com/video/JiIKXGOGg64/w-d-xo.html
Good one! That implies that a significant portion of becoming good at math is to practice a lot, and not spend too much time on theory. Of course, one cannot practice if one doesn't know the theory. But, one shouldn't let theory to slow one down.
@@amirmahallati3414 Can't one practice theory?
Math has broken me down to tears in school. I’ve struggle with it my whole life. I needed to hear this. Maybe it will help me get the confidence back to get some degrees.
I'm still broke
Same
Me too
You can do it. learn what you can and keep learning. Try and realise that learning is fun. It won’t be easy but you’ll grow as a person and so will your knowledge and you might surprise yourself for how far you have come.
Things may be harder for you to understand compared to others or the other way around. But why should that stop you or anyone. What makes someone great isn’t never falling, it’s how they recover from a fall. Don’t just lie on the dirt after a fall, get up, get up and show the world and yourself what you can do. Because we can all achieve great things.
It was terrible advice. People stop trying to understand math and then we get a society with conspiracy theorists, flatearthers and people with imaginary friends. You want to understand math not because you want to do Lorentz transformations in your free time, but because you want to have critical thinking.
Neil deGrasse Tyson said in an interview about calculus: "If you don't understand something immediately, it doesn't mean you're not good at it".
This quote has given me sooo much motivation in my mathematics journey.
Too bad "immediate understanding" is what schools expect of you.
@@BeekersSqueakers Yeah exactly
No, it means u better work your ass of on it. LoL.
I have learned so much on my own after high school.
@@kun_fu_taco4775 Lol same, found a book and followed it. Learned a lot more on my own then in school.
Was always taught never to give up....this is very ...liberating
❤️
Well, especially when taking a test -- "I'll come back for this one later". Really, it once really saved my ass during a Calculus I midterm, that I didn't even know what Question Two was asking, but then the second to last problem was almost the same thing but set up differently, but in a way it EXPLAINED what I was to do for Problem Two. Heck, examples can go back years.... remember back in Algebra when you still couldn't see Dif Squares and Complete Square Identities a mile away.... just Come Back To It Later is just the thing for coming back and Seeing What You Missed Before.
This guy is so passionate! It's so inspiring
Summary:
don't spend too much time on a problem
refresh ur mind
interleave, do something different
realise it's okay to be stuck
but not stay stuck
“Young man, in mathematics you don't understand things. You just get used to them.”
― John von Neumann
@@jose-pe It's a quote.
i love how this comment is right under the one it was stolen from (for me right now). cmon man, don’t repost a comment for likes, they’re just worthless numbers
Literally the advise my prof told me today when we asked him how to come up with that approach to solve a specific integral he just showed us. Told us we will get used to integrals, though we probably would never have come up with that solution on our own as it took a long time to be discovered xD
I thought you were going to start singing the YMCA song
He meant , I cannot teach you even the basics
I'm studying mathematics at a relatively prestigious university and the workload is TOUGH man, both in terms of volume and difficulty. I just wanted to say that your videos are so wholesome and they are a big source of motivation for me to keep going, keep studying, keep being curious.
👍
@@TheMathSorcerer facts
@@TheMathSorcerer thanks i have the same problem in coding
Ironically it’s those prestigious universities that tend to kill people’s passion for math, be careful to not get sucked into the hype my friend.
@@RENCIOL What makes you say that?
I am studying mathematics with an interest in physics. However, the math is presently beyond my understanding. I have been hitting a road block with derivatives of trigonometric functions and identities. But inconsistent study habits and back tracking to review math concepts slowed me down. Your advice to just move on is valuable. After looking at more advanced material, I can see the relevance of what I was trying to learn and it started to make sense. Persistence is the key. You have not failed until you stop trying. By the way, I am 73 years of age with over 40 years in the computer field.
could you elaborate on your time in the tech field, if you don't mind?
I've never been good at math in high school and I never got the help I needed at the time. 6 years later I'm really fighting to accept that I am just 'bad' at math. And I am looking to get a degree in my current field of software development because a diploma is not enough for me. And getting a degree is another thing that I really feel I need to achieve. I started with math again as its part of the admission requirements for any comp sci field, I really hope I can do this 🥺
@@Haniefatries_ focus on linear algebra (matrices and vectors) thats what compsci needs most.
and if you are doing 3d graphics linear algebra is pretty much compulsory.
@@Haniefatries_ congratulations and keep pushing .
@Chris M lol most likely
I remember I used to spend hours (3 or 4 sometimes even more) trying to prove some induction problems, every day I tried so hard but I wasn't able to solve them, I didn't want to give up but eventually I did, and I started to wonder what is wrong and so on, I realized my algebra background wasn't good so I spend winter holidays to get better at algebra something like 1 o 2 months, when I got back at those problems everything was so clear now, I was able to solve them in less than 30 minutes.
The lesson was, learn to when give up, you cannot fight all your battles.
Yeah, I've learned not to fight the idea that I need to do some review. If I'm blocked for more than a few seconds, I get up and get the old book and flip to the section and go through the examples. the more you review, the less you need to review.
That makes more sense when i see guts in your profile
Ya that happened to me with the induction inequality proofs. I didn’t really get those until like a year after seeing them.
Something a Guts profile picture would say.
i thought it's just me that have a really2 long time to prove induction problems,and it's not bcs im dull,like i can understand concepts quickly than my friends,but yes maybe i need to move on
this brought me to tears. after an incredibly frustrating relationship with math this is what i needed to hear. i was going to drop my class and change my major because i'm feeling so beat down and stupid trying to learn calc. thank you.
Your teacher is everything for calculus imo
Khan academy works better than college lectures for me. Hope it helps you too.
I felt the same but it was because the class was tanking my grades. Not because I physically couldn't understand it but because I did not see the point in memorizing Taylor series
@Dr Rock ? Why did you say that? Nothing in that person's comment implied they didn't take algebra, geometry and trig.
I am abysmal at maths! I am a brilliant speller, and an excellent writer. I aspire to be a novelist. I score highly on everything else.
Find out what works best for you.
I believe the key to learn math (specially abstract topics) is to accept that you ain't gonna understand anything but, you'll get used to it. The more you practice, the more you get used to a concept and thus you will develop "your own" understanding/intuition of a topic.
That's what I did for analytical geometriy 😂
Practice develops the muscle memory to do Math problems
My struggle is that I can't practice without understanding it though unless it's very basic just fill in the formula type of math. If I go to a lecture, work through the material (which is practically impossible if you don't understand it) and start with the assignment... well, what then? Unless it is a math problem that we have done already the exact same way in the lecture, I just blank. I can google for hours but still nothing. "Just practice" worked super well for me in school, I ended up as the best student in math with a straight A on my final exam but advanced math/comp science at the university just destroys me at the moment. Sorry for the vent, just casually breaking down here.
So true. I know for me there were times, particularly in my various physics classes, where I got caught up in trying to understand the why, finally just learned the math with understanding why the math worked. And then found that as I trusted the math I just got used to the physics concept to where it made sense.
@@GeoRedtickI am sucker for trying to understand it too much and not accepting it as true. Do you feel that you find those concepts that you let yourself practice actually make sense now? Could you answer those questions that you had prior?
"Just take a walk. Go for a long walk."
Me: **has two Calculus assignments due in a few hours** Well, that's not happening...
XD
Opens door to go outside only to see someone getting gunned down
Wow, all of a sudden I feel the urge to study
@@diags_1109 wtf bro
walking is honestly the only thing that works for me. walk while unpacking your thoughts
I feel sorry for you dude 😂
I legitimately hate it when a professor states that a problem is “easy” or “straightforward” and I’m on the other side struggling to figure out what’s going on. I think it would help a lot of math teachers/professors to get through to their students if they put things into perspective from the majority that truly struggle with understanding the concepts. That’s why I appreciate your videos, Math Sorcerer. You’re constantly letting the audience know that math is hard and it takes a lot of time and practice. It reminds people like myself that it is okay to struggle on this topic and just as long as you keep at it, you will improve, and that is ultimately what it is all about. Are you better today than you were yesterday? When I assess my math skills today relative to a year ago, I could honestly say yes. It’s important not to lose site of that measurement when times get tough and you’re struggling trying to learn a new mathematical concept.
th-cam.com/video/JiIKXGOGg64/w-d-xo.html
I think most professors lack that ability to motivate through just empathising with struggles of students. Most professors aren't like this channel.
Empathy is the single most important skill a math teacher must possess. the absolute worst teachers of math are the people who were naturally gifted at it. They cannot understand, appreciate, or empathize with the struggles of others. They should not be the ones teaching math at all. In my opinion, mathematicians should be barred from teaching math below the level of Differential Equations. Engineers and others should be hired as math teachers instead, people with practical understanding of its applications, who have struggled themselves, and who possess empathy.
The curse of knowledge supresses their empathy
@@thewryneckarchivist no, that's not it. They lack empathy to begin with. Empathy tends to grow with knowledge, not diminish.
Those who become mathematicians, tend to be those who never struggled with math growing up. They never struggled as their students do/will. They can't understand why students don't understand things, because they never struggled with it. To them concepts came easily, and too often they only know one right way to solve problems, their way. The Way that came so easy to them, even if that way is a more complicated way to solve things.
Teachers who also learned math through struggle make better teachers. They can see how a student is stumbling, recognize the struggle with a given concept, as they once experienced it as well. They can explain the problem in different ways, to help the student understand.
the problem is that in the classroom, especially during that traumatic time known as high-school years, math and other sciences are taught like something more similar to military training with live ammunition. there is no room for mistakes under fire, and especially when failiure in math and science is often viewed as a sign of failiure in life, there is a huge difference between this relaxed attitude and the pressure put on students in real time. to some extent, you can say the same about any field of study in the classroom, that there is no time for any deep engagement with the subject, if the top priority is getting good grades and pleasing others with them. from parents and teachers to future employers.
nicely wrapped up...I am sure that by this messed up concept there is damn much potential lost.
this is largely a symptom of grade inflation. That itself is largely because companies are way too selective of their employees for things that do not require such selectivity.
I'm in my senior year of high school now, and have always been a straight A student. The kind that studies the night before and still gets A grade. And due to this,usually maths is the subject that I have lowest marks compared to others.But it was always above average/good marks. This exam,I put in some effort and studied math. Even the exam itself was kinda easy for me. And somehow.. I failed. For the first time in my life I got a taste of failure in my life. All my classmates were shocked when the professor announced my grade. That I failed. I've checked the paper several times and I can't figure out where and why I went wrong. I'm stumped rn.. I have my finals in 2 months. What should I do?? I'm m worried. I'm worried of facing my parents rn.
I needed this. I just failed calculus2. I’m a single mom, have to get through these math classes to get a good career t support my munchkin and I. I am so bad about planting myself and forcing myself into attempting to understand before moving on. And then I have spent hours on one problem out of 50. I definitely need to spend more time doing problems and less trying to understand. That is such a hard mind shift for me. I’m going to do it! Lol!
You can do it😀
Hello, much love to you and your child, I'm happy for you, you're doing great, I wish you the best on your journey, joyful learning and living fully.
Have a splendid time ahead🌻❤️🍀
@@expectopatronum6241 hi expecto, nice name
@@mamabear3610 thanks!
Beeing a single mum must put a lot of pressure on top of studying.
Doing a lot of problems and choosing the right problem so you are still challenged but don't get stuck is hard. Personally i like to learn in groups. Solving and explaining your solution gives you a deeper understanding for principles, so you are less likely to get stuck.
😅 also a good portion of exams is just to get things up to speed because you don't have the time to think twice, something only practice can do.
1. Manage your Time
2. Pivot(Go for a walk just try to focus on any thing else)
3. step back and do something else
4.Its okay to Get stuck (My insight: It's okay to get stuck but its not okay to remain stuck)
5.(My advice: generally clear your concept the problems generally their solutions are simple but not easy they take sheer amount of how much did your understood your concept then that is applied inside of an question)
Stoic X, I'm honestly not trying to be a jerk, believe me. But in your #5, I got the sense that you were saying something very useful for all of us. But for the life of me, I couldn't comprehend it. Could punctuation clear it up? I'm not sure. But could you give it a second crack? I'm all ears! (Btw, #1 - #4 were quite useful...thank you).
@stoicx. Thanks for the summary 😃. I would be also very grateful if you could rephrase the fifth point. It seems there is a good idea behind an accidentally misformulated sentence.
❤
@@dodgecrockett3474I think they meant, understand how a concept is used in a question(?) Idk for sure though 🥲
🧡 Super helpful advice! Thank you. I'm a math major and these are things that I wish I had done. Right on!
I just want to add: The more you immerse yourself in math, the more you get it. The more you get it, the more you love it. The more you love it, the more you want to learn. This is such an amazing cycle!!! 🧡
This reminds me the famous Feynman quote:
“You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!”
I found myself practicing that for whatever I study and for many study subjects in parallel. Never give up any - but take a break and continue with another one from which you effectively just took a break. Often understanding more about another problem gives you inspiration or even a hint for another one in the back of your mind. This way you are always busy with what is important to you and you are never even tempted to give up any of them. It’s very productive, efficient and satisfying 🤓
This is great advice. I used to feel bad that I wanted to learn so many different things, thinking I *had to* choose one and stick to it. It helps to realize that they are all related in some way and even if they're not immediately applicable to one another there is still a connection. Also whenever I go back to a subject I always come in with more information than before, and because I can't help but want to learn more about it, I keep coming back to it.
@@whyyes6554 Yes, indeed. Maybe getting stuck is at times just a hint not to study further in depth but “horizontally”.
"favorite problems"? You guys have FAVORITE PROBLEMS?????
I agree. Just give it time. Knowledge acquisition is not a discrete event, it's not a step function. You rarely go from "not knowing" to "knowing" just like that. Just give it time for hard mathematical concepts or ideas to grow inside your brain.
unless you have a truly good math teacher who explains it properly and simply, but they are rare.
I was identified as a gifted child early on, and the bad side of that is that everything comes easily for quite awhile. This advice is particularly good for people like me, because we all reach a point where things no longer come naturally. For me it was AP Calculus my senior year of high school (which I failed for this very reason even though I got an A in every single math class before it). When you are trained as a child that things shouldn't be frustrating or hard to understand, it can be extremely difficult to unlearn that pattern of behavior. As good as this advice is, I anticipate that I will still have a very hard time putting it into practice. My life is not so good now and I attribute a lot of this to never developing any sort of frustration tolerance as a child.
Also, I'm going back to college for a computer science degree at the young age of 36, so I made sure to subscribe to your channel. Something tells me that your advice and teachings will prove invaluable as I tackle math that is very difficult. :)
Yeah, apparently your parents didn't challenge you enough as a kid and wanted the easiest route so you keep quiet and they don't deal with your screaming or crying for not getting the shiny thing you are after and they have more free time to themselves instead of raising a kid right. That's why you can quit without consequences. Most people HAVE TO get it right. Their lives depend on getting it right. There's no mom and dad to enable them or sugarcoat things for them. The conclusion is: Privilege makes people lazy and unaccomplished.
@@DiamondsRexpensive wouldnt draw this conclusion
@@DiamondsRexpensive well that's true for me
@@Arthur90 if you actually have a better conclusion, present it so I can change my mind.
I’m studying math on my own right now and I realize that for my entire academic life I have been placed in a box and not allowed to see the true beauty of math because of standardization.
How
@@nigelcardoso7653 Standardized education in math is studying for tests to get the grade, and if you get a passing grade it’s good, but you really don’t get to know math this way.
@TechWhat do you mean give an example? I just gave you an example.
@Tech Maybe you should pick up a dictionary and become well aquatinted with the definition of two words ‘example’ and ‘obtuse’. I’m sorry you’re having such a hard time with this.
@Tech obviously this is the hill you want to die on, which is sad, but I’ll give you the much needed ego boost that you’re seeking since it’s in short supply for so many nowadays. Being placed in a box means that in a math course there are boundaries set on how in-depth a student can go in their study of math. Those boundaries are time constraints as a result of students having to meet very specific metrics. Once those boundaries are lifted and math students are able to really take the time to explore mathematics in-depth. I hope this helps.
As an engineering student, this is great advice. Not only can I apply it to my maths class, but basically my whole schedule.
AJ Brewer, why is everybody saying maths lately? You're like the 6th person this week to make the same typo.
@@dodgecrockett3474In my experience it is more common to use the term "maths" rather than "math" in the UK. That could be why.
@@mimpton8861, what do you mean by UK ?
@@dodgecrockett3474 The United Kingdom.
@@ngsandwichr6722, I just looked that up. Apparently it's just a pseudonym for England.
Issac Newton? Is that you?!?!?!?!
😂😂❤
This is what I did to get a 95 percentile on the GMAT and a 99 percentile on the Indian version of the gmat, called the CAT. Go through a chapter 3 times on 3 different occasions during the week. On every attempt you’ll see yourself noticing previously overlooked concepts. Used to do this during my school days. That’s how my basics became crystal clear. But I know lotsa students doing the same before their entrance tests. Secondly, trust yourself, some folks are naturally gifted and pick up stuff on their first attempt while you may do the same on your third. Doesn’t really matter, because at whatever level of school you’re in, the quantity of chapter’s to study will always be finite. And once you’ve gone through the entire syllabus, no one will be able to tell the difference. Best of luck for you’re exams. Cheers 🍻
Thanks dude I needed this
That's so true. :,,,,,,)
That’s actually really good advice
My BS in math prepared me for the GMAT. I did not study for it. It is what I would expect anyone with a math degree should know.
That's not even maths. It's just a set of mindless simple calculations in a short time... Perhaps your achievement is important for you, but it is irrelevant for the current discussion where we are talking about "understanding maths" not "being better than 99% students to get a lucrative job".
Thanks! I always doubt my own intelligence whenever I don't get something and I'm too embarrassed to ask questions. I wish more math professors and teachers had your mindset
-"you email your teacher. you dont get a response." Most accurate quote LOL.
I can 100% vouch for walking. I've come back to programming and math after a long long while (a decade) and as usually happens you find yourself banging your head against a wall, trying to wrestle solutions out that just won't come. For whatever reason, going for a walk for an hour or so, even with some music on (without vocals) just helps the mind to flow and organise itself. I refer to walking as 'defragging for the mind'. It doesn't just help with math but any kind of problem you have, personal, logistical. I come home from a walk peaceful, optimistic and usually with an action plan for solving my problem.
doesnt help when you have an assignment 2 days over due and are failing!!!
@@cat-ph3nr That's why you gotta study a decade ahead and do math at night instead of weedahol.
I agree with you on that. Let me add another piece to it. A source from HackTheBox said that you should take a break when you feel frustrated that you don't understand a topic or can't solve a problem, because doing so let's your subconscious mind try to solve the problem instead of you actively focusing on it.
From my experience this worked plenty of times.
Dr. Andrew Huberman (neuroscientist who focuses on neuroplasticity, search him) talked about this: during intense focus your brain marks synapses for change and the change only occurs when those synapses are not in use, basicly to learn you need to have intense focus on the thing you're learning and then the least amount of focus on that thing (sleep, taking a break and doing something else, etc.).
I like the fact that you say: Go for a walk if it's safe to do so. We sometimes take security for granted.
“It’s okay to not understand.” That’s really good advice on all things. Thank you ❤
I can tell you’re a good teacher. Something the world needs more of in universities.
I agree, it is ok to allow yourself to not understand something for this moment in time. I realized, I often understood some concept or something in math when I was not feverishly chasing it. I give up today but only to fight another day. Writing questions down in a book helps too. It allows you to move on and work on other important stuff too without being overly obsessed/concerned with the stuff you dont understand YET. Also as we learn and grow it allows us to attack the problem from different intellectual/mathematical directions. So instead of telling myself: you are too stupid to understand this, I say and believe I am not just ready yet, I will continue working and growing and at some point I will be ready :)
Thanks for the video upload
Thank you for really pushing the point that it's ok to not understand or not get it. I think there is this misconception that if you're good at math, it comes easy to you and if it doesn't you shouldn't be doing it. Thank you so much for that.
"Self study is so wonderful because you can pick any book, no one's forcing you"
In the time of pandemic, "Self study" meant totally different for us students or possibly just me. Here in my country where modular distance learning is a custom for education during this time, made self study really really hard.. not only did it change the definition of self study from studying what you want on your own to studying what is needed for school on your own.. and it really hit me hard specially on math, physics and biology
Are you studying biophysics in uni or smthn along the lines of that
facts bro especially here in my country,Philippines,I can't even understand the lessons and second i don't have time for studying
@@sherwin5773 bruh we live in the same country 🤣🤣 and ye its hard... Life is hard
@@ReiiRussWentMissing haha life is hard men, bruh my previous comment got deleted so this was my short response haha, I hope we will understand the meaning of life one day =)
"It's okay to be stuck"
I'm paying this tuition myself, I literally cannot afford to be stuck on this material.
I feel you man, same.
Especially then you'd want to spend your time most efficiently.
But boring over a problem for too long isn't the most efficient way to solve it, according to this video.
I think the point here is that banging your head against the desk isn't going to work. When I don't understand something, I try to identify gaps in knowledge and fill those gaps, even if it's something basic or fundamental.
Studying all the time is not going make you learn more. Just be present in the learning environment.
when i get stuck solving anything, math engineering solution, etc, I just stop, get up, walk away. Even at work as an ME, I just stop and take a break. go for a walk, talk to someone else, go run an errand in town. Clear my head, try to prepare to come at it with a fresh perspective. Collaboration with others improves problem solving too. Some of the best solutions were achieved by working with 1 or 2 other people to solve it.
This is what I needed. I always thought about it. The more I stop caring, the more I do better at applying math. It occurred to me after I started taking treatment for my ADHD, where I would focus WAY too much on trying to understand. Thanks for this, I feel very confident moving forward to my Uni Grad and future personal studies.
Wait so what else would happen? I have adhd too
This is great advice. I tend to want to understand everything from first principles. When I was in college, I would get stuck thinking about what the prof just said when I should have just accepted it and moved on. That caused me to not catch what followed and then it just snowballs. I think it's best to just accept what is presented at the moment, don't panic, then move on. That's one piece of advice I wish I could go back and tell my younger self. A good example is the use of imaginary numbers to represent AC circuits. I racked my brain trying to understand how imaginary numbers related to anything "real" or "physical". It just blew my mind. Many years later I learned that it was just a mathematical convenience that made phase rotation easier through multiplication. That's it, nothing magic, just a "tool" that makes the math easier. And you always end up with "real" quantities because the "i" (or "j" as it's used in EE to distinguish from "i" which is already used to represent current) ultimately disappear from the result. So what used to puzzle me, now seems "beautifully clever". :)
Beautifully put
Going for a walk or doing some kind of exercise in general always helps. Your brain keeps working on the problem even if you're not actively thinking about it, and when I return to my work 2-3 hours later I almost always see the path to the solution or the solution itself.
Yeah I did that yesterday and it really helped!
Dr. Jones found that if he just sat down a solution would present itself. There is a truth to resting the mind and productive outcomes.
@@WestExplainsBest Who is Dr. Jones ?
@@sligon00 Indiana Jones' dad - I quoted him from "Last Crusade"
LOL...Aw thanks man, thought you were quoting some famous mathematician, not an anthropologilst... ;-)
I remember crying every night before my math exams as a kid. It intimidated me so much. It still does to this day. But here I am, willing to try again because it is one of the main subjects in an exam that'll get me into my dream career. Thank you for this video ❤
The way he describes this makes me realize that programming and maths are not so different. The way the connections grow exponentially with the size of the problem. And the way this forces you to decide how to use your time.
The relationship with math can turn dark and abusive. Take a walk? Easier said than done with math snickering behind your back.
Thank God for Piss Breaks ... almost anything that can pull you out of the chair and out of the rut sometimes works.
@@leovolont Yes and actually anything that takes you through a door will help a bit. When people pass through a doorway there's a context refresh that happens as you no longer need information about the room you were in and suddenly need information about the room that you're entering. It's why when people go to the kitchen they often forget what they were going there for.
The upshot is that if you're stuck doing the wrong things on a problem, sometimes you can just leave the room for a couple minutes and you get unstuck. It's a bit like rebooting a computer that's acting up.
@Artificial Hobos Yes, so can lowering the temperature in the room a few degrees or looking at something green. All 3 of these things often times happen when you go outside. (Obviously assuming it's not blazing hot middle of summer)
@@SmallSpoonBrigade Hi Chris. HOLY SHIT! That makes all the Sense In The World. the idea ISN'T to take a break, no, when stuck, YOU HAVE TO WALK OUT OF THE ROOM. Heck, I see that with my Cats... if a Cat is pissed off about something, well, I learned to just pick them up and walk them about 20 feet away and put them down someplace "fresh". Works every time. Who would have thought it works for Humans and Monkeys too. THANKS Chris!
Do a walking meditation
This is the exact thing I’ve needed to hear my whole life. Have devoted 2024 to learning to LOVE math, it is a beautiful subject of study and I have always felt drawn and inspired by mathematics and those who are passionate about it. The concept of learning math in a non linear direction has been monumental for my belief in my own capabilities. I’m working now on filling the cracks and resettling my foundation and will build from there. I heard recently “brick walls are only there to prove to yourself that you want it bad enough”.
I really needed to hear this. It’s something I’m currently struggling with in my classes. Thank you so much for making this.
The professor is speaking a universal truism. Trust him. Move on. If it is important then keep coming back, try new perspectives. Discuss the topic with others. Always share your difficulties. Don't be so foolish as to believe you can solve everything by yourself. Find out what works for you.
Then again, I am not a mathematician, just an old retired ChemE that still enjoys the beauty of math and science. Especially, when applying maths in the real world.
👍👍
Hey. I’m a senior at college and I’ve been having a hard time with mathematics. I’m so glad that I stumbled upon this video.
For the past year, I’ve been telling myself that if I don’t understand something, that’s my temperament. But it’s not.
I will always use this video to remind me that it’s ok. This will really help me.
Thank you Sir. I'm learning computer science and it is so frustrating sometimes when I don't understand the theories. Most of the times I feel like everyone is ahead of me and I'm standing alone going nowhere but this video gave me a big advice, a mental relief and a breath of fresh air ❤️🍃
This is a very good point that I still struggle with. I kinda thought of an analogy that might go with this:
It's like trying to defeat a boss in a video game, instead of going on side quests and increasing your arsenal, it might very well be possible that giving up and moving on to other things will give you the inventory you need to defeat that boss. It also might not, but I'm just being optimistic.
I like this analogy
this is a cool way to think!
This advice is pure gold. I'm a late bloomer, I'm the guy that couldn't add simple fractions or do long division in school, but always had an amateur passion for physics and science. I believed the lie that some people just "didn't have it", or that I just wasn't a "maths person". Years later, after knowing that I could never enter those fields properly without tackling the math issue, I spent hours each afternoon and evening after work, starting from the bottom up, teaching myself from books and online Udemy courses, prealgebra, algebra, trig etc. With a lot of hard work, I'm now a mature age student in the middle of university calculus and loving every minute of this beautiful subject, despite its challenges and stresses.
Thank you for your channel and everything you do, your videos have been incredibly reassuring and inspiring to me.
inspiring
Solid advice on not only just math but life in general
You're really a math sorcerer, thanks for making me realize it's okay, once I was depressed that I couldn't understand maths but now I know it's okay and that I shouldn't be stuck in one place
Giving up strategically to get the most out of your time is priceless advice.
A great message. I remember being in grade school and having a tougher time with my multiplication tables than other kids. We'd play a flash card game, and I never won. I thought I'd never learn them. Then later, after the pressure was off a bit, all of a sudden, seemingly, I just knew my times tables. They just appeared in my head and made sense. Better a little bit late than never.
This message, by the way, applies to everything. Take a break, do something else. If you're writing poetry or working on a piece of music, step away from it, distract yourself. There's a good reason why so many eureka moments happen on the toilet or in the shower. :)
Wise words.
Im an electronic engineering student and i often get stuck solving some problems.
This was really helpful :)
Thank you so much for this, letting go off the things you don't get right away is okay. I came back 10 years to math and was the best decision ever. The funny is that now I understand topics much better than I did a decade ago.
Best advice ever. Me also as engineer student tried to understand every single point of the matter, losing a lot of time . It's way better to just accept some assertions without challenge them. The deep understanding will often come with years.
"I spent a week on a problem to find out there was a typo..." I bet we've all had that happen to us at least once and man oh man is it frustrating.
Yeah definitely!
Beautiful advice! Still remember my uni days solving a Maths problem for days and not moving ahead, telling myself the story that I won't leave any weak material in my foundation. At the end of the day, it was pure intellectual ego, which harmed me more than it benefited me. There were times when I was able to come up with some unique solutions, but there were other times when my obsession for "solving" everything, led me to even depression where I thought I wasn't good enough because I couldn't solve a problem! It would take just one unsolved problem for weeks to make me forget all the other times when I came up with something good. I would suddenly sink into the blackhole of believing that I was stupid. Once I lost a complete year chasing the dream of being a perfect Mathematician!
Beautiful advice from you here. The most important words in one's life if you are suffering because you can't get something- LET GO!
I think walking is a wonderful way of practising letting go of things. Meditation is another beautiful thing. May all be free from suffering.
If you are stuck in a math problem:
1. Go for a walk;
2. Work on something completely different;
3. Remember that it's fine to be stuck.
Thanks!
thank you!
The fact that math textbooks are multiple editions old and still have the same typos, shows how much the publishers care about students.
I'm self-studying math and your videos really serve as a motivational source to me.
Awesome !
Same here, but with a tutor.
This guy speaks the truth - his words resonate so much, they always make me laugh. I'm the sort of person that wastes hours trying to understand something and can't move on until I get it - it's genuinely tiring.
"you're just not gonna get it" well... **throws paper and exits exam room
Lol
The path is made by walking. Understanding comes over time, with experience; it requires a process of delayed gratification.
well said:)
I am just a high schooler who came across this video of yours...I scored 45/80 in my pre finals and my score has never been so low...my finals are on 21 march....I aim for 80/80. You motivated me lott. thnk you so so much..! ill update my results after they are out🤞
edit: i scored 75 / 80..i kinda feel proud of myself but i expected more
you got this bud!
@@ahmetsalihsavas7745 thank you soo much!!
The fact im reading this on exactly 21st March is insane. How's it going bro?
@@anhminh9526 IT WAS SOOO GOOD. i seriously did not expect myself to do this great on this one...im kinda proud of myself
@@dilkiratkaur 👏👏👏 nice!
Take every math problem as a challenge... And develop an attitude of not giving up... Let it take time.... Frequently go through basics... Try to understand and relate concepts asked in a problem... Make friends with same attitude and who are open to discuss on the ideas to solve the sum....
"Let go and move on" is also good advice when it comes to relationships!
This is like a God sent video. Because I am trying to understand complex analysis but not getting anywhere.... Thanks man
You are absolutely correct!I am a grade 9 student, but your channel is a source through which I found very good recommend books, which helped me guiding/understanding mathematics, the whole credit goes to you!
This video should be clipped at 1 minute, concluding with: "(When you don't get something in math) you have to be able to prioritize your time and give up strategically." (The whole clip is a great watch, but that first 60 seconds is brilliant.)
this advice could change my life but there is always people around me forcing me to learn things that it has nothing to do with the things i m good at
I love the dedication of this man. Been following him for a year now and have learnt alot. Big up sir
❤️
Good advice! Also, my suggestion is that if there's a gap in your proof that you just can't fill, just write "I think it follows that " and leave out the justification. After all, it's much better to get 4/5 because your proof had a gap, than to get 0/5 because you just gave up.
I can attest to the effectiveness of this advice. I'm a software and electronic engineer, and when I'm stuck on a problem, breaking away and taking a walk, soaking in a bath*, or just switching to something else, has on hundreds (maybe thousands?) of occasions brought the solution to me. In fact it is just about guaranteed to open up, if not _the_ solution, an approach to get to the solution. This has worked over 90% of the time. I posit that during those times the brain is able to rest and allow the creative side to flow freely, unconsciously.
It took a long time for me to get this, as I used to naturally be very choleric and tenacious and would want to just pummel my way through it. By accident I started observing that breaking away from it was much more productive.
*I now call this "going to the think tank".
The advice I give to others working on coding problems is, “if you ever ask yourself whether you should keep working on this problem or go to bed, the correct is always to go to bed. The number of times I have solved a problem in a few minutes the next morning after hours of fruitless work the night before ….
1:20 - I also struggle with this. I can't just move on to the next problem, I feel like I have to get it all right.
This is exactly how I feel, I’m currently struggling massively with the Binomial Theorem (I’m at advanced higher in Scotland which is the highest level before university) and this is just what I needed to hear.
Thanks professor. I'm a 2nd year undergrad and I'm slowly realising that this is one of the most important things to do with math. Great advice!
I try to imagine it not understand it. As an engineer i see a decade after my degrees that there are things i thought I understood. Things i definitely understood. Things i understood better than others with others thinking im dumb for not understanding something trivial which they didnt get in the first place. Shift focus is true. I get glimpses or strokes of clarity when i go to sleep or shower on things i did 10 years ago knowing that i never understood just did.
This remember me when the internet spent months trying to solve the last question of the mensa norway test, reddit and you tubers coming up with all kinds of crazy theories about how to solve the puzzle. Eventually someone emailed Mensa and got in contact with the creator of the puzzle and ... ups... the instructions were actually typed wrongly, it wasnt possible to be solved, so the question was removed and all internet theories from the geniuses were all just completely wrong. All time spent for nothing.
Yes, I agree. In studying electronics, I’ve come across some things that I just can’t grasp, and it is easy to get discouraged and think that maybe I’m not made for this endeavor. But then I remember that there are SO many things to learn in electronics, there’s no point in banging my head over just one thing, when I could branch in a different direction and then circle back around some other time.
I really needed this. I’ve been teaching myself algebra (trying to catch up where public school failed me) and I’ve been really stuck on the “why” on certain things. I’m an analytical person, I love figuring out the reasons behind what’s done, but as long as I can get the how I can let that go. Thank you💕
How is it now
"Sometimes you are just not gonna get it". I can't live with that, sir. It'll keep me awake at night.
Thank you so much. I am currently taking an asynchronous course in Multivariable Calculus and I find myself spending hours on just one problem or topic. Last week I was stuck on a few problems from my textbook and couldn't see why my answers were wrong. I spent so much time on these problems, only to find out later that the answers in the textbook had typos :(. I will try to apply what you talked about to avoid this happening again in the future.
Can't control curiosity about specific math problems😅
Thank you! I needed to hear this. I have been self studying differential equations for the last month. I’m preparing for that class this upcoming semester. I’ve heard some… questionable things about the teachers teaching style. But, I have been stuck on this second order homogeneous differential for 2 days and I finally moved on. I was woken up this morning at 5 am for some reason and then it clicked! I knew the answer! I went to my chalk board and immediately solved the problem! Long story short I needed a break. The brain is a muscle and needs rest just like every other muscle after extensive use! Thank you for your content, your advice is sound and gives me hope every time!
Thank you sir, i'm a physics major taking math courses and i find myself trying to micromanage every part of math and getting frustrated. Taking a break is a definite must, it stops you from burning out or getting as frustrated
Another thing about learning math, esp. up to the undergraduate level, is that there are two aspects to it -- 1. mechanical and symbolic fluency, and 2. conceptual and theoretical understanding. It is very common (at least, in my experience) for one aspect to outpace the other at various times. This is completely normal. So sometimes when you feel "stuck", it might be that the other aspect needs more work. For example, maybe you're not getting the theory or abstract definitions of a topic. Rather than hitting your head against a wall reading the same theory over and over, try to work some problems, and don't worry if you can't justify all the steps. Just try to complete them. Working many problems mechanically will help you understand the theory. On the other hand, maybe you feel overwhelmed and exhausted by the homework problems. You're trying to just memorize all the mechanical steps, but there are too many cases and no two problems are ever exactly the same. Rather than spending all your time memorizing steps that don't mean anything to you, try to see the bigger picture. Read the definitions and the theorems. Look for general conceptual patterns. You might begin to see that all those unrelated steps you were trying to memorize have some structure to them.
Wow is this applicable to other disciplines 😍🧐
Well said
I got stuck on a problem in math while trying to sleep and went for a walk and it helped a lot, simple and really affective, thanks
This is a skill I really need to pick up but I absolutely get so sucked in to certain problems and concepts and can’t make myself move on and I end up getting behind on other things. There has definitely been times when I have found just moving on or coming back to it has helped a lot. I’m terrible with procrastinating so that’s another thing I need to work on: to allow myself time to not understand something and let that be okay. Thank you for this video!
Euclid famously quipped: "Sire, there is no royal road to geometry."
You can never learn anything when your mind is filled with thoughts.
"You need to work hard to do math"
My lazy ass: well fuck...
Thank you for this message, I have been struggling with math 099 and its hard for me doing graphing problens and when I get fraustered with someone my performance on testing can be horrible. Recently, I didn't do so well on my first test, I felt crummy and total unprepared. So when I saw your video, I feel like the weight has been lifted.
What sometimes helped me was when im stuck at a perticular question for hours, then i simply move on to another similar question. This way you might solve a different question correctly and you develop new ideas for calculating the previous question you were struggling with
People keep teaching formulas but not break down how they work.
I'm 33 haven't touched math since highschool. Well I decided to finally go to school for computer science and I have to take calc 1 and linear algebra. So before I start my journey I'm going to do a couple of your Udemy courses and hopefully have a decent foundation to start on 🤞
Good luck. Let me know if you find any decent course. I