You Don't Get Better at Mathematics
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- เผยแพร่เมื่อ 1 ต.ค. 2024
- In this video we discuss mathematics and learning. What do you think? Do you have any advice for people? If so, please leave a comment below.
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The actual quote is : "Young man, in mathematics you don't understand things. You just get used to them."
Easy for genius to say that
"Genius, is no guarantee of wisdom"
His point still stands.
@@GIGADEV690 Maybe geniuses don't exist... only people who get used to things.
@@rwharrington87ok get used to things then :)
I'm in my early 30s and I recently started to self study math. I thought I could just jump back into Calculus since I did well in Calculus I in college, but I realized I had forgotten a lot of basic algebra. I ended up grabbing some algebra books from my local library and it has been pretty fun and rewarding studying on my own and gaining understanding not because I have a test to take, but just because I want to understand it.
It's incredible how many resources there on the internet now. There hasn't been a better time in the history of humanity to independently study math. I find so much joy and inspiration in your videos, so thank you for that!
I tried a similar jumping back in, and man, found a similar result: algebra needed a revisiting.
So true! Its truly amazing :)
Did you study Calc II/III or DiffEQ in college as well?
I had an easy time in Calc I while in college. I struggled in second semester because I wasn’t as strong in algebra as I thought
@@devon9374 solving integrals with different techniques in calc II was hard during tests. However, practicing LOTS of solving integrals = easier time during tests.
Von Neumann could say that.
Tackling Calculus before 10. He was a polyglot.
I once read about the phenomena called the plastic brain.
Supposedly, jugglers/acrobats, waitress, assembly line workers, mechanics, taxi drivers, accountants, translators, etc. were tested for specific tasks while their brains were being monitored. In every case, the portion of the brain associated with their job description showed higher than normal activity compared to those, that didn't do those specific tasks regularly.
The belief, according to the study, was that our bodies (brains included) react to stress or effort. Like growing calluses on our hands, or muscle growth and strength from bodybuilding. The brains grow glial cells and networks in response to repeated tasks to accommodate efficiency and survivability.
So the more you consistently practice math, it's possible, the more proficient you become. Added to the tool bag of math tricks and skills you aquire
Love this comment
See, for example, James R.Flynn, "What is Intelligence?" for a discussion of this. It's not a belief, specific parts of the brain associated with specific tasks have been measured and shown increased volume due to high use. New York City taxi drivers with enlarged hippocampus, are an example.
@@robbieburns1664 Wonder what effect GPS has had on the enlarged hippocampus of New York City taxi drivers? And taking it further...what effect will accessiblity to such vast information and solutions from sources such as ChatGPT have on the average person's ability to "learn" and "create"?
@@idontknow-ms8mcabsolutely. You can feel this difference in college and its very noticable
Waiting for the future think tank of Von Neumann clones to save us from ourselves.
Mathematics is no different than natural language in this regard. You just don't become "fluent" in a language overnight. It's always a bit fuzzy as you are learning and speaking and you just "get use to it" and it "clicks" over time.
Agreed but you can make new math with more knowledge
@@marfmarfalot5193Just as you make more language for new, groundbreaking concepts.
@@locrianphantom3547 eeeeeh not really
I think with real analysis, one of the 'hardest' parts for me was trying to realise how on Earth they came up with such proofs. I could follow along with the proofs, but I could not fathom how on Earth *I* could come up with such a proof. Once I saw the solution it made sense, but I struggled to think how I could ever be the type of person who comes up with that solution. Eventually you see dozens of such proofs, and you forget the particulars of each solution because you begin to see the underlying pattern in how proof works. As you go back over theorems and try come up with a proof yourself because you've forgotten it, you get better and better at just improvising a valid proof. It's unbelievably satisfying to write a proof, check back on your notes, and see that your proof is valid but not exactly the same as what you were taught - this demonstrates that you've actually *gotten used to it*.
As a side note, if you're doing real analysis, invest as much time as possible into just understanding the epsilon-delta definition of limits; I spent an hour or two reading and re-reading those two lines, applying it to basic limits, and I think that really helped significantly with being able to follow later lectures.
I’m logging on for my second day in my Cal 2 summer course in fifteen minutes. Your videos always soothe my math anxiety. Thank you!
Good luck! With enough exercise you will pass :)
Smart lady good for you
Fake it til you make it. They need to teach kids procedures even before they understand exactly why it works. There’s a push to make kids discover everything that is not practical imo
Most of the teachers don't even know why it works
@@triple_gem_shining If they do they absolutely should explain it while teaching the steps but after a certain point just focus on the how to part for everybody and hope that the explanation reached a few students capable of grasping it.
Yeah, but Zig Ziglat was almost entirely unhelpful except for your quote from him. But a good point, sir.
As a math teacher, I agree with this! This push by the education field is putting our country behind.
@@stevensweet8834 It's really crazy. I taught high school math this past school year and the number of kids who have essentially no concept at all of how to do math was crazy.
If you're making kids approach basic problems from their own new and creative perspective every time they're not going to be able to move on to harder concepts. Creativity and discover is really cool and fun in math and we should give students a chance to try that but then show them how to do it in practice.
Teach times tables and the arithmetic algorithms some of these kids don't have a basic understanding of what multiplication even is!
Two thoughts: years ago, a math teacher friend of mine, was covering a topic in his class. After his third attempt, he understood it.
In college, a professor who once taught at the US Naval Academy, told us that at the USNA, calculus was made optional as calculus wasn’t used by officers while at sea. Later it was realized navigators and others who used trigonometry had difficulty. By requiring calculus, officers learned to use trig more effectely.
i can relate to that so much. i’m taking calculus 2 now and apparently calculus 1 was a breeze.
You don't get better at math because you always move on to something harder.
You can learn how to proof things by induction without fully understanding why it works. It is of course best to fully understand the why but maybe that will come later on, it is not 100% necessary at the beginning.
Hi MS!
Your video sound is too low, in my opinion.
The sound quality of your previous videos from a month ago was much better.
To watch your videos now, I need to set the volume to maximum on the same model of MacBook Air you are using.
Please check it on your own device.
Thank you math sorcerer for your videos, you provided me with motivation to study, I recently got a 98 on my grade 11 math final and I believe my success was due to your videos!
I think he was so smart that he didn't really understand math, at least on a concious level. He might have been so good that he unconsciously understood it and that things to him could come natural after a while (when he got used to it). The same way i'm putting this tought into speech: i'm not activly and conciously selecting words, i'm just writing what comes to my mind
In my first serious quantum class we explored the Schrödinger equation. The professor said you won't ever understand quantum physics, but you can "get used to it" through these math equations you'll learn. Basically, with higher math you're learning math from a formalistic, axiomatic standpoint. That completely overturns how you learned before. That's why I say high school math should do more with axiomatic approaches. For example, most high school Geometry is _not_ strictly Euclidean axiomatic anymore. Sad, bad. All in all, you'll never understand why so many things in math hang together the way they do -- but they do, and sometimes it can be mind-blowing out to cosmic.
My interpretation would be that he is saying you just memorize techniques and formulas, which is how school teaches students to pass exams.
If you truly understand the equations, you can write proofs of the equations.
As we know, this is an advanced subject inside of mathematics.
So, I would say the quote is only applicable to those who use math as a tool.
To those who explore new math concepts, they MUST get better at math because a tool cannot create itself.
Someone has to do the initial research to find out what problems exist and how to engineer a tool to solve them.
We grow by challenging ourselves, continually. THAT'S what we're getting used to. Another level, another devil! This is true even with weightlifting, language learning, studying world literature, practicing law and medicine, or doing any other great thing.
We get used to the delayed gratification of the learning process and of real-world problem solving.
Your enthusiasm is contagious!
There's so many secrets to math I can't help but want to understand it on a deeper level but sometimes it's a fruitless endeavor because I'm just left more confused. Sometimes you just gotta learn it and stop trying to understand it
My initial interpretation was almost the opposite of yours... I thought it meant you don't get better at solving novel math problems, but you get used to dealing with the struggle that leads to you getting a good understanding. (This is how I felt after completing my 200th project Euler problem)
It's probably not true, unless you let 'novel math problems' mean progressively harder math problems.
This is marvelous!!! The key ingredient here is 'EXPOSURE'
YES!!
Love the humility here. I haven't taken any graduate level classes yet, but I just finished going through/reviewing Professor Leonard's calculus 1 class for the second time, and the disc/shells method made so much more sense the second time through. It's almost just intuitive now when you are able to visualize it geometrically-which I couldn't really do the first time around because my brain resources were still processing integration.
What's good is watching your lectures while thinking about personal problems. Then, logically working those problems out in a relatively quick manner.
Hello Math Sorcerer
Where do I start with University Math if I am in school.
I want to be able to do enough math so that I am able to Classical mechanics in physics
I think you should start with differential, integral and vector calculus, then linear algebra and (ordinary then partial) differential equations, and finally some variational calculus.
Of von Neumann has said this because he had an inborn talent for math and had an IQ over 160. Not everyone interested in math has IQ over 160, so yes they do have to work hard.
In fact I think those who doesn't have an IQ over 160 shouldn't waste their time pursuing a career in math.
His name is pronounced "Naw-men," not "Newmen". There are at least two recordings of his actual voice, including film footage. You can hear him speaking, and in one of them he says his name.
Hey math sorcerer you could start a series explaining famous mathematician quotes uncovering what they had in mind when they said it
I know another quote by him:
Young man, in mathematics you don't understand things. You just get used to them.
It's about the fact that very often it's nearly impossible to understand something on the first try. But once you familiarize yourself with the topic, then you get the impression that you understand. But according to the quote, it's just an impression. Nevertheless it allows to use the knowledge to go further.
I do really well at high level math (finishing senior year with a 4.0) but I still haven’t gotten over bad test anxiety, and because of that I’ve hated every single math course I’ve taken.
You must first learn wax on and wax off. Before learning the flying kick. 🥋
12:00 I struggled with math on my first semester as an econ major and it haunted me on all my tests until recently, 6 years later, when I'm finally getting used to it. But this certainly holds true. My boyfriend has never had issues through hs and college and he has no test anxiety whatsoever.
The fancy word is "inculcate": to teach and impress by frequent repetitions or admonitions.
One gains maturity (skill) in a field with practice. It is an eye-opener to revisit topics from your past ("Crack open that old textbook.") after accumulating some work experience. The accumulation of experience doesn't make a topic "easier" but makes it more familiar.
It's like riding a bicycle! Math is like never falling off any more while not using your hands.
You inspire me so much. I am also a math professor 👩🏽🏫, and I absolutely agree with you 😊. Wow thanks for getting deep into this quote!! I love how you communicate and explain. Thank you so much, mil gracias por compartir tus historias 😊🎉.
Such quotes are really evergreen. They give us a lot of motivation. There's no meaning in trying to understand everything but something you can. What if you spent years together to learn a subject and don't advance. As I do with trigonometry.
Study another branch of math, calculus and trigonometry I don't understand but I have progressed in number theory
The best of best Integral Calculus book.Please suggest me.
Textbooks don't explain well. Begin with "Quick Calculus" by Kleppner.
Khan academy
I love this quote. They have this posted on the wall just as you walk into the Math department at my school. Beside the quote is a whole biography of Von Neumann. I used to pass it everyday and it crosses my mind each time I get stuck in math.
"I'm not stuck in this math class. This math class is stuck with me!" --The Math Watchman
This was a really useful video. I am studying independently as a hobby and have been scared of progressing without knowing everything off by heart. I now realise it doesn’t really matter if I leave little gaps (within reason).
This was a helpful watch. It hasn’t been an easy journey for me with math. A lot of self doubt, a lot of circumstances outside of my control and a lot of competition. I went to a great school for undergrad and I was not prepared for the environment I went into. Recently, I started talking an odd course while working full time and the experience has been night and day. I was able to understand ! This video has helped give me the words for my renewed adventure into math !
My favorite idea in this video is "I miss that". I feel like that encapsulates a lot of getting used to difficult and complex topics progressively. It also explains the joy of going back and exploring ideas from previous learning in light of things learned subsequently.
The concepts we learn in math took our species thousands of years to happen on.
And each little piece of math came from separate people.
People need to understand that its ok not to get it the first time, or even the second or third time.
I actually believe maths is so important and so challenging that students deserve multiple opportunities to try and fail at it throughout their development.
I was never great at it but I was able to channel my passion for it into computer science which I was much better at. It was a lot easier for me to appreciate the application of maths in service of a tangible goal.
Really cool video, I found you yesterday and you really inspire me to keep studying math. Thank you so much for being amazing!
The first time I saw the banner of your video, I thought it was a guitar class from a metal band player. Thank you for sharing such precious knowledge that goes beyond what I already know.
This happens to me in my topology class lol
Yes the arms come back=)))
hahahahaha
Welcome to the gun show!💪
I see it like working out, you don't get "better" at working out per se, you just get used to showing up at the gym every day and that consistency is what changes your body.
I remember a quote from a physics book, not correctly, and not sure from who, but it goes, "The solution should be clear, the equation is telling you what's happening."
true as life!
Hi Math Sorcerer!
What you said reminds me of Stephen Krashen’s theory about language acquisition, also known as “Comprehensible Input”. This theory states that we don’t learn languages, we acquire them when we understand the messages we hear or read. Krashen says that learning is a conscious process, whereas the acquisition occurs at a subconscious level; according to this idea, the best way to trigger the subconscious process of acquisition of the language is through the constant exposure to the language itself. The more we get input in our target language, the more we acquire it.
We don’t have to study list of vocabulary or set of grammar rules, we just have to let our brain do the heavy lift, and, by exposing ourselves to the language we want to acquire, our brain will figure out the mechanics of the language (Exactly the same thing we all experienced when we were children)
So, “mutatas mutandi”, “You don’t get better at mathematics, you get used to it”, just as “You don’t learn a language, you get used to it”!
Hi from Italy
Stefano
Yeah, the hardest part should be left to be done by nature🎉. Is there some "universal" rule for how we learn (or aquire) things in all fields?
@@Englishforstudy The answer to your question is the reason why I wrote my comment: I wanted to know the opinion of the Math Sorcerer about it, if there might be analogies between how we “get used” to languages and how we “get used” to everything else.
peace be upon you sir
Very much found this useful. My 14 year old grandson might benefit from this sentiment.
Thank you.
I’m engineering student, i did pass all my calc and math courses, however I want to get better at math , how can i practice the things I learned
Appreciated!!!
Man I super appreciate your vid’s! Thanks for sharing Von Neumann’s quote!
I think von Neumann was just venting his frustrations at people who want to achieve understanding but are taking too long. You can do maths with habit and keep within guidelines and do something that way. But there is something pretty special about understanding, it is an experience, and its also exploring the nature of reality, ie. metaphysics. But such understanding comes expensively.
“It’s like lifting heavy weight , once the weight gets heavy make it heavier. Then the heavy weight becomes a feather.”
-
Paul Kane
Thx!!!
So glad there are honest academics out there. Your videos are very helpful.
The freedom of mathematicians is the freedom of mankind, if they don't know they are in a prison, none of us know!
this is threpeutic. I sometimes come here and listen to him talk just to make myself feel better.
Can you please name some math book title for a little starter that loves Math.
sorry for my english
Categories theory for working mathematician
Which resources can we use for imo
This quote can be extended to anything in life that's difficult or brings torment and frustration. Some people who get captured by maths even develop Stockholm syndrome and start to enjoy it 😅
Wow great video
"You don't get better at mathematics, mathematics gets better at YOU!"
"... what?"
Are you threatening me or claiming my aura is “bed at mith and learneding”
it's true, i don't
You get better at getting used to it.
I feel sure that somewhere here, there is a connection here with the concept of "crystallized intelligence versus fluid intelligence".