Math texts, pi creatures, problem solving, etc. | 3blue1brown Q&A for Bilibili

This Q&A video was originally made for the 3blue1brown Bilibili page reaching 1M followers.

Books mentioned in the video:
Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach, by John and Barbara Hubbard

Nonlinear Dynamics and Chaos, by Steven Strogatz

Proofs from The Book, by Aigner and Ziegler

The Cauchy-Schwarz Master Class, by J. Michael Steele

How to Solve It, by George Pólya

Solving Mathematical Problems: A Personal Perspective, by Terence Tao

I listed a few more textbook recommendations here:

Table of contents
0:00 - Textbook recommendations
4:05 - Avoiding frustration with math texts
6:47 - Not being "gifted" enough
8:53 - Researching for videos
10:02 - Story behind the pi creatures
12:35 - Manim
16:50 - Training problem-solving skills
22:13 - How much should visuals be used in math
25:00 - Probability series when?

[yurigouveawagner]

i will now write all my texts and articles with the following notation:

:) signifies the end of a proof
:/ signifies a question
:( signifies a limitation in the experiment

edit: :o signifies a theorem or lemma

[durian]

To any of you wondering, the outro (下次一定) is a common Chinese phrase/meme to say "maybe next time" or "take a rain check".

[joaqbadillo]

This guy also speaks Chinese, Grant has everything covered.

[markkennedy]

12:00 this is why Grant is among the best maths educators out there. He talks about the emotion in maths, about stressing what's important vs the detail. It explains why the first time I properly intuited linear independence was after looking at his Linear algebra series. Some people will argue you can't visualise all maths but I think there's a happy medium between slavishly following symbols on a page and characterising what they represent more fully. This is why Grant is a bit of a hero for me.

[almoni]

I would recommend Jiří Matoušek's "Thirty-three miniatures".
It's about 33 beautiful applications of linear algebra.
Also, all textbooks by him that I checked out are gold.

[zxosfyw]

Thank you, sir!
I come from China, and I learned quite a lot from your teachings. They are very insightful!
Thank you very much!
感谢！

[OrigamiMarie]

When talking about natural talent, I think about crafting. When I have just started teaching someone to knit or crochet, at some point, after they've gotten just good enough to reliably make stitches, they'll watch me do the same craft and say something like "gosh you're so fast and I'm so slow, I wish I was fast". And when it's about crafting, the response to this is actually really intuitive. I say "well, I've been doing this about two decades longer than you have, so I should be faster; if I wasn't, there would be something going rather wrong".

[Umarology]

Being a practicing engineer, I'm really interested in theory of nonlinear dynamics and mathematics behind. The Nonlinear Dynamics Book will be a real help. Thanks very much, Grant! ❤

[jaredlichtman]

For the room problem: a "physical/intuitive" interpretation of the sum-of-squares is as a weighted count of the population, where each person is weighted by the number of their roommates.

[rollingsnowball]

Competition math can be really discouraging for students who want to get into math but can’t “keep up” with everyone else. I never even thought that I could ponder problems for a day or more. Everything was kinda fast-paced. It’s funny that continuity can work perfectly fine only using rational numbers. Talk about lifting up your pencil! Oh and that room problem, I didn’t find that easy at all lol. Although, convex functions ARE quite interesting *cough* *cough* Legendre transform. Love your content! Can’t wait for more on diff eqs and probability

[wallacealbert]

Dude, you're a legend. Thank you for the hard work you put into your videos to make things clearer. Seriously, thank you!!

[omarbourhani]

Please do not stop making those videos 🙏🙏
You are changing my life 🙂

[mincraftfrontiersman]

6:47 Regarding the concept of being gifted vs. not:
I've always held to the belief that there *are* people who are better in a given field by their nature, but *anyone* can become skilled through effort. Anyone can become skilled, but some people have a head start.

Regarding math specifically, yes. There are individuals who are naturally good at it; their brains are wired in a way that makes learning mathematics natural. These are the individuals we'd typically call "gifted." For others, learning math is harder. The ""not gifted"" individuals. It's very easy to see someone breeze through things that you struggle with and come to the conclusion that you're just not gifted enough to progress, but that's categorically untrue. Just because it takes more effort for you to learn something doesn't mean you can't. If you're willing to put your head down and push through, you can learn any skill you want. Whether you're gifted or not determines where you start, not where you end up.

[mixti]

that question about not being gifted enough was hard to hear. coming from a competition math background, i often felt that the community could be very toxic and make me feel like i was not "gifted" enough

[akshaysriram]

I have been following and looking up to this guy for years, and never would have expected him to speak Chinese so fluently.

[TheAcer]

I bet whoever came up with that sum of squares solution had some connection to Cambridge. They used to grade their exams by taking the sum of squares of the scores to each question, to encourage people to prioritise answering fewer questions more completely rather than doing a lot of questions partially.

As you say, problem solving is a lot about your experience....

[josemesquita_]

You are an extremely talented communicator, for real.

[GurpreetSingh-engx]

5:00 Yes yes yes yes, I am obsessed with Valadmir Arnold's writings, I have been collecting his works in English but most of his writings are in Russian. Currently learning a lot from his book on Catastrophe Theory. I feel VI Arnold changed my life, his essays on mathematical pedagogy are revolutionary and I feel you are the one who will make his dream come true of unifying maths of physics which were divorced by the Evil Bourbaki's.

[JoelRosenfeld]

I am really enjoying these videos on this second channel. Great to hear conversations and interviews that give more depth behind the characters in mathematics.

On the nature vs nurture aspect. I really do feel that there is an in-built ability to engage with mathematics in some people. I know that I saw friends with whom I performed on level with in undergrad really outpace me in graduate courses. It really showed me there was a difference in ability. There is a spectrum of human ability and Tao and Von Neumann are really at the peak of this. If there are people at the top and the bottom, there are going to be people at every point in between.

Of course, this is really hard to quantify, and I don’t think there is value in approaching education this way. I think most topics taught in school should be approachable to everyone, but after a point, you see real differentiation between students.

[skilz]

I've always enjoyed math and physics. The one thing I have learned over time is that numbers, math and all that follows they are nothing more than a product of the mind as they are all conceptual ideas. At the end of the day, math is nothing more than a model and it is what you make of it! I enjoy hearing all different kinds of perspectives and approaches. 3Blue1Brown is one of my favorites along with Mathologer and a few others... I love their presentations and visualization methods. It's almost like comparing or listening to a monotone college professor who'd soon enough put you to sleep on trying to explain the phenomenons of the Mandelbrot Set as opposed to writing a simple computer program to graph it visually being able to see and interact with the infinite patterns and levels of details that a simple equation produces. Grant and others like him allow mathematics to be fun and engaging instead of being monotonous, drab and dreary... Keep up the great work!