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The Mind of a Mathematician

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Re: The Mind of a Mathematician

#41

Post by knzhou »

imbusy111 wrote: post #39
knzhou wrote: post #37

Earlier quoted context omitted.

Sure, Tao's an outlier among outliers, but in general nurturing a prodigy does not require a lot of parental time or money. I've met a number of such prodigies in the course of my work, and generally their parental involvement amounts to buying them a book every few months, at their kid's insistence. The kids then teach themselves, often by sneaking glances at their books or math problems while hiding out at the back…

How does a child even know what book to get?

These days, you use Google. I personally have a list of books for intro physics [0] and help maintain a meta-list of books up to graduate level [1], and there are hundreds more lists out there.

Heck, when I was a kid I learned from just checking out books at random from the local public library, and even that was fine. There's just an avalanche of great free resources out there.

0: https://knzhou.github.io/#writing 1: https://physics.stackexchange.com/questions/12175/book-recom...

Re: The Mind of a Mathematician

#42

Post by knzhou »

lonesword wrote: post #38
knzhou wrote: post #37

Earlier quoted context omitted.

Sure, Tao's an outlier among outliers, but in general nurturing a prodigy does not require a lot of parental time or money. I've met a number of such prodigies in the course of my work, and generally their parental involvement amounts to buying them a book every few months, at their kid's insistence. The kids then teach themselves, often by sneaking glances at their books or math problems while hiding out at the back…

> I've met a number of such prodigies in the course of my work If you don't mind, can you elaborate more on what kind of work you do? Do you run a school for the gifted (assuming such a thing exists)?

I've taught at the U.S. Physics Olympiad's training camp, and also tutor high school students who want to learn a ton of physics quickly. (These kids usually find me themselves, through Google.)

My most obnoxiously smart student was this 12 year old who would interrupt my lectures on classical mechanics with tricky questions I couldn't solve. The next year he came back, doing the same thing but for quantum mechanics, and the year after that he got bored of this and enrolled in an elite college. I want to stress that none of this required great wealth or privilege. The cost for his books was a small fraction of what other middle class parents would pay for, say, music lessons or SAT tutoring.

Re: The Mind of a Mathematician

#43

Post by avip »

usgroup wrote: post #18

I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…

I'd (conservatively) speculate most of us here are in the global 1% in terms of "ability to understand math".

Have tried multiple times to follow his work (from the blog). But I'm not math-fluent enough to understand or otherwise appreciate the content. Possibly I could but it requires so much effort.

It's much easier to enjoy Bach's or Messi's genius :)

Re: The Mind of a Mathematician

#44

Post by MauranKilom »

impendia wrote: post #36
jeswin wrote: post #28

> Yitang Zhang, a mathematician at the University of New Hampshire, proved that there are an infinite number of primes that are separated by, at most, 70 million. > To date, they have managed to prove that there are an infinite number of primes separated by, at most, 246 I'd like to ask a very noob question. What kind of an approach would give us such an exact upper bound, when primes as a concept (in a layman's intu…

Analytic number theorist here. I can answer your question. The method doesn't really yield "exactly 70,000,000". If you traced through his method, and worked out each step in more detail, you'd probably get a bound of (say) 64,189,288 -- or some random number of like that. If you read through it still more carefully, and tried to introduce genuine improvements , you'd improve this further. Indeed, the bound has been…

I know you just threw together a random formula for illustrative purposes, but I was curious:

https://www.wolframalpha.com/input/?i=maximize+%7B+%28e%5E%2...

-> You can find C by imposing equality for x = 5.

Re: The Mind of a Mathematician

#45

Post by jl2718 »

knzhou wrote: post #37
imbusy111 wrote: post #17

What strikes me the most is the amount of support he received and the people he was able to meet when he was a child. I don't want to dismiss his talent, but this level of support is NOT available to 99%+ of population. His parents have done a wonderful job. To recall my days as an undergraduate at a well-known UK university studying mathematics - large classes (300+) where everyone is disposable, nothing to do but s…

Sure, Tao's an outlier among outliers, but in general nurturing a prodigy does not require a lot of parental time or money. I've met a number of such prodigies in the course of my work, and generally their parental involvement amounts to buying them a book every few months, at their kid's insistence. The kids then teach themselves, often by sneaking glances at their books or math problems while hiding out at the back…

This might sound weird, but, some parents are not at all supportive of their children’s interests. Their relationship can be one of rivalry and antagonism that punishes success. I met a bunch of misfit prodigy hacker types in the military. At some point we realized that we were all there for the same reason.

Re: The Mind of a Mathematician

#46

Post by opportune »

knzhou wrote: post #35
usgroup wrote: post #18

I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…

This is an unsolvable problem. There already is plenty of expository content about what Tao actually does, e.g. his excellent blog. It's just that it can't get popular because it's technical; that's the iron law of STEM popularization, you can only choose one. The most press he's gotten recently has been from this "eigenvectors from eigenvalues" thing that he solved three ways in two hours, probably because it's the…

He is also active on mathoverflow, even answering not very popular questions, which I think is really cool: https://mathoverflow.net/users/766/terry-tao

Re: The Mind of a Mathematician

#47

Post by opportune »

bhntr3 wrote: post #40
usgroup wrote: post #18

I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…

I became a "fan" of Tao after reading this piece in the NYT: https://www.nytimes.com/2015/07/26/magazine/the-singular-min... . It talks about how normal and well liked Tao is. How much he collaborates and assists others in his work. I think I saw it linked along with this article about the warped portrayal of genius Hollywood feeds us (especially in the Imitation Game): https://www.huffpost.com/entry/turing-the-myth-…

It's easy to say you don't need to be a genius to be a mathematician when you're a genius celebrity mathematician.

Personally I gave up on math as a career once I realized all the people who got into top grad schools for math were like international IMO participants, USAMO or equivalent at least, started taking classes beyond calculus in 10th grade, etc. Even though I love it and even have an undergrad degree in it, and maybe could have performed that well if adults in my life nudged me in that direction, the fact that there were so many people who would always have massive advantages turned me off from it.

Re: The Mind of a Mathematician

#49

Post by ska »

avip wrote: post #43
usgroup wrote: post #18

I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…

I'd (conservatively) speculate most of us here are in the global 1% in terms of "ability to understand math". Have tried multiple times to follow his work (from the blog). But I'm not math-fluent enough to understand or otherwise appreciate the content. Possibly I could but it requires so much effort. It's much easier to enjoy Bach's or Messi's genius :)

This (Bach) is a parallel that comes up often in both lay and professional music on the nature of "genius".

I've had some success with the following analogy. Music is not math, but the conversation between research mathematicians is a bit like the conversation between composers. In order for them to understand each other well they must understand the notation, but also the instruments/tools, the history, etc. However we non-composers can still listen to what they wrote if someone performs it for us - we may not catch everything another composer does, but we can enjoy it. The tough thing about mathematics is that there is no orchestra or possibility of one; in order to consume it at all you have to learn some of the details.

Re: The Mind of a Mathematician

#50

Post by lonelappde »

opportune wrote: post #47
bhntr3 wrote: post #40

Earlier quoted context omitted.

I became a "fan" of Tao after reading this piece in the NYT: https://www.nytimes.com/2015/07/26/magazine/the-singular-min... . It talks about how normal and well liked Tao is. How much he collaborates and assists others in his work. I think I saw it linked along with this article about the warped portrayal of genius Hollywood feeds us (especially in the Imitation Game): https://www.huffpost.com/entry/turing-the-myth-…

It's easy to say you don't need to be a genius to be a mathematician when you're a genius celebrity mathematician. Personally I gave up on math as a career once I realized all the people who got into top grad schools for math were like international IMO participants, USAMO or equivalent at least, started taking classes beyond calculus in 10th grade, etc. Even though I love it and even have an undergrad degree in it,…

Math isn't a competition. You can study and research math as a hobby, just like hundreds of thousands of people do with computer programming
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