Can someone explain what the author meant with the following passage? "... Navier-Stokes equations, which govern the flow of fluids, including air currents. In this case, let us hope that it does not have a real-world application."
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The Mind of a Mathematician
31–40 of 68 posts
Re: The Mind of a Mathematician
#32What 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…
It is important to note that it is indeed about his parents doing a wonderful job, and not about them being very rich or something. The article http://www.davidsongifted.org/search-database/entry/a10116
describes this nicely.
Nothing that has been done for his early education required lots of money. (Obviously, being in a developed country like Australia helped a lot --- but one can imagine something similar being done in almost any densely populated urban area in the world.)
However, almost everything in his very early age required large amounts of time, thinking, and attention by his parents.
If you have enough time, and your young children are interested in something, don't leave them to figure it out themselves.
Re: The Mind of a Mathematician
#33I 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…
> However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it.
I wonder though if such narratives may be necessary (in the world as it is, rather than how it should be) in order to generate fame, specifically the kind of fame that is best able to propagate and reach the eventual endpoints who may be inspired to follow in his footsteps. Annoyances like this may be some sort of social evolutionary adaptation.
Re: The Mind of a Mathematician
#34> 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…
Not an expert, and not answer to this exact question, but the video https://www.youtube.com/watch?v=PtsrAw1LR3E and these slides https://pdfs.semanticscholar.org/41c5/e01cf7e3975efdc5a27f74... could answer some of your questions. One way to think about this, without any number theory requirements: if we keep throwing a coin with probability of heads p which is around 1/2 at the beginning, but then keeps decreasing on…
Thank you. Very informative links too.
Re: The Mind of a Mathematician
#35I 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 least technical thing he's done.
Re: The Mind of a Mathematician
#36> 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 improved to 246. You can see the(long!) proof here:
https://www.dropbox.com/s/85pt6mvzf5ghukw/newergap-submitted...
Zhang stated 70 million because it's easy to remember.
Anyway, the basic strategy of the proof is to attempt to prove the twin prime conjecture, and not fall too short.
Where do these numbers come from? You end up needing to do lots of random computations in the course of the proof. For example, can you compute a constant C such that the bound
e^(.1x^2 + .4x) + 5cos(pi * x) - sqrt(x^2 + 1) holds for all x between 3 and 5? If this appeared in the course of an analytic number theory proof, you probably wouldn't try to compute the absolute best value C. It would be tedious and boring, and nobody would want to read it. You'd just compute something that was good enough, and move on.
Re: The Mind of a Mathematician
#37What 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 of a standard school classroom. They are not more privileged or supported than the average middle class child in a first world country.
The world's best educational resources are dropping rapidly in price; with some searching, you can even get an mathematical education up to what Tao knew in graduate school completely for free.
Re: The Mind of a Mathematician
#38What 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…
> 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)?
Re: The Mind of a Mathematician
#39What 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…
How does a child even know what book to get?
Re: The Mind of a Mathematician
#40I 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-of-the-heroic...
So Tao's celebrity status as a genius does have that positive aspect. I think he disproves many stereotypes of genius and helps people believe that it's possible to brilliant, decent, humble, social and likable. I think that's useful.
He talked about this eloquently in his own blog where he argues against the "cult of genius" and says one needn't be a genius to be a mathematician: https://terrytao.wordpress.com/career-advice/does-one-have-t...
So, by lionizing him as a genius I think media actually undermines its own narrative about what genius is. In that sense, maybe the cult of genius is bad but if we have to put a genius on a pedestal, it's great to have it be one who seems so normal.
With respect to his work, I always think of what Richard Feynman said in the start of this book "What do you care what other people think?" (https://www.amazon.com/gp/product/0393355640) He tells a story about an artist who holds up a flower and says "I, as an artist, can see how beautiful a flower is. But you, as a scientist, take it all apart and it becomes dull." Feynman thinks he's nutty. He can see the beauty of the flower and the beauty of the science.
People who don't understand Tao's work probably think it's dull. I can't understand Tao's mathematical work. I'm studying math and I really hope someday I could. But math and science have gone so far now that work at the cutting edge really is incomprehensible to people outside the field. So, I'm inspired by the person who does the work. It's just the surface but it's what I have access to.
Feynman talks about this at the end of the chapter that starts with the flower. His father helped him love science and taught him how to think. Then he sent him to university to learn all the things he hadn't. But when Feynman came home, he couldn't explain quantum mechanics simply. So his father never learned what he didn't know. I hope he still loved his son for understanding it.