The Singular Mind of Terry Tao
nytimes.com
The Singular Mind of Terry Tao
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Re: The Singular Mind of Terry Tao
#2The idea of a world class mathematician as as weird genius is common and may be said is not totally without base (Perelman comes to mind). Tao's interactions on his blog is always unassuming, trying to help, "super normal" as this article puts it.
But to me the even more amazing thing is how good an educator he is. Most mathematicians I have encountered were of the "proof is left as an exercise" type, where if you didn't see how things done would't or couldn't help you in learning how to proceed. Tao is a big outlier in this regard. His How to Solve Mathematical Problems (http://www.amazon.com/Solving-Mathematical-Problems-Personal...) is more focused than Polya's famous book but is a much better help in learning how mathematicians think. You can get the first chapter for free (http://www.math.ucla.edu/~tao/preprints/problem.ps), an excellent way to finish off a Friday.
Re: The Singular Mind of Terry Tao
#3Authors routinely cherry pick mathematicians / scientists to perpetuate the 'scientist as weirdo' myth. It is fundamentally dishonest and misleads the general population. Here, the author chooses, Newton, Nash, and Pearlman. Of that, Nash was diagnozed and treated for a mental illness. That doesn't make him a weirdo at all. There is very likely no causative relationship between passion for math or science and schizophrenia. However, in Newton and Pearlman's case, their singular passion for math / science probably did lead them to be 'weirdos' in other matters.
Now, coming to the cherry picking part, the author may well have chosen, Bohr, Einstein, Feynman, Von Neumann, and Witten and come to the exact opposite conclusion that Tao is in the mold of the 'typical' otherwise-normal scientific genius.
I think journalists, etc. owe it to the general public, and in particular, to young aspiring scientists, to not perpetuate the myth of the mad scientist.
Re: The Singular Mind of Terry Tao
#4The write-up about Tao when he was ten years old [1] by Miraca Gross mentions Tao's connection to Julian Stanley, the founder of the Center for Talented Youth (CTY) at Johns Hopkins University. I had opportunity to correspond with Stanley before he died, and the evolution of his views about the education of mathematically precocious young people is quite interesting. A 2006 retrospective by Stanley and co-author Michelle Muratori[2] examines the education of Tao and of Lenhard Ng, another very precocious mathematics learner. A key paragraph from the earlier article quotes Tao's father: "There is no need for him to rush ahead now. If he were to enter full-time [university] now, just for the sake of being the youngest child to graduate, or indeed for the sake of doing anything 'first,' that would simply be a stunt. Much more important is the opportunity to consolidate his education, to build a broader base." I wish every parent of a precocious child had that kind of healthy perspective on the child's overall development.
Tao's father's attitude reminds me of the advice on mathematical education given by Fields medalist William Thurston.[3] "Another problem is that precocious students get the idea that the reward is in being 'ahead' of others in the same age group, rather than in the quality of learning and thinking. With a lifetime to learn, this is a shortsighted attitude. By the time they are 25 or 30, they are judged not by precociousness but on the quality of work. It is often a big letdown to precocious students when others who are talented but not so precocious catch up, and they become one among many. The problem is compounded by parents in affluent school districts who often push their children to advance as quickly as possible through the curriculum, before they are really ready."
AFTER EDIT: Tao's write-up of his experience taking the Princeton University general examination for his Ph.D. program in mathematics is quite interesting, and certainly makes him look very normal indeed.[4]
[1] http://www.davidsongifted.org/db/Articles_id_10116.aspx
[2] http://gcq.sagepub.com/content/50/4/307.abstract
Re: The Singular Mind of Terry Tao
#5Tao's work on Navier-Stokes: https://www.quantamagazine.org/20140224-a-fluid-new-path-in-...
Re: The Singular Mind of Terry Tao
#6I was disappointed that the author repeatedly mentioned the Twin Prime conjecture, but neglected to mention the recent work done by Yitang Zhang: http://www.slate.com/articles/health_and_science/do_the_math...
Re: The Singular Mind of Terry Tao
#7This article does a much better job than many explaining what math research is actually like. I particularly like the "chess with the devil" metaphor:
The steady state of mathematical research is to be
completely stuck. It is a process that Charles
Fefferman of Princeton, himself a onetime math prodigy
turned Fields medalist, likens to "playing chess with
the devil." The rules of the devil’s game are special,
though: The devil is vastly superior at chess, but,
Fefferman explained, you may take back as many moves as
you like, and the devil may not. You play a first game,
and, of course, "he crushes you." So you take back
moves and try something different, and he crushes you
again, "in much the same way." If you are sufficiently
wily, you will eventually discover a move that forces the
devil to shift strategy; you still lose, but — aha! — you
have your first clue.
Another perspective I really like on genius in mathematics is (the late) Bill Thurston's response to the Math Overflow post "What's a mathematician to do?", asking how a non-genius can contribute to mathematics:
It's not mathematics that you need to contribute to.
It's deeper than that: how might you contribute to
humanity, and even deeper, to the well-being of the
world, by pursuing mathematics? ... The real
satisfaction from mathematics is in learning from
others and sharing with others. All of us have clear
understanding of a few things and murky concepts of
many more. There is no way to run out of ideas in need
of clarification...Re: The Singular Mind of Terry Tao
#8Authors routinely cherry pick mathematicians / scientists to perpetuate the 'scientist as weirdo' myth. It is fundamentally dishonest and misleads the general population. Here, the author chooses, Newton, Nash, and Pearlman. Of that, Nash was diagnozed and treated for a mental illness. That doesn't make him a weirdo at all. There is very likely no causative relationship between passion for math or science and schizop…
This is why I'm so thankful for scientists like Neil DeGrasse Tyson and Carl Sagan, who have put themselves very much in the public eye as positive representatives of hard science.
Similarly, the Mythbusters cast, Bill Nye, and others that are not particularly "notable" scientists (as far as I know) but have done a great deal to make it more accessible to aspiring scientists.
Re: The Singular Mind of Terry Tao
#9I was disappointed that the author repeatedly mentioned the Twin Prime conjecture, but neglected to mention the recent work done by Yitang Zhang: http://www.slate.com/articles/health_and_science/do_the_math...
Though Zhang did get a profile in TNY: http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
And quite a bit of news coverage: https://www.quantamagazine.org/20130519-unheralded-mathemati...
Re: The Singular Mind of Terry Tao
#10The idea of a world class mathematician as as weird genius is common and may be said is not totally without base (Perelman comes to mind). Tao's interactions on his blog is always unassuming, trying to help, "super normal" as this article puts it. But to me the even more amazing thing is how good an educator he is. Most mathematicians I have encountered were of the "proof is left as an exercise" type, where if you di…
I used Tao's books on Real Analysis during college and my feelings are mixed on his capabilities as an educator. On the one hand his books were really great as he gave a lot of proofs (although most proofs were still left to the reader, but I guess that you can't really learn Analysis without proving Rolle's Theorem or the First Theorem of Calculus on your own) and what I also really liked was that he made no assumptions about your knowledge and started from scratch (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences). On the other hand there were a lot of errors in his books and sometimes he is hard to follow, I guess the books contents are too easy for him and he wrote the book without ever reading back. Even though his books weren't perfect I learned so much about pure mathematics as a non-math major and I don't think I could have learned so much through Rudin's books.