
The Singular Mind of Terry Tao - dctoedt
http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html
======
Jun8
The 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...](http://www.amazon.com/Solving-Mathematical-Problems-
Personal-Perspective/dp/0199205604)) 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](http://www.math.ucla.edu/~tao/preprints/problem.ps)),
an excellent way to finish off a Friday.

~~~
solidangle
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.

~~~
qmalxp
It's probably worth pointing out that Good Educator != Good Author. I have
heard from people who would know that your guess is not so far off, but having
taken classes from him I can attest he is an excellent teacher in addition to
being a world class mathematician.

I also want to add that although he is extremely friendly and helpful, it'd be
dishonest to say he isn't a bit weird. However, that is probably just an
ingredient/consequence of greatness; I reckon most of the big name tech
founders discussed on these forums are a bit weird.

~~~
javert
How is he weird? Just curious.

~~~
overpaidgoogler
Not in any specific way, but he has a nerdy demeanor. There are many
interviews of him online your can watch.

------
davmre
This 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.
    

That said, the article does still have a hint of genius worship about it. Tao
himself has a good blog post "Does one have to be a genius to do maths?"
([https://terrytao.wordpress.com/career-advice/does-one-
have-t...](https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-
genius-to-do-maths/)) pushing back on this sort of thing.

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...

([http://mathoverflow.net/questions/43690/whats-a-
mathematicia...](http://mathoverflow.net/questions/43690/whats-a-
mathematician-to-do/44213))

~~~
gohrt
To be clear, Tao doesn't say that _he_ is not a genius. Tao was known as a
once-in-a-generation mathematical genius before he was 10 years old. (There
was a magazine article about him and super-gifted education in Australia.)
Both of Tao's brothers have extremely high IQ (>150).

Tao claims that you can contribute nonzero progress to mathematics without
being a genius, but even so, the requirements he lays out aren't requirements
that anyone with a childhood <120IQ has ever done.

What is blog post is saying is that math is not magic -- it takes brilliance
AND hard work, not just brilliance.

~~~
mikeyouse
Completely off-topic ethical prompt; Should society fund the harvesting of
eggs / sperm from his parents to serve as a genius bank for surrogate parents?
Could 1,000 children with equal capabilities dramatically alter the course of
humanity?

~~~
davmre
It's not clear the genetic component is what matters here; you could equally
well suggest that Tao's parents should adopt and raise lots of other smart
kids. Though cloning 1000 Terry Taos would certainly be an interesting
investigation into nature/nature.

In any case IQ >150 is not that rare; there are hundreds of thousands of such
people alive right now even just in the US. Clearly there are other
qualifications to be a mathematical genius. It'd be a wonderful thing if we
could reproduce those qualities, but I don't think we know enough right now to
say that genetic cloning is the appropriate path.

------
shas3
Authors 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.

~~~
nsajko
Surely you meant to say 'Perelman', not 'Pearlman'. :)

~~~
shas3
I guess I'm allowed to correct _a posteriori_ , when my spelling evokes the
true 'Pearlman'.

------
overpaidgoogler
I met Terry in 2002. I had heard about him when I did the IMO training, but at
some point someone said he was in the department so I should talk to him. He
showed me some work he was doing related to what happens to the determinants
of matrices when you sum then. I remarked on how I was surprised at how
"elementary" this work was, and he replied that if math was really that deep,
no one would be able to do research. I suspected then that this work was
especially elementary and most research math was deeper (and thus more
inaccessible for an undergrad), but I appreciated the sentiment.

I wouldn't read to much into how "normal" Terry is portrayed as being. Terry
struck me as somewhat nerdy in his demeanor. Certainly not crazy or eccentric
(and as the above anecdote suggests, a nice guy) but also different from the
average person.

I say this because I feel like when people say "your don't have to be a weirdo
to be a great mathematician" this actually denigrates the personality type
that is common among most actual mathematicians including Terry.

On the other hand I do feel that all children should be given the opportunity
to grow and express themselves in all aspects of their life. It was nice to
see the positive and supporting attitude is Terry's parents.

~~~
darkmighty
Yea it bothers me a little too. Some people will actively put down anything
that doesn't conform the norm even down to your gait, as the reporter said,
and I find it really hard to accept this.

Mathematics is a matter of mental bandwidth: you're dedicating all your
attention to it, save for reserves to your kids and loved ones. Normal jobs
don't have this -- with the lack of more interesting things to think about,
you can spend your whole day thinking about other people and critiquing their
dressing, their gait, the way they talk, etc, which is all part of being
"normal" and is a set of really shallow conventions for me.

------
cschmidt
Since no one seems to have mentioned it yet, here is a remarkable photo of
Terry as a ten year old child, working on a math problem with Paul Erdos:

[https://plus.google.com/+TerenceTao27/posts/fiZbgKv4Yew](https://plus.google.com/+TerenceTao27/posts/fiZbgKv4Yew)

------
klenwell
The first paragraph describing Tao's musings on the explosive potential of
water reminds me of a singular experience I had not too long ago.

One evening I was going to pour myself a glass of lemonade. I put a otherwise
ordinary ribbed juice glass[0] on the counter, got a couple ice cubes out of a
tray in the freezer, and lightly tossed the first one in the glass.

The ice cube hit the rim and the glass shattered utterly. There was no piece
fragment left much larger than a small piece of gravel. I was stunned. I
thought for a moment maybe a sniper was targeting my glass from somewhere
outside in the darkness.

It seemed like a fairly sturdy glass. My hand wasn't more than a few inches
from it when I released the ice cube. The only explanation I could come up
with is the universe is essentially probabilistic and I had just witnessed
some kind of winning-the-Mega-Lotto-odds improbable sort of event.

My brother is a material scientist and I ran the episode by him next time I
saw him. He had a slightly different take on it. He said, "Glass is weird.
It's like water in some ways." And then he dove into some interesting
technicalities that I can't recall.

Closest I can say I've seen to water spontaneously exploding. Unless you count
this.[1]

[0] Looked sorta like this, but clear:
[https://img1.etsystatic.com/046/0/8523418/il_340x270.7059824...](https://img1.etsystatic.com/046/0/8523418/il_340x270.705982403_hx07.jpg)

[1] [http://www.surfline.com/surflinetv/featured-clips/worst-
wipe...](http://www.surfline.com/surflinetv/featured-clips/worst-wipeout-ever-
at-teahupoo_129724)

~~~
iglookid
Prince Rupert's Drop behaves similarly.

[https://youtu.be/xe-f4gokRBs](https://youtu.be/xe-f4gokRBs)

------
tokenadult
The 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](http://www.davidsongifted.org/db/Articles_id_10116.aspx)

[2]
[http://gcq.sagepub.com/content/50/4/307.abstract](http://gcq.sagepub.com/content/50/4/307.abstract)

[3]
[http://arxiv.org/PS_cache/math/pdf/0503/0503081v1.pdf](http://arxiv.org/PS_cache/math/pdf/0503/0503081v1.pdf)

[4]
[http://web.math.princeton.edu/generals/tao_terence](http://web.math.princeton.edu/generals/tao_terence)

~~~
wooderson
Terry did attend university at a very young age. He got his PhD when he was
21.

If he sounds normal in talking about his generals, it's because his peers are
some the best young mathematicians in the world (and about 4-5 years older)
and his evaluators are some of the absolute best mathematicians in the world.

------
retupmoc01
Tao's work on Navier-Stokes: [https://www.quantamagazine.org/20140224-a-fluid-
new-path-in-...](https://www.quantamagazine.org/20140224-a-fluid-new-path-in-
grand-math-challenge/)

------
IntoTheSwamp
Design question: Why do authors take nice sounding quotes from the text and
put them in large text aside the article? Is it to keep people interested, as
in the reader is thinking "This article is awful" and then they see an amazing
quote farther down the page and decide to keep reading? Maybe the writers at
nytimes have a picture quota and putting pictures of lines from the article
technically counts? Maybe WE as readers require pictures to stay interested,
and these large quotes somehow satisfy that need? I just get tired of reading
the same lines twice.

~~~
cschmidt
That's called a pull quote. Magazines have used them in print for a very long
time.

------
ajays
I 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...](http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html)

~~~
digital55
Though Zhang did get a profile in TNY:
[http://www.newyorker.com/magazine/2015/02/02/pursuit-
beauty](http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty)

And quite a bit of news coverage:
[https://www.quantamagazine.org/20130519-unheralded-
mathemati...](https://www.quantamagazine.org/20130519-unheralded-
mathematician-bridges-the-prime-gap/)

------
presty
> Tao became notorious for his nights haunting the graduate computer room to
> play the historical-­simulation game Civilization

Yay, I'm not lost!

------
comrade1
Finally, a child prodigy that actually continues with their talents into
adulthood, and also is socially adept, based on his education skills.

~~~
plonh
The 1986 magazine article linked elsewhere in this thread talks about the
great effort his parents put into cultivating his education+exploration
without pushing him into burnout.

It also helps that his field his math, where a person and their books can grow
up together without delicate social balancing.

------
guyzero
Clearly Tao's problem stems from having a singular mind. I have three of four
that I warm-swap overnight depending on what I need to do the next day. This
is only problematic when I get called into unexpected long meetings when I'd
loaded my Creative Mind the night before as opposed to the one that deals with
Unending Boredom.

Tao needs to expand his repertoire.

