The Singular Mind of Terry Tao | Hacker News Reader

The Singular Mind of Terry Tao

nytimes.com

218 pointsdctoedt41 comments

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...) 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.

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.

Sounds like he just needed a few math grad student editors. A real reason for a new edition!

> (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences)

This is the standard presentation in every textbook I have read.

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.

How is he weird? Just curious.

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

For anyone looking for a Real Analysis textbook, I’ve heard several recommendations for Pugh as an alternative to Rudin.

I used Abbott in college. The best math textbook I've ever read.

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...) 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...)

I had a less dark version, saying nature is a fair bitch. You'll fail but everything was under your nose from day one. You just had to explore the black space of ignorance, lighting it spark after spark.

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.

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?

I would venture to say 'yes', assuming that top-notch resources are given to the children.

Also, there seems to be a precedent: https://en.wikipedia.org/wiki/Repository_for_Germinal_Choice

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.

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.

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.

While I very much agree with the point you're making here, I don't known if Witten (assuming you mean Edward Witten, of string theory fame) and Einstein were the best choices. Einstein basically is THE stereotype of the aloof genius.

> Einstein basically is THE stereotype of the aloof genius.

'Aloof' is a subjective term and you are entitled to judge him that way if you want to.

I'll assume, 'aloofness' to mean that his thinking was confined to his work and that he lived by himself without much contact with the outside world (a la Pearlman).

The reality may have been the exact opposite of this, if you look at his biography. My main source is Walter Isaacson's book. Einstein was a humanist who cared much for the well being of humans. He was a social person by all accounts, forming warm relationships with people from all walks of life. As a youth, he was a keen student of music and philosophy, as evinced by his deep involvement in a study group with a couple of his friends. His personal relationships and tribulations (e.g. divorcing Mileva Maric and marrying his cousin) seem no more deviant than that of many normal people. He was a committed pacifist who campaigned for many issues by using his standing in society as an intellectual. He supported the Zionist cause, decried racism and bigotry, etc. He wrote many essays and expressed very clear and reasonable opinions on a wide range of topics ranging from the American society to nuclear weapons.

Compare that to Pearlman declining the Fields Medal and Newton dabbling with alchemy and occultism, which are both representative of fairly weird behavior. To reiterate, 'weird' by societal norms, which individuals may or may not be expected to uphold (unlike, laws).

It doesn't necessarily mean that his thinking didn't extend beyond physics or that his social contact didn't extend beyond his office. In this case it's more about an indifference towards social conventions, e.g., his famous messy hair which is now the definitive image of the mad scientist.

As for Witten, I just looked up a video of him on YouTube. One of the top comments, unfortunately very inflammatory:

"If Witten wasn't a mathematician he would have been a serial killer."

I supposed this is referring to his unorthodox mannerisms of speech.

(The video: https://www.youtube.com/watch?v=Y6b3DjOnv3I)

It's incorrect to label Isaac Newton's (1642 - 1726) alchemy as fairly weird for that era. Modern chemistry was invented during the same period. For example, Robert Boyle's The Sceptical Chymist, which argued that chemicals were composed of atoms, was published in 1661. It was not until the 1720's that the distinction between chemistry and alchemy was thoroughly established.

"The terms "chemia" and "alchemia" were used as synonyms in the early modern period, and the differences between alchemy, chemistry and small-scale assaying and metallurgy were not as neat as in the present day. There were important overlaps between practitioners, and trying to classify them into alchemists, chemists and craftsmen is anachronistic."

- https://en.wikipedia.org/wiki/Alchemy

I don't think popular culture is on your side. Even Time Magazine's biography of him describes him as aloof:

http://content.time.com/time/magazine/article/0,9171,993017,...

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

I guess I'm allowed to correct a posteriori, when my spelling evokes the true 'Pearlman'.

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.

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.

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

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...

[1] http://www.surfline.com/surflinetv/featured-clips/worst-wipe...

Prince Rupert's Drop behaves similarly.

https://youtu.be/xe-f4gokRBs

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

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

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

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

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.

Tao's work on Navier-Stokes: https://www.quantamagazine.org/20140224-a-fluid-new-path-in-...

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.

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

The need to fill story space so they have enough places to put ads, and ideally they fill that space without doing any expensive content creation.

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...

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...

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

Yay, I'm not lost!

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

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.

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.

Reply on news.ycombinator.com