Since the discussion here focuses mostly on child prodigies in general, I'd note that there are many studies showing that the usual outcomes for gifted kids are not all that great.

I think the issue is that it's just harder to fit in. I remember being way ahead in some classes in middle school, and I actually ending up drawing the ire of some teachers when I had answers to every question (let alone corrected them). I eventually learned to disengage and just look out the window. But if you develop that attitude, you never learn how to cram in knowledge for tests, which actually increases the odds of failing some "less interesting" classes down the line.

Another problem that I've seen with a lot of really clever folks is that if you're told your entire childhood you're smarter than others, but you see these "others" sometimes get more successful, it's really easy to fall into profound cynicism. You never try anything and just undermine others on the internet.

Ultimately, stories like this are an exception, not a rule, even for kids who are truly brilliant. And yeah, it's easy to underestimate the role the parents play, mostly in creating the right opportunities and instilling the right way of thinking about the world. A child doesn't learn to play piano at the age of eight unless there's a piano in the home and a family member or a paid tutor to show them the ropes. Even for stuff like math, it's a parent's choice to buy the right books versus just giving the kid a smartphone.

As a father of an 8 years old, this is very moving.

While Terence is -without a doubt- born with prodigious abilities, I think credit should also be given to his parents Billy and Grace who seem to have managed to simultaneously nurture these special abilities while still letting Terence have a happy (?) childhood. This is not easy to do.

I just read this yesterday in Conversations with Walter Murch, a well-known film editor. Not exactly the same, but I do get the sense that Tao still feels the same way about math:

As I've gone through life, I've found that your chances for happiness are increased if you wind up doing something that is a reflection of what you loved most when you were somewhere between nine and eleven years old.

Interviewer: Yes—something that had and still has the feeling of a hobby, a curiosity.

M: At that age, you know enough of the world to have opinions about things, but you're not old enough yet to be overly in by the crowd or by what other people are doing or what you thinkyou “should” be doing. If what you do later on ties into that reservoir in some way, then you are nurturing some essential part of yourself. It's certainly been true in my case. I'm doing now, at fifty-eight, almost exactly what most excited me when I was eleven.

This brings to mind the childhood of John Stuart Mill:

- Learned Greek starting age three.

- Was studying Plato at age six.

- Studied Latin starting at age eight.

And more: https://en.wikipedia.org/wiki/John_Stuart_Mill#Biography

I guess it helps that he had Jeremy Bentham hanging around his house from an early age.

Incredible. Knowing about Abelian groups, being able to graph y = x^3 — 2x^2 + x in one minute, and performing integration at age 7. Chomping up university-level math textbooks by 8. A classical math prodigy.

I definitely empathize with "his preference for using an analytic, highly logical problem-solving strategy" (I'm not a genius ofc). It's often more immediately clear for me than visual/spatial manipulation.

Don't miss the program he wrote after teaching himself BASIC from a book at age six (Fig 5 / book page 222 / PDF page 10):

> 320 print "(brmmmm-brmmmm-putt-putt-vraow-chatter-chatter bye mr. fibonacci!)"

This really reminded me of the first part Flowers for Algernon. The main character undergoes a treatment which improves is intelligence and the story is narrated via a series of diary entries which become successively more fluent and sophisticated.

I know it must be obvious but this proves to me that biological intelligence hasn't nearly reached its peak. If we select for pure intelligence, biological brains can get much smarter. Imagine if we had 5 million geniuses as smart or smarter than Tao doing quantum physics. But life doesn't select for pure intelligence, it selects for survival.

In the Dune books, they banned computers so they bred super mentally capable humans.

At 8 years old I was able to expertly dismantle many radios.

Was still a few years away from reassembly.

Especially interesting since intelligence is much more environmental than most people assume: https://theinfinitesimal.substack.com/p/no-intelligence-is-n...

I found it very interesting that Terence Tao also did not like doing mental visualizations and preferred non-visual analytic methods (page 225). This strongly matches my own experience. I am also not a fan of doing visualizations in my head. I was once asked to do a visual test that’s similar to tower of Hanoi, and I just can’t do it visually, even though I have studied this problem when learning recursion and could formulate a solution easily analytically.

I like that test where some of the questions are wrong and wonder whether we should have that kind of thing in maths textbooks.

I think people need to be trained to be more confident in what they know, and if we gave them that kind of thing we could maybe train them to become so.

My brain initially parsed the title as an obituary title and I was really sad for a moment.

Cultivating that passion is an art. A modern tool which I've found great to let my kids grow their math ability is the game Prodigy Math. Worth checking out - it's fun (do math to gain spellcasting ability in the game) and gently pushes the envelope of what they can do. It emails parents with details on what math problems the child didn't get right and with sample exercises to address those areas. I have no connection to them other than being a customer.

I am interested in his new book, "Six Math Essentials", but I doubt it will be on my very low level of math understanding..

Loved this piece. Especially that it is written in a Gonzo journalism style, including the author as part of the narrative, like a Hunter S. Thompson essay.

How interesting that it describes "meeting Terence's special needs". In isolation, that sentence today would mean the opposite of what that person intended it to mean. For a bit in my childhood "differently abled" was the one people went with, but it seems that "special needs" was contemporaneous and just seems to have won. Differently abled does seem awfully obviously euphemistic.

I’d kudos his parents. The parents deliberately brought themselves out of the picture, but as a parent I know how hard it is.

No, I don’t mean it is hard to feed a kid and educate him a bit. That’s like at least 70% of the parents can do. What is remarkable is that they not only found Terence’s interests and nurtured on it, consistently without any major error. God you have no idea how hard it is. So many constellations have to be on the right places. And it’s definitely way more than luck.

For a starter, as a parent of a five years old kid, I always feel I failed and will fail my kiddo. I’m so unsatisfied with my own lives that my mind has to be focused on improving myself other than devoting time for anyone else, including my wife and my son. I know my son has some potential, just like pretty much every kid out there, but I didn’t, and won’t take the time to learn early education and use the knowledge to nurture him properly. I know he has some shortcomings that could use some guidance, but I don’t want to spend months, years to figure that out. I’m swarmed by my own thoughts and needs. That’s why I always tell my friends, don’t get a kid if you are not contend with life —- you won’t have the capacity.

And then there is the question of what to do even if I have enough time. Kids aren’t robots. They don’t automatically do things you want them to do, which is understandable. But when you have to fight for simple things in life, or fight with wife if you don’t always agree on certain things, God it’s such a mess that struggling to live like a normal human being is not a trivial task.

Anyway, I’m really glad that his parents brought out the best of him, and his brother’s too. They should be recognized for that.

I really wonder what motivates a seven year old to persistently work on that „one thing“ and not get distracted/bored. I guess he knew he was special?

I watched a video of Terrance Tao - https://youtu.be/ukpCHo5v-Gc?si=7MqSwDanZycSEVmm & noticed he speaks fast and assumed he must be high functioning.

Then realized, I mistook him for his Autistic brother Trevor. Trevor too is a mathematician.

Like others called out their parents must be great too. It is not easy.

> he entries marked with an asterisk (*) were to take place at Bellevue Heights Primary School (Year 5) and the others at Blackwood High School (year 8: General Studies, Year 11: Physics, Year 12: Mathematics).

So he was able to attend classes out of his own year. What country is this? USA? Is that normal in the USA? I think here in the UK this isn't possible.

What's his secret to eternal youth? He's 50 now but he still looks 25.

I would really like to know the origin story better. Accounts make it sound like Terence learned to read and arithmetic completely on his own by being plopped in front of Sesame Street.

That strains credulity. Those familiar with common Chinese parenting strategies know how involved and directly instructed they can be at times. How much of that has been downplayed (And for what purpose)?

I don’t mean to undermine any of Tao’s achievements. They are unassailable. But I genuinely want to know a true account of what it took to get him there.

Proving, that the idea that "no matter how good you are at anything there's some 8 year old who is much better" held true even before social media had to tell it to my face every day.

Wow, incredible read! Amazing what motivated peple (and children!) can achieve.

One of the most fascinating and moving writings I've read in my life.

Genuine curiosity: if you are gifted with a certain “wiring” (genes, brain chemistry etc) why is that considered an accomplishment? Also - We, as a society, tend to celebrate people with “natural didn’t really need to work for” type gifts quite inconsistently - eg A supermodel who is gifted with the gift of looks, beauty etc is also in the same category of “natural” talent but sure doesn’t get the same celebration as a prodigy in maths or science. In both cases the people are fundamentally bestowed with abilities they didn’t really have to work extremely hard to acquire but are perhaps looked at differently. What’s kind of psychology is at play here? Would love to understand how we tend to interpret such things and then form beliefs.

I realize and acknowledge both sets had talents and the spent thier time doing something with it to produce something extraordinary but we seem to tend to overlook the massive head start they also had. Why so?

(Totally understandable if you feel like downvoting but I would ask you to articulate and share the cord it struck with you if you down vote)

He’s on Star Talk this week. https://overcast.fm/+AAzXlUoaiV0

When will a SOTA model beat the best mathematician on earth? Similar to Chess and Go examples. It has to be getting close.

> Terence tends to read whole books rather than parts of books.

Funny remark.

I read this earlier today and was thinking: how many such mathematically gifted individuals exist I. The world at one time? Assuming there are probably 20-30 Tao-caliber people in the US and an adversarial multiplier of 0.1 (only 1 in 10 such kids are nurtured), we reach 300 for this generation, about 1 in a million.

That means in a generation there are ~ 10k such people in the world. Think about connecting them or nurturing them with AI companions.

Fun read. Math makes so much intuitive sense in his head.

I like this part very much:

More than three years after this episode took place, Terence, still a little boy, happily played hide and seek with his two younger brothers when the Tao family visited the Clements household. He is a happy, well-mannered lad who obviously loves and respects his parents and his two brothers. He gets on well with others, too. Mr John Fidge, his Year 11 Mathematics teacher at Blackwood High School for the first two terms of 1983, told me that after he had been attending the Year 11 Mathematics classes for about a fortnight he was accepted as just another member of the class. He is always willing to volunteer answers to questions asked by his teachers and was regarded as a friendly, humble, but very bright boy by his classmates.

Humbling.

I'd love to know what his true introduction to mathematics was. What books, etc. What created that spark and interest.

Well I was playing doom 2 and tinkering with old computers. Guess I ended up doing what I loved despite a brief stint where I fancied myself some big wig powerful broker on Wall Street having studied economics at uni.

I wonder if Terence agreed to have this published. This is an intimate look into the private life of an eight year old, written up as something like a lab report; it's not research on bacteria or monkeys or anonymous study subjects. It's possible that he did give permission, of course.

Interesting it's hosted on gwern...

I have watched some interviews with Tao as the guest. I must say, despite his insane abilities, he also seems like a down to Earth individual. I never have gotten the impression that he is arrogant or thinks he is truly better than anyone else. In fact, I have seen nothing but the opposite from him. It's quite a nice change of pace from some of the other elites in various fields.

Terence Chi-Shen Tao FAA FRS (born 17 July 1975) is an Australian and American mathematician. He is a Fields medalist and a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, analytic number theory and the applications of artificial intelligence in mathematics.[4][5]

...

A child prodigy,[18] Terence Tao skipped five grades.[19][20] Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of only three children in the history of the Johns Hopkins Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just eight years old; Tao scored a 760.[21] Julian Stanley, Director of the Study of Mathematically Precocious Youth, stated that Tao had the greatest mathematical reasoning ability he had found in years of intensive searching.[7][22]

Saved you a click...

He was a prodigy, but I believe the average American would be surprised that almost all classes in China have a person like him, or even more. Raw IQ, analytical and rational minds are common there.

His biggest talent though, I believe it's something more rare. He can get people excited about mathematics, make people dream and imagine.

For a split second I read this headline as "Terence Tao dead at … years old" and was shocked

I could have been just like him if I tried hard enough.

Okay, so? Has any of this research been used for anything? Or is it all nerd snipe set theory nonsense?

Fascinating read! And very interesting in the light of recent advances in AI to think about what makes this ability possible. How far can we go with increasing long-term memory and working memory? Does increasing comprehension follow with competence?

Long-term retention is is hard when encountering new symbols. He seemed quite comfortable at that age absorbing the new stuff and manipulating it. Where does that comfort come from? Is there a way to test that explicitly? Finally, there is the ability to take the new and use it well. What about creating new shorthand? Being able to divine hidden patterns and articulate them?

Ramunujam seems to have had this.