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.
I think one thing that hurt me, in particular, is that I repeatedly got told "you're really going to go places some day!". And, so I waited for things to happen.
It took me way too long to realize I had to make things happen.
If you're reading this and you're young and gifted, you need to make things happen. You'll have people help you along the way, but odds are, you will never be discovered and have riches lavished upon you.
By high school, I was a 1.4 GPA student who was also on the Academic Decathlon team winning state-level medals. My upbringing was extremely abusive, which definitely contributed to the academic problems, but what I really needed was someone in my corner pushing me to explore and actually try. Being told I was smart wasn’t just useless, it was actively harmful. I became afraid to try and leaned on what came naturally (hence doing well on Decathlon tests) while consistently failing to finish things (no homework, no papers... and the GPA shows it).
What would have made a huge difference for me was being explicitly taught how and why to study, how to take and review notes, and how to manage my time. And just as importantly, someone consistently emphasizing that effort matters a lot more than being "smart."
Even now, I’m honestly surprised by how many people I work with in tech equate being "smart" with being good at math, algorithms, or pattern recognition, while seeming almost oblivious to some pretty big gaps in other areas. That mindset isn’t doing anyone any favors.
No, there's not, and they do do great. And this goes back to Terman: there's a handful of highly selected examples (eg the Australian kids recruited from child psychologist referrals, the self-selected self-diagnosed Mensa adult survey), furious anecdotes, and then every systematic prospective sample like Terman or population registers or SMPY shows the opposite.
And while Tao is, of course, exceptional, the results for accelerated gifted kids are generally great. And Tao was part of SMPY (note the URL path, supporting documentation for https://gwern.net/smpy ) and helped demonstrate this in practice.
I'm viewing on chrome from an Android device.
I'm trying to figure out what your certainty on smpy is.
Also thank you for your site. I read your n back analysis some years ago and found it to be very interesting.
Debating something is, as my grandmother said "the ultimate concession", you only ever really debate something if you feel that there is a chance you are wrong. If there is an impasse, and you are confident in your response, there is usually no reason to continue, especially when there's a teacher-student asymmetry, they take it personal, and you gain nothing but make an enemy out of your teacher and spend your "question" points.
There's only so many times you can interrupt a professor, and spending your question points on correcting them isn't very useful to a student. And that the student believe that on one ocassion they know more than the professor, does not mean that there is nothing to learn from the professor.
Both of these mistakes (overextending a challenge and conflating a specific dominance over a general dominance) I think often come together under a personality trait that is generally identified as "arrogance". I do think there's a middle ground between believing one is superior and dropping all contentions of giftedness, but it's a thin line, and I think it's especially notable when the difference in talents (between the student and teacher, or between the gifted child and the average) is very marginal anyway, if it's undisputable then most tensions dissipate with the clarity.
1: https://t3x.org/files/vidya_324-325_NH_reprint.pdf (on HN 2015, 170 comments: https://news.ycombinator.com/item?id=13145853)
It’s a lie many start believing, that they don’t put in effort.
I think it was very beneficial to have to work hard to catch up with more advanced classes. I feel flexibility around this is something parents and schools should take seriously.
(Tbf I was also super lucky to find a very accepting group of nerdy friends in the new year that would tolerate someone younger.)
oof, I felt this one.
I got suspended for three days, and also the enmity of his best friend the advanced social studies teacher. Yet, somehow I didn't get kicked off the basketball team. And I actually got a girlfriend, who punched me at the wrestling match, then we kissed behind the school during the dance.
I learned a valuable lesson that day.
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.
A boy in my high school class made IMO and got a gold medal (and later on won the Putnam one year). They interviewed his parents and it was a similar story.
More importantly, it's not as though individuals like Clements or Erdos was corresponding with Terrence directly to arrange a meeting. His parents clearly played an important role in facilitating and allowing these encounters. That deserves a lot of credit!
In contrast when I was a kid and was thinking about optimizing my program to print all prime numbers, my mother, instead of telling me about the sieve of Eratosthenes, told me to do school-approved math instead.
Now shoutout to my actual math teacher, who, having been told that I got stuck on writing a program to solve simultaneous linear equations, told me about Gaussian elimination.
With our society being ostensibly meritocratic regarding intelligence, people generally don't like to listen to stories that suggest that nurture and hard work aren't as important as they presume.
But I could be wrong. He is definitely a genius so maybe he did grasp the ideas rather early, like from 3 or 4.
Just the once, though, huh? [0]
He learned to read and write by himself. I'm pretty sure he would've been fine regardless of shape.
My problem was everything was too easy. I was bored. I would get reprimanded for not working because they gave us an hour worth of work, I finished it in 10 minutes and then did other stuff. I basically didn't have to study for anything, I just showed up and got Bs. If I put in 10% effort I got As. And all I ever got for it was yelled at for having done everything they asked me to do too fast.
So I started sitting in the back of the classroom minding my own business and trying not to be noticed. I'm convinced my life would have been very different if I hadn't been completely jaded from most of my teachers basically punishing me for being better than the rest. By my mid teens I didn't give a shit, I was happy coasting along doing better than the rest just by showing up.
My choices were my own and I'm doing pretty well now. Got my shit together in my late 20s and got a CS degree. Best decision I ever made. But I can't help but think I could have ended up on a path like this much earlier if my teachers actually supported me rather than treating me like a problem.
I was very 'school-shaped' if by school you mean I could sit quietly and read books and solve problems. More school-shaped than the other kids.
If by school you mean that bullies don't find you interesting, that nobody threatens to kill you, then I was not 'school-shaped' at all.
I was really excited to go to school on day one, within a year it tuned very bad and I wish, retrospectively, I'd had the courage to stay home.
- 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.
Not to say the results weren't incredible, but certainly required sacrifice.
https://www.gutenberg.org/files/10378/10378-h/10378-h.htm#li...
Most people who learn three languages as a kid are surrounded by other speakers, not books.
Especially when you actually know the language these kinds of people claim to speak and you realize they actually don't speak 7 languages but maybe know 2 or 3 fluently and know 'kitchen' versions of all the others. I'm not going to name names because I don't want an argument and don't have the spoons for it, but lots of these international luminaries and leaders and such with "speaks 7 language" are often little more than conmen or simply enjoy building their own little hagiographies for their own PR goals.
There's this wonderful deep-dive on youtube on Feynman's high-questionable personal mythology that is a great example of this kind of self-promotion and how easy it is to sell one's self, especially in academic and techie circles, if you have a certain amount of charisma and drive.
Also as a lefty, I'm also not impressed by breathless ambidextrous tales either as most lefties are forced to be ambidextrous and its not actually exceptional at all. I can write with both hands, play musical instruments either way, play sports either way, etc. The left hand is better at these things, but my right-hand is okay-ish at almost all these things and I use a right-hand dominant near everything in my life anyway. I even like to switch it up to keep wear and tear down. At work the mouse is on the left, but at home for gaming its on the right. This is all boring everyday stuff for lefties.
There's a toxic 'great man' mythology that humanity still can't get over and its weird seeing it taken seriously when so many 'great men' have been debunked or seen as recipients of the system they were under (Mills' father pushing him so hard and being in the privileged class that would allow all this instead of back-breaking farm labor all day). Personal talent is important but its vastly played up in dishonest ways for dishonest gains. We probably pass many highly talented people a day on the street, but only some had the opportunity to grow those gifts into something they can use.
The famous quote comes to mind. "I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." - Stephen Jay Gould
And this is utterly unremarkable where I live.
When we visit my family (who are all monolingual), they think she is a prodigy.
She’s not. She’s just a normal kid.
But if you imply that philosophy as such isn’t useful, it’s simply wrong, if not arrogant. Everyone needs philosophy.
"“However, by being so long in the lowest form I gained an immense advantage over the cleverer boys. They all went on to learn Latin and Greek and splendid things like that. But I was taught English. We were considered such dunces that we could learn only English. Mr. Somervell—a most delightful man, to whom my debt is great—was charged with the duty of teaching the stupidest boys the most disregarded thing—namely, to write mere English. He knew how to do it. He taught it as no one else has ever taught it. Not only did we learn English parsing thoroughly, but we also practised continually English analysis."
Even better if you can do both!
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.
I know many computer science colleagues who were not exposed to programming during that age and only later came to it.
I feel kind of lucky that somewhat randomly I stumbled into computer programming (because XtreeGold could show the content of files, and I was learning to understand BAT-files by looking into them) during that age, and that's what I do now.
There are probably a lot of things you were not exposed during that age, that could have been the perfect match.
There are also lots of kids who just play games, or video games, do sports, watch films or so during that age, without really being exposed to any "potential useful" activities. Some parents would maybe even say that this is how it should be.
As a parent, I guess a good advice would be to try to expose your child to as much things as possible, without forcing it to do anything of course.
So for him, as a video editor, it was using a tape recorder to record sounds, and reorganize them in an aesthetically appealing way. He didn't actually get into video editing specifically until after college IIRC.
It does't matter when the plug finds the socket - it is always electric.
As endearing as it sounds, that's pure selection bias on Walter's end rather than something even remotely common.
Clearly there are cases of this sort, like arts and other creative tangents, but on average it's a result of a discovery process much later in life.
And so the thing you were interested in at that age is probably similar to what you’ll be interested in now, if you remove social and financial expectations.
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.
I wonder how I ought to train up problem solving, given that I have an engineering degree to finish.
In the Dune books, they banned computers so they bred super mentally capable humans.
I think we’d be better off optimizing for conscientiousness or empathy, frankly. Even a world run by gardeners would probably be more beautiful and meaningful than one run by math geniuses.
(I do agree biological intelligence is not close to its peak)
The question is: what do we want to optimize for?
Minimize pain and suffering for humans? The spread of mankind throughout the universe?
I’m pretty sure your idea would help with the latter. Not so sure about the former tbh.
This is a real possibility in our lifetimes due to AI.
No, they couldn't. And neither could most adults, for that matter.
Innate ability is real.
It's hard to say whether the motivation came from the good skills (understanding, memory) e.g. "I'm good at this, I like it!", or that the good skills came from the motivation. I believe both are important though, and that they are intertwined.
As someone wrote here innate ability is a real thing
Any child who read maths textbooks with enthusiasm for 3-4 hours a day for years could in theory at least get close to doing what he did, but what kid had that level of motivation?
I think that is the main obstacle to most people doing highly effective work and putting in long hours. You hear some call people who don't 'work hard' lazy, but my impression is that it's emotional capacity, and a lot of that comes from family.
I wonder if there is a correlation between prodigies and emotionally stable, healthy, present parents. It's hard to imagine children under a lot of stress - e.g., from abusive parents, highly unreliable parents (e.g., overwhelmed by addictions to drugs), emotionally unstable parents (e.g., narcissists), highly neglectful parents (e.g., who abandon their kids) ... - it's hard to imagine those kids doing what Tao did, regardless of their talent.
> 320 print "(brmmmm-brmmmm-putt-putt-vraow-chatter-chatter bye mr. fibonacci!)"
I remember when I was 6 or 7 teaching myself Applesoft BASIC and writing programs with funny (to me) little print statements all through them - when computing was just exploding with possibility.
I wouldn't have had a clue what a Fibonacci sequence was though ;)
Was still a few years away from reassembly.
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.
Making mistakes in lecture is a standard technique used by good teachers, to promote active listening and critical thinking.
I think this kind of thing is extremely unusual.
Have you tried Dragon Box? I've had my son doing that for awhile. Parent reporting is lacking.
Also briefly did Khan Academy Kids but he's so far ahead that seems pretty useless now.
Disregarding the unusual age in this case, I believe that most people could be significantly better at mathematics than they are, if only they found it interesting enough.
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.
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.
Like Terence I also had "out of band" classes and free time to read advance material in both primary and high school.
During that period Australia also had good federal and state programs for clustering advanced kids on yearly subsidised specialist camps - optional and free if parents couldn't afford to chip in.
I bumped into him at the same time Paul Erdős was doing the rounds and hanging out with anyone that might show promise.
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.
And I don’t have the time, will and experience to guide mine.
Before becoming a parent I'd always thought "when I have a kid I'll teach him such and such" but now turns out that my kid just wants to jump around and break things.
I don't know, let me know if you want to talk. Mine is little over 4yo.
I guess parenting is a bit easier if your interests/work align with the kid’s interests. But if not then it’s going to be tough, because parents only have time to do one thing extra, so they either have to ignore the kids and do what they love, or forfeit what they love and do what the kids may or may not want.
And then most kids are average in most of the ways but have sparks here and there, so it’s again the question of “do I invest here for a bunch of money and one year or just skip for the next?”. My father was very into building me as a pianist and a math wizard from early on, neither of which I had strong interests in, but nevertheless I dragged on for many years. I think he gave up the Math part when I was in early middle school and the piano part when I said I don’t want to go to a music school.
I wouldn’t be surprised if I cost him a whole career. He was one of the top Mathematicians in my country back then but he didn’t publish much after I was born. All for what? I don’t want to repeat his mistake.
...
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...
The HN mods apparently have a sign in the HN control room
It's been [ ] days since the last Terrence Tao submissionI 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)
Ability to persevere is also wired in.
If you pull this thread to it's conclusion, then nothing is worth celebrating. Just law of physics doing their thing.
Case in point, that dance...
Society rewards 'good genes'. Which is interesting because it is effectively the club of good genes rewarding themselves by co-opting the ones without, either by amassing actual gold or by amassing gold medals. And we all let them because we recognize that they really do have good genes and they put in the hard work.
The problems arrive when the ones that are good at amassing actual gold and that are intelligent do not have a similar endowment in the ethics department. And weirdly enough we don't have a backstop for that unless they act in a limited number of ways that we consider 'criminal', usually reserved for the ones with 'bad genes'. So as long as they stay away from those we just look at the grit and the money and go 'that's ok then'.
And if you have amassed enough shiny rocks even those criminal laws seems to no longer matter and you can do whatever the hell you want and expect to get away with it.
Even among the people who have similar "luck" in that respect, some still stand out. The people we think of as elite performers aren't just elite relative to the 99% of us. They're also elite within the top 1% that makes up their field: they're dominant even among the people who should be their peers.
It's complex; first of all society has an interest for exceptional people to be respected and well compensated; if there was absolutely no prestige or compensation in being a math genius it's quite possible Terrence Tao would have become a schoolteacher. So a well functioning capitalist society has both monetary and prestige tools to incentivize extreme accomplishment.
Second, I think it's human nature to like and want hierarchy. Admiring figures for their looks, charisma or intellectual accomplishments could very will be in our wiring - 20 thousand years ago we would admire the shaman, the great hunter or the storyteller.
But ultimately I totally agree with you - not only were these people born into the unique genetic and envrionmental circumstances that made the accomplishment possible , I also don't believe they had any say after being born in becoming what they had become; e.g I don't believe there's a "free will" and that Terrence Tao "chose" to become a math genius. He was born into that reality in a fluke.
I just want to point out that this is most likely not true, and that this is cultural. The long argument you can find in the book "The Dawn of Everything".
In short, when the West came into contact with other civilizations, one of the most striking features of our culture from their point of view was how hierarchical we are.
We living on the same planet?
Pretty sure the supermodel gets infinitely more attention and certainly makes orders of magnitudes more money than some math prodigy, at least on mine.
We might as well chose to praise those of us who were gifted with abilities that we aspire to.
That being said, supermodels are more famous, have a much larger following and earn much more money than math geniuses. That says we, humans, care more about entertainment than value.
They can also produce a lot of damage unless they refrain to an extent.
There may not be many other things which can contribute the same advantage.
Too bad humankind is almost never paying attention.
He currently attends a normal school and I feel this a such a waste.
(not my kid).
That means in a generation there are ~ 10k such people in the world. Think about connecting them or nurturing them with AI companions.
The most important part of nurturing, as I understand it, is to be seen and loved by other humans, and to be made to feel safe and lovable.
Yes, let's give them only the blandest, most boring interactions possible.
Funny remark.
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.
Thank you
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.
I guess it's being one of the biggest geniuses in the history. Why people find it so hard to accept that there can be HUGE differences in intellectual capabilities and that parenting does not account for even 1% of that? I can bet that if Tao's parents did same things they did for him to 1000 of random children, none would come even remotely close to Tao.
His biggest talent though, I believe it's something more rare. He can get people excited about mathematics, make people dream and imagine.
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.
Some people appear to have a capacity for learning, retention and understanding that is well outside the normal range. People like Ramanujan or von Neumann, or Tao. They learn at a speed that far exceeds the speed of what we would consider gifted students, they reach a deep and intuitive understanding of the material, and go on to make many discoveries / inventions of which even one would be enough for an ordinary scientist to be considered successful.
It seems there is something very different about their minds, but just what is it that allows those minds to operate at such a level?