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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.

My experience was very similar to yours. I was definitely not prodigious. I was slightly gifted, for the most part, and exceptionally gifted in other non-notable ways.

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.

This comment really resonates with me (I’m old now, for context). I was put in the gifted program, but the truth is I wasn’t very good at math while I was wildly strong in language. I was a pretty solitary kid who read a lot of quality literature and was endlessly curious about the world. I ended up getting kicked out of the program early in elementary school for being "immature," but the gifted label stuck and I kept hearing how smart I was.

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.

> I'd note that there are many studies showing that the usual outcomes for gifted kids are not all that great.

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.

Gwern on that smpy site what does the O-like character next to certainty: log mean?

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.

Nils M. Holm's essays about highly intelligent people and IQ are worth a read here -- "Where Do The Failed 0.1% Go?" [1] and others [2].

1: https://t3x.org/files/vidya_324-325_NH_reprint.pdf (on HN 2015, 170 comments: https://news.ycombinator.com/item?id=13145853)

2: https://t3x.org/#essays

These stories are quite common. It just goes to prove that the point of modern mass schooling is just to corral the kids in and provide daycare, not really an education.

Exactly! 12 years of 'knowledge' half of it useless, the other half could be taught in 3 years--if done properly.

I was in a similar situation as the parent post and skipped/was moved up by two years of high school.

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.)

I think a big one you didn’t touch on is being told you do well in school because you are smart, not because you put in the effort.

It’s a lie many start believing, that they don’t put in effort.

Not sure that's true. I am by no means gifted in the sense of Terence Tao, or even people much more gifted than me but far less gifted than him, but I did well in school up to a certain point in college. I never really learned how to study until I got fairly far in my education process. I put very little effort into school up until that point. That's when I actually had to put effort in and it was quite a wake up call.

A trick I learned is to respond "Oh, ok", at a certain point.

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.

I finished my assignment in advanced 8th grade Math real quick, busted out MAD Magazine. Relatively quickly it was taken by Mr. P-------. Not missing a beat, aloud in class I said, "thanks a lot... asshole."

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.

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.

Can't find the reference but from an interview with his parents there apparently there wasn't much "nurturing" other than simply making available the necessary materials which he gobbled up. Its not like they put a made him practice for an hour a day.

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.

I think you might be underrating the value of even that enabling work. Some parents would not have the financial resources to provide those learning materials. And some parents would take a normative stance on how an 8 year old ought to behave.

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!

> I think you might be underrating the value of even that enabling work. Some parents would not have the financial resources to provide those learning materials. And some parents would take a normative stance on how an 8 year old ought to behave.

And most modern parents would swamp the child with a bunch of mind rotting auto playing TV and video games. There's an account of Terence's time at university where he nearly fails his oral qualifying exams as he spent most of his time playing Civ rather than studying anything. Imagine the travesty for the world if 5 year old Terence had been handed an Xbox.

He would just become a software engineer like the rest of us, and probably would have started google or netflix.

Yeah I agree, an 8 year old isn't setting up these meetings and correspondences.

I think beyond even having supportive parents, the most important part was that he had a parent that had a degree in the field that he happened to be a genius in. His mother knew exactly how to guide her child through the material, even if it just was to let him go off to a corner and read the books she guided him towards for 3-4 hours a day for fun. So many children have advanced proclivities for certain things and parents that just can't even see what it is their child is brilliant at.

Having someone that knows the path and can point it out to them is a beautiful thing to have as a child.

I think gene and characteristics are more important than knowledge and degree. I happen to have two parents who are both in education, one teaches in university and one teaches in middle schools. Because of this I also know many friends whose parents are also teachers.

Without any statistical significance, but nonetheless the sample size is greater than 5. None of us consider their parents to be great, or even good teachers. All kids squandered sometime after they are free from the parents, usually in universities.

This experience impacts me so much, that I have a bias that teachers should not teach their own kids.

A parent of mine was also a teacher, and other than grading their student's 9th grade math exams when I was in elementary school, I was on my own for most of my learning.

So I agree that yes, just having a parent who is a teacher doesn't necessarily get you much, outside of likely being in a home environment where school is deemed important (many don't have this unfortunately). But where things become slightly magical is when you have a genetically gifted child and a parent that both knows how to guide that genius and has the resources to do so.

Yeah, and can be worse if they are arrogant and thinks they know everything about teaching. That’s why I said characteristics is important.

Sure. But what about the parents who struggle every day with normally gifted children? They deserve even more credit. This seems like an easy child :)

One needs to be a (long term present) parent to understand these subtleties.

You also hear just the success stories which are often extremely marginal, when such approach wouldn't fit development curve of some other potential genius we would not be hearing their less successful story, would we.

Not diminishing the overall message, in 80s even in western democracies deeper info was not so readily available so its not like his parents just threw him wifi-connected tablet with wikipedia opened and that was it.

But I think what should be celebrated more is some proper hard long term effort and not just usual approach with exceptional results.

It is unclear to me what you are trying to say.

Apologies I am not a native speaker so sometimes more complex thoughts take long sentences to explain.

We are discussing his parent's contribution to his growth. Some, like me, tend to agree they just gave him (good) tools and he found his interest and way through and beyond due to superior analytical skills and overall intelligence, not through some super duper tutoring by them.

I have cca such cousin. He was way ahead of his class (which was already math-focused class from secondary school), geniune interest in deeper math, physics and philosophy from early age. Even very good at software development in old Pascal or C. Nobody was tutoring him in any way, he just went to public library and borrowed what he liked.

The stuff thats not hard but still counts as discovery and learning must be self-motivating in way more average folks simply don't experience, not with same topics.

His parents, as an old saying in my country, must have done a tremendous amount of good things in their previous life to be rewarded with an easy kid :P

That’s simply not quite true if you read the article. When Terence Tao got stuck on a continued fraction problem, his mother told him to use the quadratic.

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.

Agreed. It's been decades, but personally being acquaintances with IMO and IOI gold medalists made me rethink a lot of things.

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.

At the individual level of a newborn infant, all the genetic gifts collapse into a fixed quantity. Nurture and hard work (and self care and many other things) become 100% of the controllable factors.

Nurture and parental mental health are not controllable by the child, so those become fixed from their perspective as they grow to maturity. That still leaves a lot.

All the former G&T kids on here talking about whether they could have been this or that are likely discounting their own contributions that they made and make every day to their own trajectory.

No, you were never going to be Einstein, no matter what, but you can still be the best version of yourself- the kindest, the most capable, the happiest, the least resentful.

Maybe that’s happy talk? Certainly some people have been dealt a tough hand, and it’s an American naive attitude to think that can always be overcome. Sometimes it can’t.

> All the former G&T kids on here talking about whether they could have been this or that are likely discounting their own contributions that they made and make every day to their own trajectory.

I completely agree. I commonly see such sentiments online. People claim that if they were truly challenged more or had better resources, then they would truly become something noteworthy. However, I disagree with them after a certain point. If you need someone to coddle your abilities, then I would argue you aren't nearly as gifted nor talented as you may have been lead to believe. I am not claiming that only the truly talented will be able to white-knuckle their entire way through life on their own. Rather, I believe people contribute equally to their environment, which I believe is similar to what you were stating.

> you were never going to be Einstein, no matter what, but you can still be the best version of yourself- the kindest, the most capable, the happiest, the least resentful.

Tao himself would say that one does not have to be like him nor the best at anything to make a meaningful contribution towards something. I think the example he once used was a lot of the technology we currently have. Sure, perhaps some exceptional people designed it, but how many thousands upon thousand of people contributed to turning the design into an actual product?

> it’s an American naive attitude to think that can always be overcome. Sometimes it can’t.

While true, what kind of world do you want to live in? I rather go to the grave believing I had a chance versus knowing my destiny was essentially invariable. I believe that even ordinary people can be full of surprises given the right catalysts and circumstances. Maybe not Von Neumann level of surprises, but humans are pretty clever creatures.

It's still meritocratic even with dramatic genetic differences between individuals. A peer comment mentioned an anecdote of Terence nearly failing his orals because he ended spending all of his time playing Civ instead of studying anything.

It's basically the Gattaca story. Somebody can have the most brilliant mind in the world, but without actually applying it, they're not going to do great in life. If you give a person of average intellect Tao's life of dedication and work ethic, then he's going to end up a world class mathematician. He probably won't end up at the top of the top, as that's going to be reserved for those that hit the mega-lottery of genetics + dedication, but will also have no problem leaving his mark on this world and living a comfortable life.

"Dedication and work ethic" is almost certainly nonsense here. Some people do the activity a lot without having any ethic or dedication - they like it.

I don't know whether Terence Tao nearly failed because he spent all his time playing Civ.

But surely you're not going to mention this as potentially factual, and then praise his dedication and work ethic... right?

I seriously doubt a person with average intellect can become a world class mathematician, let alone a decent one. Just on grid. I have seen people in college that were tremendously hard working fail math classes and just not understand it. At some point saying they should just try harder is cruel.

If it's so easy to be a world class mathematician, why can't most mathematicians do it?

Which part of "lifetime of hard work and dedication" are you misreading as "so easy"?

There is zero, absolutely zero chance of the 50th percentile IQ becoming a world class mathematician. People who say this have no idea exactly how smart these guys are.

It seems like a bit of a pointless and unanswerable argument about semantics, the only bit is the irritating "ohh if it's SOOO EASY" about something that was definitely framed not to be easy.

If your cutoff of "world class mathematician" is a few hundred or thousand people, then no chance. If their cutoff is "earn a comfortable living" and the top 10% of the world is 800,000,000 people most of whom don't study mathematics, then can an average intellect with an obsession for math end up working a job a normal person might call 'mathematician' by working on AutoCAD or 3D rendering game engine or industrial statistics and process control or economics or vehicle aerodynamics and be in the top 10% of the world in mathematical ability? Possibly yes. And you can adjust the numbers and criterion to get a yes or no whichever way you like.

A mathematician is someone who creates or advances math. Not someone who uses math. If you don't understand how the word is used, that's your problem, not a problem with the statement.

>you can adjust the numbers and criterion to get a yes or no whichever way you like.

Good idea, I'll do that :)

>can an average intellect with an obsession for math end up

>working on AutoCAD or 3D rendering game engine or industrial statistics and process control or economics or vehicle aerodynamics and be in the top 10% of the world in mathematical ability?

I think this does happen quite a bit and the need for strong math in these difficult areas is so great that there will never be enough people as briliant as Tao to fill the positions.

That's so far outside the mainstream anyway, most systems are going to screen the rare person like that out without understanding why.

Now what happens when those having top 10% of ability are very excellent themselves, but cases come up that would yield only to a Tao level of "natural-born" problem-solver?

Nobody would ever know :\

> absolutely zero chance of the 50th percentile IQ becoming a world class mathematician.

Good, we don't need billions of them anyway.

I wish modern society would quit focusing on individual intelligence over collective intelligence. We can take something like the microprocessor, for example. The smart group that designed the microprocessor was not the same group that designed the software nor the group the built the parts nor the group the assembled the device. However, every group is equally important.

yes, 100%. But nature seems to be wired for competition, so we have the leftover genetic material even if it is to our detriment at this point.

>> people generally don't like to listen to stories that suggest that nurture and hard work aren't as important as they presume

Having grown up in australia but living in the us, this attitude is very american. It's quite funny to see when you don't grow up thinking it. I married into a very athletic family and have a child who is a precocious athlete. Many parents ask us what training regime or practice sessions we do. The answer is nothing. People don't react well.

So, what do you tell children that do well/poorly?

If you work at it you can get better. It's true in both cases. Getting better and getting as good as the very best are two very different things. One is about you. The other is mostly about others.

I don't think our society is even remotely meritocratic regarding intelligence. Maybe it is meritocratic regarding psychopathy.

We merely have a few pockets, where the very brightest are rewarded. However going from average intelligence up to those pockets, there is a ton of people, who are clearly more intelligent than most others. Much more intelligent than the typical lie-your-way-through-life people, who haven't shown any significant skill, yet are elected by the masses.

OK, this is making it political, but it's true in many countries, if not most. The truly very intelligent people rather focus on their area of expertise, where not many other humans are able to understand what they are doing or able to achieve a similar result. Similar thing happens in businesses. Talkers rise in the hierarchies, doers who don't self-promote massively remain low in the hierarchies, in most businesses. I don't see many scientists becoming millionaires for advancing humanity. We don't recognize great skills and smart people collectively in many cases. We chase silly trends and make-believe.

I could see "meritocratic regarding intelligence" somewhat in the way that smart kids don't have many problems at school usually, and then later at university, and then can maybe get a well paid job. But that's where the meritocratic system ends. In the job world it's mostly about other things. Like how well people fake being social with their higher-ups. Or how they have less worries about lying about their abilities. Or how they promote first and foremost themselves, rather than everyone, who significantly contributed to some achievement.

Hierarchies are promoted because they coordinate the work of large numbers of people and make them vastly more effective at scale. That's quite meritocratic.

Hierarchies are promoted because they concentrate wealth and power among a few people, who distribute it to a few people they more-or-less trust. It's just feudalism with less violent feuding.

That's a pointless observation though, the interesting point is that hierarchies manage to concentrate benefits because working as part of a functioning hierarchy makes even the individuals involved a lot more effective, to the point where they're better off even with much of the benefit flowing towards the top.

Do you have any evidence to back up that claim? I've never heard of any study that showed that cooperatives are less productive than hierarchies.

Even co-ops have hierarchy-style management, which is often professional management. It's just done on behalf of the collective membership instead of answering to a corporate board. (But the oversight is often weak in any such scenario, so the professionals involved can accrue significant benefits.)

The benefits of coordinated cooperation are called “civilization”.

While meritocracy in high dimensional humans is a muddy thing, as being capable, and being capable at what is actually needed often diverge.

But at the organization level, the benefits of strong coordination of the right things are clear. Virtually every business study, studies this. Virtually every political leadership study, studies this.

Cooperation has so many efficiency and effectiveness benefits. Institutionalizing the right kinds of cooperation, i.e. coordinating it, even more so.

This is the civilization superpower.

This is why billions of people can spend their days doing other things than food production, and can live in places with no food production in sight.

I don't disagree. That's why I qualified my statement with "ostensibly".

But being really intelligent, at least for the top 1% or so, is often advantageous enough to offset any disadvantages from your class/cultural background etc.

I also wonder whether your "psychopathy" is just "ambition". After all, while intelligence alone doesn't guarantee anything, "intelligence + ambition" takes you quite far.

Personally, I can see how even an honest-to-god meritocratic society ends up with psychopaths at the top. For most people with normal-ish psychology, the risks and stress that comes with being on top of anything high stakes is just too much.

Please elaborate

We pressure our kids into grit, but genius comes from the inside.

Be grateful when it happens, but be happy if it does not.

Laszlo Polgar would disagree [1]. He contends that raising a genius is something you can actually target intentionally (whether or not you should). His proof being 3 daughters who became GMs and one that was a generational talent. As far as audibles go, that’s quite a flex. Yes, the daughters are not all equally talented and chess isn’t quite the same as math, but we’re talking about gradiation within an achievement only reached by much less than 1% of all active players. To me that’s genius level. Also, it’s not necessarily an accident that the youngest is the one to have attained the best result. Evidence is quite clear that older siblings can help their younger ones achieve more faster because the younger ones see it as a path to follow/if they can I can.

[1] https://slatestarcodex.com/Stuff/genius.pdf

Even if you disregard the anecdote (n=1) thing, it's quite obvious that genius has a genetic component to it, and the father being a good chess player tilts the odds in his favor quite a bit.

Also, the idea that chess is a good proxy for genius is a bit out of date.

Laszlo was casual amateur at chess, and it's an n=3 sample at least. Though one sister 'only' made it to IM, but that was likely more due to social reasons. She decided to get married, have a family, etc rather than continue on with chess as actively as the other sisters.

Yes, but that kind of aristocratic tutoring is not scalable to the bulk of the population. You need the equivalent of deep PhD expertise in every subject to accomplish that, and even AIs are nowhere close to that level.

That showed that you can be the best at something low value if you spend more than it's worth.

Most of the people so could be chess grandmasters are busy applying their brains to something else.

That's just utilizing potential already present there and nurturing it far, the father was an established chess player and university professor and their mother is probably in similar range. Sure, it works, why would anybody argue against or find this shocking or relevatory?

Try the same with babies who are already visibly not the brightest (say in kindergarden group), their parents are also average or worse regarding intelligence. There is a ceiling, it may be high or not but its there. If you haven't experienced it in your life you are one of lucky few (and certainly didn't push yourself hard enough to sense it).

Same goes with memory - you can train it far, use various techniques. Then comes somebody natural (yet still far from what we would call genius) who didn't bother with any of that and immediately surpasses whatever was achieved. We are not created equal and all have hard boundaries, be it health, cognition, body regeneration and so on.

> the father was an established chess player

Where did you find this information? I haven't been able to find any source that states he was above an amateur level.

Data point: my comment prompted different reasons for why Polgar was successful: it’s genetic, he had time to spend with his kids, he was a professor, his kids all happened to be gifted, if you go to a kindergarten class you’ll already see kids that aren’t bright. Clearly more comfortable for explaining away because it forces us to look at why maybe we aren’t geniuses or our kids aren’t.

> Same goes with memory - you can train it far, use various techniques. Then comes somebody natural (yet still far from what we would call genius) who didn't bother with any of that and immediately surpasses whatever was achieved.

It’s always hard to compare how much effort and for how long they’ve been applying it between people. Someone starting earlier can make them seem like a genius. Someone who spent time developing their memory through various games may feel like they spent no time on it and “it’s natural” while someone else had to explicitly work at it instead because they never were encouraged to play memory strengthening games.

> We are not created equal and all have hard boundaries, be it health, cognition, body regeneration and so on.

Thats true, but the same was said of height but height only became 90% genetic once we fixed nutrition. I see no indication that our systems of parenting and child rearing are robust enough to make intelligence and academic outcomes purely genetic. It’s far too chaotic and you need to apply consistent effort daily almost from birth before the intentional learning stuff even happens. Making sure the mother is in good physical shape before birth, taking all the supplements before and after birth, limiting exposure to toxic stuff, making sure the baby is getting a good mix of engaged play, time to be chill, and exercise, making sure both parents are able to keep the child engaged and studying and understanding of expectations, adjusting the environment appropriately as they develop so they’re constantly challenged and enjoy and seek out challenges, that’s it’s emotionally and psychologically safe for the child, riding the balance of a little bit of frustration and recovering from that vs no frustration or frustration without a break, etc etc etc. a bunch of that happens before you start academic play to teach verbal and math skills and each of these is an add on (eg we know physical education is important for brain development).

Data point: I was at a prenatal class and after the nurse said marijuana isn’t good for the baby, one of the parents was asking “but like what’s the actual limit before it’s harmful”. So don’t be too sure that “surely kindergarten is early enough that kids are still on equal footing”. Another data point is I know a parent that has a 4 yold that doesn’t know how to read nor write because “he’s stubborn” nor is he going to preschool. Yet every parent that I know of that’s applied effort has their child typically by 2 or 3 and writing by 4/5 which is when basic math should already be going.

Nowhere did I state that there aren’t natural limits. But I also think academic achievement isn’t 90% genetic - there’s plenty of “naturally gifted” people who go on to not achieve anywhere as near as much as those who just work - perseverance trumps almost everything and environment trumps that because that’s how you learn perseverance.

The closest to the truth for Polgar is he had time to spend with his kids, but mainly because he prioritized doing so in a way to help them grow. Also, he did so with help from his wife. He wasn’t a chess prodigy. He chose chess because there was a clear demonstratable progression that a) could be used to demonstrate his theories b) his kids had immediate feedback on success c) could repeat the game endlessly to try out various tactics d) they studied chess as a family.

I agree, not every child can become a genius. Most of the reason for that today is less because of a learning disability or “physical limits” and more because of the environment the children are raised in (and the need to teach them perseverance and to keep trying regardless of how others are achieving).

I think they deliberately underplayed their role in this. Especially with Asian parents who think such nurturing is part of the "norm". I wouldn't be surprised that they spent TONs of time tutoring him when he was young -- and when he was more or less self-bootstrapped they don't need to spend too much time.

But I could be wrong. He is definitely a genius so maybe he did grasp the ideas rather early, like from 3 or 4.

> and later on won the Putnam one year

Just the once, though, huh? [0]

[0]: https://news.ycombinator.com/item?id=35015#35079

Hehe, that one will never die. It's the comment that more or less defines HN.

In my house we discuss a macro feature of children as being "school-shaped". If Terence Tao wasn't school-shaped, would he have been as successful? The counter-point to that is to ponder how many children fail to achieve a similar level of success because they don't fit into the school system so are left by the wayside.

> If Terence Tao wasn't school-shaped, would he have been as successful?

He learned to read and write by himself. I'm pretty sure he would've been fine regardless of shape.

And that's probably the opposite of being school-shaped. School is hellishly boring if you're ahead of the curve.

That's a specific school problem. I think being school-shaped is not about being bored, but more about being willing to do tasks on a schedule and can learn a lot of material through a lecture style.

The pdf linked seems to disagree with your assessment, at least for Tao.

Agreed. But generally it very much depends on the school and the effort of those in and around it. Terrence was very fortunate to have parents who supported him and likely lobbied for his unconventional high school/primary school split education, and equally fortunate that his schools were able and willing to accommodate him.

At that age I thought it was perfectly normal, just not universal.

What sticks in my mind from the pre-school Mad magazines was the mascot philosophy; "What, me worry?"

There is the ideal of school and then there is school.

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.

Where I grew up there wasn't any way to deal with those of us who did better. If you did worse there were all sorts of programs, they would move you to a separate small class so you could get extra help and stuff like that.

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.

> 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.

It's interesting you raise your teachers / organized schooling when Tao's parents were cited earlier in the thread for providing him materials.

Where do you see mothers and fathers stepping in (or not!) with children of greater ability?

My parents did provide me with materials. They were happy to buy me books and stuff.

But school is where I spent most my time and did most of my learning. My single father had enough to deal with, working full time alongside being a farmer. He isn't exactly an academic. He did what he could. The school system failed me massively. Both in not supporting nor encouraging my exceptional performance, and in ignoring my bullies even when they walked in on it and when I told them about it.

Thanks for sharing, I appreciate how hard it can be to revisit challenges from our youth.

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.

I wonder a bit about that. What activities or possibilities are you exposed at during that age.

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.

Murch actually expands on that a little more in the interview. He doesn't mean the specific activity is what your job should be, it's more like "the basic similar activity."

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.

I first touched a computer after completing my university degree and I still remember the happiness I felt by simply running a DOS command and seeing the expected output.

It does't matter when the plug finds the socket - it is always electric.

> when you were somewhere between nine and eleven years old.

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.

I don't think Walter is implying anything about how common or uncommon this is. His core insight seems fairly objective and plausible to me: "...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". I.e. if you do end up being lucky and wise to do something as a profession closely related to what you *loved* doing when you were ~11 , because you end up spending time doing what you love (and equally importantly not spend that time doing something that sucks up energy) you increase your chances of being happier.

I think you completely missed the point of his anecdote. It’s not a scientific study, he is merely saying that at age 9-11, you’re old enough to have a decent understanding of what you’re interested in, but not old enough to start worrying about social and financial pressures and expectations.

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 wonder if you could test this. Maybe someone has a longitudinal study where they check what people thought they liked to do as kids against what they do as adults.

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.

This was mostly down to enormous pressure from his father, causing him to have a breakdown in his early twenties.

Not to say the results weren't incredible, but certainly required sacrifice.

https://www.gutenberg.org/files/10378/10378-h/10378-h.htm#li...

J.S. Mill's autobiography is a fascinating read. He spends quite a lot of it discussing his early childhood, explaining that in his opinion he was not particularly special, rather, it was his father who pushed him to all those accomplishments. His father sheltered him from other kids so he was not aware that his accomplishments were unusual!

I learned to read at age three or four, I think and I consumed every book I could find, including various math books, old chemistry books, etc. I didn't really understand anything there, but it was just fascinating to me to even touch that knowledge. So I'm a bit skeptic about these stories of children studying Plato.

Talk to an average college freshman that studies plato and you might be similarly disappointed

Learning three languages at an early age is completely unremarkable for millions of people around the world. It's just notable which ones his were.

It's notable if he learned Greek and Latin from books. Being classical languages, it sounds that way.

Most people who learn three languages as a kid are surrounded by other speakers, not books.

His father who oversaw his education and possibly both parents, and Bentham that played a role in his education as well, would have known either Greek, or Latin or both as they were considered essential to a rounded education at the time.

I learned two languages growing up and was speaking both as soon as I could speak and could write in both not long after. This is typical for nearly every kid in the world outside of countries with strong language monocultures. I certainly think Mills was a very talented person, but there's this weird cult of being impressed by "speaks 7 languages" hagoigraphies which aren't helpful. People bring up it as some acid test of intelligence and its just not very accurate.

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

My daughter spoke four languages at age 3. Not because she is gifted, but because she grew up in an immigrant environment. One language with me, another with my partner who speaks a different mother tongue than I do, and the two local languages where we live.

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.

Learning by immersion is a completely different process from learning by being tutored, never mind learning by oneself from books.

Latin and Greek are classical, 'dead' languages.

Latin/Greek were considered part of the core curriculum for a well-rounded classical education in the upper-class for hundreds of years (some degree of retained proficiency wasn't unusual in graduates of the elite schools in Britain even through the mid 20th century). Not spoken as a primary language, sure, but far from "dead" in education.

Latin was required for philosophy, law, rhetoric, and the classics. Greek skewing more towards the sciences, logic and also philosophy. One would be constantly encounter Latin/Greek in their materials and not just as a obtuse code to memorize like how a modern biology student typically views e.g. binomial nomenclature today.

So when viewed through the 21st century lens of English dominance throughout education, it loses the context that makes it much more understandable why and how a young student, especially a precocious one, would pick up those languages specifically in the course of their tutoring, reading, etc. (And not as some kind of genius parlor trick as modern retellings tend to portray it).

Latin was the common lingua franca for scholarship even into the 18th century so studying the classical languages was genuinely useful, not just a parlor trick. It's the equivalent of a modern child prodigy in a non-English speaking country learning English as a young age to access present-day research.

In the time of J.S.M. they were languages used by academics and upper classes regularly enough that in his circles he and many of his peers had early exposure.

Hence that scene in Monty Python's Life of Brian.

Still fun today: https://www.youtube.com/watch?v=Mip30YF1iuo

That there are no native speakers doesn't mean there are no tutors that speak it.

Learning by immersion is still a very different process from learning by being tutored. One is something that young childrens' brains do almost entirely subconsciously, the other is conscious academic work.

His book 'On Liberty' is the subject of a recent In Our Time episode (BBC Radio Four series on the history of ideas) [https://www.bbc.co.uk/programmes/m002pqnc]. They discuss his childhood and his (apparently very warm) relationship with his father. (Sidenote: first proper In Our Time episode with the new host; he seems fine, but I miss Melvyn Bragg.)

Didnt he went through a major burnout and depression because of that? I remember reading something like that.

And imagine what he could have done if he had done something useful at such a young age!

Knowing Greek, Latin, and Plato is very useful for a philosopher of his times. I’m far from being a fan of Mill’s contributions but he aligned himself well with the western history of philosophy.

But if you imply that philosophy as such isn’t useful, it’s simply wrong, if not arrogant. Everyone needs philosophy.

Unusual to study Latin before Greek. It's usually the other way round.

Tangential but am reminded of Churchill's comments" "And when in after years my school-fellows who had won prizes and distinction for writing such beautiful Latin poetry and pithy Greek epigrams had to come down again to common English, to earn their living or make their way, I did not feel myself at any disadvantage." and

"“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!

Great quote!

Your final sentence seems a bit odd in that context though: Churchill's point is that Latin and Greek actually isn't useful at all, so it would follow that it isn't better to do both (i.e. study the classics as well as English), especially as time to learn them would have a huge opportunity cost, e.g. you could use that time to study more English composition instead.

(If you think they're worth learning just for their own sake then that's another matter, but the quote seems to imply that Churchill wouldn't agree.)

Latin was a lot more common than Greek in schools in the UK. But even that tended to be private schools after the sixties and seventies. Greek was a subset of that.

I was lucky, I had two or three excellent English teachers. Very inspiring and helpful. I wish I could say the same about mathematics (most of my teachers were terrible and one didn't even teach us how to do the problems)... Or my French teacher. I think we spoke better French than he did at the end. Since I spent a lot of my childhood in rural Scotland I was effectively bilingual anyway.

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.

Curious. I admire the analytic side since it's what I consider myself personally weak at. I have always preferred visual and spatial problems (then again, I spent a long time playing with Lego and making things).

I wonder how I ought to train up problem solving, given that I have an engineering degree to finish.

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.

Had me in tears by the end. One of my favorite books. So glad a friend recommended it to me.

I read it decades ago, and from time to time I mention it to someone who has not read it and I end up telling them the story.. and I'm usually tearing up before getting to the end. Such a moving piece.

Next time think of it as a story of a nice guy, who turns into a jerk, and at the end he's a nice guy again.

We had to read it in middle school and man did it have me in tears at the end.

Good book, but the film is underwhelming. Saw it fairly recently for the first time.

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!)"

That program listing hit me right in the feels.

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 ;)

This does feel like something a super smart alien pretending to be an 8 year old would write.

Sometimes I wonder if HNers have met more aliens than 8 year olds.

Most 8 year olds haven't met any aliens.

Many have, from their perspective.

Found myself counting characters in case there was an easter egg in there. Spoiler: there isn't an easter egg in there.

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.

Physics is not stuck because we don't have smart theoreticians who have good ideas: it is stuck because we don't have big enough particle accelerators and detectors to distinguish correct from incorrect theories.

Sure. But it doesn’t really seem clear to me that selecting for intelligence actually results in a better world. It’s a fallacy to think that intelligence = more rational or immune to human flaws, as a cursory glance at any “intelligent” social group should make obvious.

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.

Intelligent people tend to reproduce a lot less than other people. You wanna be average (or slightly above) for the best chance at successful procreation. And hyper-intelligent people are especially bad at procreation.

it's been a while, but I think mentats in Dune are trained not bred. Also, they use mind enhancing drugs (sapho juice IIRC). Which I guess makes a interesting point too, though different from yours :D

(I do agree biological intelligence is not close to its peak)

There is a slightly unexplored tangent in Brave New World about an experiment on Cyprus, where a society of humans bread to be intelligent descended in to civil war because nobody wanted to do menial work.

This is the theory of Elite Overproduction

Interesting thought experiment.

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.

Strictly speaking, evolution selects for viable offspring, not simply surviving. But that’s a nitpick, quite beside your point.

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> Imagine if we had 5 million geniuses as smart or smarter than Tao doing quantum physics.

This is a real possibility in our lifetimes due to AI.

Careful, we live in a society which has taken a side in the nature vs. nurture debate and if you're deemed to be on the wrong side of that then you'll be accused of being a nazi

Not sure it works like that, I think his biggest superpower was intrinsic motivation. 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?

> 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

No, they couldn't. And neither could most adults, for that matter.

Innate ability is real.

> No, they couldn't.

Isn't that a bit too certain for something that's not settled at all? How else would you explain the Polgar sisters? I'm sure there are other examples, but this is the most famous one.

Few claims in the social sciences are more fully settled. I don't think you could find a researcher in the world at a major university making that claim that randomly selected children could be reliably turned into world-class mathematicians with enough training.

> How else would you explain the Polgar sisters?

Genetics is the obvious explanation. The father was clearly very intelligent.

Also to clarify: I agree that training and effort can have large effects, and that focusing on them is a good strategy. Over-believing in them is probably a good bias, even. But the idea that everyone is more or less the same except for effort is ridiculous.

I simply disagree. Yes, they could. Same with adults. Basically no one does.

Also I didn’t say innate ability doesn’t exist. But in my opinion is a small multiplier on top of effort. That’s why I said close to.

As a TA, I've seen adults try to pass initial college calculus many times (and failing - you were allowed to try several times) with enormous effort. It's not a small multiplier

And this was still people selected from the small subset of the population choosing an engineering major. Human are much, much more different than you seem to think

There are many, many people (math majors, competitive programmers, chess players, etc) who devote incredible effort to becoming better, and simply cannot reach elite levels. And while in most cases elite players are also putting in a lot of effort, there are many cases where it is still relatively less than their peers who are trying harder but still lagging them.

Would you ever be tempted to make such a claim (that everyone is close to the same in ability and effort is the main determiner of success) about athletes? It's so obviously untrue that it's laughable. Why would you think that mental ability is magically distributed evenly?

> Would you ever be tempted to make such a claim (that everyone is close to the same in ability and effort is the main determiner of success) about athletes?

Well yes, absolutely. People don’t do quadruple axels on the ice because they were somehow born with the ability, they can do it because they practice figure skating every day for years. Innate ability (or in this case, let’s be honest, mostly genetics determining body shape) certainly makes the difference between becoming an Olympic gold medalist and just being very good at the sport, but you need to get very far in the field before it truly holds you back.

I don’t have a lot of experience with high-level professional sports, but I’m a classically trained violinist, and I’ve seen first-hand how a lot of the abilities that many people chalk up to “talent” (sense of rhythm, perfect pitch, composing music) are just skills that can be learned. Some students might need to practice more than others, sure, and some might reach a higher ceiling, but I firmly believe anyone can reach a high level with applied effort.

“I don’t have the talent to paint so I won’t learn to do it” is a self-fulfilling prophecy.

> People don’t do quadruple axels on the ice because they were somehow born with the ability, they can do it because they practice figure skating every day for years.

You've changed my claim. My claim isn't that world-class athletes, or even good athletes, don't have to work hard because of their talent to achieve elite levels. It's merely that talent is a huge determiner in success. It's also a huge determiner in how effective training is. An hour of training might improve a talented person 5 or 10x more than an hour of training would improve someone else.

This is all blindingly obvious if you've seen a sample of kids growing up. I remember the sister of one of my daughters friends, at age 3, was easily out-performing her brother and my daughter, who were a couple years older. This little 3 year could fearlessly climb up jungle gyms with ease, and kick around a ball, and swim fast. She hadn't practiced more. She could just do it.

That's probably why some competitions are called Math Olympics.

OTOH maybe there is no posibility whatsoever that genetics can determine mind shape no matter what.

Your post reads like someone is bitter because he is a midwit

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The important factors seem to be intrinsic motivation and other good mental faculties like great memory for concepts and formulas, understanding.

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.

I actually agree with you on the first part, that is his super power is more on that persistence. But I’m not sure about the second part.

No .. not really. Not even close. Just like even if I practiced music 8 hours a day I wouldn't be able to come up with the music Kurt Cobain has or Mozart. There are plenty of musicians who try really hard but lack the innate talent - at best they can learn to play other people's music but never can come up with good original music, at least not something other people want to hear.

As someone wrote here innate ability is a real thing

I think you’re confusing mastery with marketability. “Other people want to hear it” is at best adjacent to someone’s skill at composing or playing music.

There’s plenty of mediocre musicians who became world-famous, and plenty of great musicians who nobody’s heard about. Skill and success are pretty weakly correlated.

> I think you’re confusing mastery with marketability. “Other people want to hear it” is at best adjacent to someone’s skill at composing or playing music.

This is a fun and complicated topic. Yes, sometimes things outside of the music influence our perceptions of the music. If the Red Hot Chili Peppers were a bunch of bald fat dudes maybe they would have had less fans; if Kurt Cobain hadn't killed himself he would still be a legend but perhaps in the calbire of Eddie Vedder and not what he became. But the following underlying principal I believe to be true : it's impossible to survive the test of time in music without producing "good" music. Example of music that survived the test of time : The Beatles, Queen, Pink Floyd and I'd argue Nirvana, Pearl Jam etc. How do I define "survive the test of time" is another discussion I'd rather not get into lol.

I actually think you could. If you’d done that, with enthusiasm* - and not just practiced but guided, trained practice, you 100% could.

whatever helps you sleep at night, brother.

  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 don’t say everyone has the same mental ability. But I stand by my point. Those people you mentioned might be dimwitted in part _ because_ their lack of enthusiasm for learning is low, so they didn’t do it. I don’t care how smart you are, effort matters.

Yeah, Fermi was such an unmotivated slacker.

Relayed by Nick Metropolis: Fermi and von Neumann overlapped. They collaborated on problems of Taylor instabilities and they wrote a report. When Fermi went back to Chicago after that work he called in his very close collaborator, namely Herbert Anderson, a young Ph.D. student at Columbia, a collaboration that began from Fermi's very first days at Columbia and lasted up until the very last moment. Herb was an experimental physicist. (If you want to know about Fermi in great detail, you would do well to interview Herbert Anderson.) But, at any rate, when Fermi got back he called in Herb Anderson to his office and he said, "You know, Herb, how much faster I am in thinking than you are. That is how much faster von Neumann is compared to me." [0]

[0] https://news.ycombinator.com/item?id=39965802

There is a massive body of research showing this is not true

I think it has to be both. You need some ability to understand and thus find happiness in the thing that you are reading which leads to the motivation.

Yes, the “with enthusiasm” bit is very important.

That's why I loved comic books.

There are probably hundreds of people on this site who had the same enthusiasm for math and time dedication as Terence Tao, but lacked his extreme outlier fluid intelligence, processing speed, perfect memory, and even handwriting talent(!). Terence Tao mastered calculus at an age when most future-mathemician geniuses weren't yet strong readers of chapter books.

Another requirement is the emotional capacity at 8 years old to focus, feel confident, and feel safe.

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.

Yes the correlation is there but it doesn't really matter. There are hundreds of millions of kids growing up with stable healthy parents and a handful of prodigies.

There are a only handful of prodigies regardless of what we're talking about, but I think that is a misguided way to look at the situation:

If my GP comment is true to some significant degree, it matters for people who are prodigies. It matters for the world, which benefits from the prodigies.

But I don't want to underemphasize the first or overemphasize the second. These are human beings, which is the overwhelming issue. They have the same needs and same importance as everyone else. That means we don't want to disregard their needs either because they are unusual and therefore more expensive to nurture, or because the world benefits from them and and doesn't care about their individual needs or thinks their needs can be sacrificed.

And on a similar basis, it has strong implications for all the other kids in the world, who need stable, loving, nurturing family.

Very true! Lots of things had to go right for Terrance.

I take it you've never met another human before

This can descend from a hive-mind of not ever giving credit to anyone different than themselves.

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

Was still a few years away from reassembly.

At 8 years I recycled filesystem directories. I didn't know you can create new folders, so when I needed one I grabbed a random one from C:\Windows, moved it to my desktop and deleted its contents.

Makes total sense, it used to be called "Recycle Bin" after all!

I wonder if Microsoft did focus group testing and found understandably computer illiterate people were concerned about "trashing" files meant they were somehow permanently using up HDD space

Worked ok til it was a system dir and the system wouldn’t boot anymore? :)

No better way to learn System32 folder was essential is Windows than by destroying your family computer by removing it.

I deleted the files from there to free up disk space

I don't need autoexec.bat or config.sys! it's got some garbage in there that I don't understand, so it must not be important.

When I was a boy all we had were high-voltage vacuum tube electronics, it was fun.

I was doing that at three or four and was reminded of it constantly for the next ten years or more. (I actually raised the subject on my mother's death bed.)

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.

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

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.

Actually - do they do this in LLM benchmarks? As a measure of overconfidence/confabulation? Seems immediately applicable.

"incomplete information" is a standard concept in word problem curriculum. But usually it's explicitly an option in the test, as a fairness to the student.

Making mistakes in lecture is a standard technique used by good teachers, to promote active listening and critical thinking.

I didn't see that in the document. What page is it on?

I think they mean at the bottom of p216 (pdf page 4), where he says he doesn't know, r+s=80 but there isn't enough information to solve for r and s.

There's two questions that are intended to be wrong (probably to test confidence). One with insufficient information and where the question itself implies falsehoods.

The questions are on page 215 (3/26) and Tao's answers are on the next page.

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.

This brings back great memories of a game I played as a kid called 24. Not so much modern, just cards with four numbers that you would add, subtract, multiply and divide to get the center number. Then you would slap the card and explain. It did something to my brain as even the thought of those cards makes me smile.

Hey thanks for this recommendation I'm going to check it out.

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.

We haven't tried Dragon Box. Thank you for the recommendation, we will check it out

The music in that game is sublime

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.

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’ve settled on the idea that my job as parent is to introduce my kid to a bunch of different things, help them process that information, but ultimately the decision of where they choose to focus their energy is up to them. I’m proud of whatever they do, as long as they try their best.

That’s a good choice. I just feel each kid has so much potentials in them, but there are always something, like a shortcoming in the genes or a bad characteristics that prevents them from achieving a lot more.

And I don’t have the time, will and experience to guide mine.

Phew this resonated with me.

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 get it. 4 years old is a threshold. After that you can reason with them. Before that they are just mini terminators.

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.

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.

In a school context, it is (or should be) just as important to consider each child’s need for being appropriately challenged as it is to consider their need for support.

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?

> His primary school principal described him as ‘a happy little fellow who has a clear understanding of the fact that he is different’.

I believe it comes down to intrinsic interest, that he would not consider this something boring he needs to work through, but rather something fun and intriguing to spend his time on.

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.

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.

As others said, Australia.

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.

Do you have any idea how one would go about understanding the current status quo in terms of advancing kids? E.g. which countries do it etc.

Presumably Australia where he’s from, but also possible in the U.S.

Australia

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.

> 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.

You _guess_. It’s quite acceptable, but still learning from watching Sesame Street?

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

He looks around his age to me, were you looking at old pics?

Asian.

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)

Roughly for the same reason that we put Olympians on a pedestal. Sure, there is a lot of grit involved. But it starts off with good genes and while you won't find anybody that didn't put in the work you also won't find people with bad genes because they will never make it to the entry point, and even if somehow magically they did they'd never stand a chance.

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.

Why for you is innate grit any more commendable than innate intelligence?

Can’t speak for others but I think I learnt grit. Didn’t really show it very young but by 16 I was just able to grind through anything.

Do you celebrate people who persevere despite despite their hardships?

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.

There are people wired like Tao (or superstar athletes, supermodels, or other remarkable people) that don't achieve the same results.

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.

There are very very few people wired like Tao; how many child prodigies like that are there ? He seems to be one in a million but its pretty much impossible to assess IQ at those levels. Sure, it's not enough. YOu need the obsession for math, but lets not trivialize his intellectual ability - he's definitely not only top 1% that would just put him in the smartest 2-3 kids in his class. No, he was probably among the smartest 10-20 kids of his age group in the whole United States.

I was speaking generally, and wrote that people like him (not him specifically) are elite within the top 1%. So basically 1% of the 1%.

Not that I mean the percentages factually, more like an order of magnitude.

But my point is, in terms of "natural ability", I don't believe there is that much of a gap among top performers, but that things like work ethic and determination, and also some luck in environments, is what ends up setting them apart.

That's why I think they're worth praising: it's not just a spin of genetic roulette (unless one believes every single attribute about us is genetic, I guess).

> But my point is, in terms of "natural ability", I don't believe there is that much of a gap among top performers, but that things like work ethic and determination, and also some luck in environments, is what ends up setting them apart.

You could be right; I tend to disagree but its all speculation. My 2 cents is that the vast majority of researches/professors are motivated and driven people; you can't reach those levels if you don't know how to sit on your butt and concentrate. They all have good work ethic. I tend to think what separates Tao from the rest of the smart researchers is not that he works 15 hours a day while the rest work only 9 but rather his very very rare genius. But yeah, speculation of talent vs work ethic.

> Genuine curiosity: if you are gifted with a certain “wiring” (genes, brain chemistry etc) why is that considered an accomplishment?

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.

> Second, I think it's human nature to like and want hierarchy.

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.

Real answer, none of us can do anything more than what you are given by your parents. You get the brain you get and that's it. You can either work hard and improve and become a genius or you become a drug addict and die in a gutter. Determinism and the laws of physics rules us all.

We might as well chose to praise those of us who were gifted with abilities that we aspire to.

> 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

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.

I think Terrence Tao makes at least 600k at UCLA. Not too bad if you ask me.

There is an inequality between the sexes here. A female model does indeed get more attention and money based purely on the genes they didn't have to work for. It's not the case for men, though. Men also have to actually deliver something, whether it's being a performer like an actor, singer, footballer etc, or winning the Field's medal which you don't just get for being quite good at maths when you're 8. Trying to think of men who are famous just for genetics is quite hard. I guess like Orlando Bloom or the members of K-pop bands and whatnot, but they still have to perform and can't just prance around in fancy clothes and call it a day. In the case of Tao, if he had just decided to do something else or not accomplished anything you'd never have heard of him. Men always have to work for it. Women often don't, and if they try it doesn't work. It's the source of a lot of disgruntlement between the sexes, but probably a "grass is always greener" thing.

> based purely on the genes they didn't have to work for

Modeling is notorious for its negative impact on models' health.

They absolutely work for it, and in one of the most toxic work environments.

All I can say is before you assess the inequality of outcomes across the sexes, perhaps consider the differences in their inherent qualities to begin with.

David Gandy merely lolls in his pants.

I wonder how Tao - or a supermodel - might feel about the idea that they don't have to work for their "gifts"

Not a mystery, Tao has written about how, child prodigy aside, he has to work at math on a regular basis with grit and perseverance.

There's story of how Tao almost failed at university due to playing so much Civilization

I like a massive head start.

There may not be many other things which can contribute the same advantage.

It depends on how much value their talents can bring to humankind, I guess.

Very good guess, right on the money

Too bad humankind is almost never paying attention.

The two types of talents can be judged by the impact they have. A scientific gifted individual can produce value while a good looking individual has mostly entertainment value.

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.

>A scientific gifted individual can produce value

They can also produce a lot of damage unless they refrain to an extent.

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.

> Think about connecting them or nurturing them with AI companions.

Yes, let's give them only the blandest, most boring interactions possible.

How about nurturing them with human beings? We have no idea how nurturing children with a computer program would turn out but probably poorly.

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.

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.

Indeed. He definitely knows more Math than I do.

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

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.

He was 7 years old, so it was impossible for him to give consent for anything. His parents gave consent on his behalf.

I didn't realize this was published at the time. Still, I wonder what the current, adult Terence thinks. Whether or not legal recourse is available doesn't change Tao's feelings about it and isn't determinative regarding republishing it now is a good idea.

Interesting it's hosted on gwern...

Gwern hosts a lot of PDFs -- see https://gwern.net/archiving

I guess that makes sense in the light of her previous post and work on making a new archiving solution for being able to host singlefile archives more efficiently.

Thank you

https://www.google.com/search?q=Gwern+Branwen

her?

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 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...

See also: https://hn.algolia.com/?q=Terence+Tao

The HN mods apparently have a sign in the HN control room

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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?

Honestly a quick google would tell you what you want to know. But something tells me you must consider yourself an other worldly genius if you consider any part of set theory as nonsense.

Well its not nonsense, and its very interesting, but its just a certain formulation of logic in the end, nothing more or less.

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.

This is one of the most interesting questions to me about human brains, and as far as I know no significant progress has been made in answering it.

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?

Could be something even more difficult to identify that keeps everyone else from doing it.