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Comment by brianyu8 | Hacker News Reader

Makes me think of Ramunjan. It's quite tragic to think about how much more knowledge humanity would have if these two lived a little longer.

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Add Turing to the list, having him around during the naissance of molecular genetics and the flowering of computation would have made those fields all the more lively.

Turing death made him famous, I wouldn't bet on that

Can I assume you know little of Turing's accomplishments?

Like von Neumann, he's famous for a reason.

I rather think making arguably the biggest individual contribution to winning the biggest war in history is a pretty big contributor to his game. His role in the founding of computer science also doesn't hurt.

Or von Neumann. Of course he was older at 53, but still lots of time left.

We should throw Galois in there as well.

A small and incomplete list of mathematical tragedies (by wiki articles) I keep, to which I'll add Frank Ramsey:

https://en.wikipedia.org/wiki/Kurt_G%C3%B6del

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

https://en.wikipedia.org/wiki/William_James_Sidis

https://en.wikipedia.org/wiki/%C3%89variste_Galois

https://en.wikipedia.org/wiki/Niels_Henrik_Abel

https://en.wikipedia.org/wiki/Alexander_Grothendieck

https://en.wikipedia.org/wiki/Alan_Turing

Why is Grothendieck a tragedy ? his departure to reclusion ?

Good question, maybe he shouldn't be on that list. I'd read a long biography about him in German ("Wer ist Alexander Grothendieck?"), and was left with the impression that he was unfulfilled and unhappy at the end of his career; of course he lived to old age and there were certainly worse fates on that list, so perhaps its inclusion is not so appropriate.

I'd tend to think that he's not a tragic figure. Maybe dramatic in a way. But since he had a full life and even free choice to do it on its own term..

In any case I hope you didn't feel attacked. It was half curiosity half critic :)

In terms of a metric akin to "mathematical DALYs", Galois was perhaps the most impactful early death of all, followed by Abel. Both Galois and Abel founded entire branches of mathematics before the age of 25.

QALYs, surely? :)

Dying early would boost DALY count.

No, it wouldn't. They both account for years of early death, just in different ways.

Blaise Pascal should be in the list as well! Death at 39. https://en.wikipedia.org/wiki/Blaise_Pascal

Curious if there are any young people with established once in a century kind of talent alive today ?

Terence Tao - https://en.wikipedia.org/wiki/Terence_Tao

Peter Scholze -https://en.wikipedia.org/wiki/Peter_Scholze

And doubtless several more. By the way, not only are Scholze and Tao outstanding talents, but very nice and humble, as in ACTUAL nice and humble, and they (especially Tao) write in a crystal clear way so they are wonderful as expositors and academic writers. Makes one chuckle comparing that to so much unrestrained ego online.

Yes, my favorite thing about Tao is how well he explains concepts on his blog [0] and on mathoverflow[1]. He does not put on airs of being an unapproachable genius. I guess he knows he has nothing to prove

[0] https://terrytao.wordpress.com/ [1] https://mathoverflow.net/users/766/terry-tao

He thinks in a very expository way, it seems. There's aother guy, Gromov, who is the opposite. He is famously mysterious (people sometimes joke about "speaking Gromovian").

His mathoverflow responses are surprisingly intuitive and elegant.

Intuition for visualizing/imagining high-dimensional geometry: https://mathoverflow.net/questions/25983/intuitive-crutches-...

Intuition for convolution: https://mathoverflow.net/questions/5892/what-is-convolution-...

This is much more satisfying way to think of these concepts. The idea of thinking of convolution as a 'fuzzy' optical phenomena, the idea of thinking of n-dimensional space as a probability distribution.

It's interesting the way he grounds his intuition in practical applications. For convolution for example, a common application is to convolve a 2d image with a gaussian kernel to fuzz the image. I know that, but always still had a not-very intuitive, but very dry and technical understanding of convolution as a sort of dot product of two vectors representing the underlying image and the kernel. Terence Tao in contrast exploits the practical intuition of 'fuzziness' in this process to suggest thinking of convolution as a fuzzy (probablistic) addition of functions. It's a subtle step, but giving some sort of physical, or visual intuition for mathethematics like this is so helpful.

Yep being a lowly engineer who loves math I always wanted to learn a more rigorous approach, but then again I am lazy, so for example I started with Rudin, but gave up as soon as I couldnt grasp something, same with other analysis books and lecture notes. Then comes Terry with his 2 jewels of books on Analysis, but I thought to myself, no way I am going to understand anything from arguably the best mathematician in the last decades. But not only the prose is clear and unpretentious the motivation of why analysis is "needed" is presented perfectly, the books are self-contained and the progression is very smooth,no pun intended. Highly, highly recommended.

I'm so curious what it must be like to have that kind of mind. Just did a quick Google and his IQ is around 230. I mean, it's hard enough to really understand what anyone else's subjective experience is like, but I think it's literally impossible to get a true sense of what it would be like to be that intelligent (for those of us who are nowhere close). With that great a difference it's got to really be a difference in kind, not just degree.

I wonder if you constantly challenged yourself to see and feel from others perspectives, all the time. Perhaps one day you may understand what it’s like to have that kind of mind. At that point, would your IQ also be around 230?

I think challenging yourself to see from other people's perspectives is probably a great thing to do. But no, it's not going to somehow increase your innate intelligence to super-genius level.

Owing to the way IQ is defined, nobody has an IQ over 200.

IQ doesn’t measure absolute intelligence, but rather assumes it is a normal curve and maps that to human friendly numbers: mean 100, standard deviation 15 or 16 depending who you ask.

The same thing has the curious side effect that if the number of people in comas at any given time is greater than 1, then coma patients must have an IQ > 0.

OK, so if all IQs could be mapped accurately onto a normal curve with a SD of 15-16 you wouldn't expect anyone over 200. But standardized IQ tests can most definitely give results over 200, and do. And presumably someone who scores 250 on an IQ test is likely to be more intelligent^ than someone who scores 200 on the same test.

^in the sense that it measured by IQ tests, anyway. Point being it shows a real difference; deltas over 200 aren't meaningless.

Terence Tao's intelligence is not predicted by IQ. Plenty have higher IQ and achieve less. Some lower and achieve more.

IQ is total pseudoscience nonsense of zero value to anyone or anything.

It's one genuine use is as a fig leaf for the very worst kind of racism. Treat it and anyone touting IQ an indicator of anything with extreme suspicion. Nazis love IQ. Goodwin's. /Thread

Why do you consider IQ to be pseudoscience? It's the bedrock of psychometrics. Just because some people use some IQ data to justify racism doesn't mean the measure is unscientific. Nazis loved nuclear physics too, it doesn't mean the field is pseudoscience.

I know this isn’t your main point, and I might just be remembering British wartime propaganda (my parents told me several things that later turned out to have been that), but…

Wasn’t the Nazi nuclear program severely delayed by their race-based hatred of Einstein for being Jewish?

This is an argument against doing physics the way the Nazis did (ie deriding certain theoretical paths as "Jewish physics"), not an argument against doing nuclear physics at all because the Nazis did.

The latter is what this thread is talking about: it's obvious that we shouldn't be studying psychometrics the way the Nazis did, but it's not obvious that we shouldn't be doing it at all because they did (as with nuclear physics).

Hilariously, even harry8's complaint that the Nazis loved IQ is precisely backwards: Hitler banned IQ testing for being "Jewish" too.

EDIT: I actually was curious about this last claim, so I checked the source that the Wikipedia article points to. While this text was written by one of the most-cited psychologists in history, there's little else out there to concretely corroborate or refute that IQ testing was _banned_ by the Nazis. The evidence indicates that their attitude was somewhere between apathy and hostility towards the tests.

No you're a bit too literal. Nazis sadly are not dead and gone, not limited to 1930-45 Germany.

IQ is loved by Nazis as proof of master race bullshit. Really.

Treat IQ with contempt. It's an indicator of idiocy in a discussion. (All of us are capable of idiocy in discussions, including me, don't fall for the IQ trap. You're above it. We all are).

Environmentalism is an important part of neo-Nazism (and other strains of fascism) too. Do you think that automatically tars anybody who thinks we should pollute less? I appreciate the point you're trying to make, but you're letting labels do the thinking for you (or as I've heard it put recently, "engaging in idiocy").

I don't personally believe that racial IQ differences are significant or salient to differences in population outcomes, nor am I convinced that claims are well-founded that IQ determines individual outcomes to a significant degree. But I don't advise treating it like a magic word that shuts off the thought centers of your brain. If you think it's a useless concept, you should be able to articulate why by pointing to the science (or lack thereof), not by letting Nazis tell you what you're allowed to think critically about.

Support for Nazism is the only use of IQ. It's magic bs pixiedust nonsense that needs to be called out loudly as such.

It's not only that it is used by Nazis. It's that it is used for literally nothing else of positive value to anyone. It's a disgrace.

Sorry for dancing around it not not starting it as plainly as possible.

"Anyone quoting IQ scores as justification for anything at all is talking bullshit. The end."

And they are using a technique of bullshit argument support favoured by goddamn Nazis.

The jury is back. IQ is guilty. Put it right there next to lobotomy as a gift from psychology to the world. Stamp it out. NOW!

This is getting closer to making a reasonable claim, but unfortunately, an unsupported assertion is the _beginning_ of making an argument, not the end.

Most of the relevant scientific community disagrees with your assertion that IQ is purely pseudoscience. From Wikipedia:

> Clinical psychologists generally regard IQ scores as having sufficient statistical validity for many clinical purposes.[25][68][69] ... "On the whole, scholars with any expertise in the area of intelligence and intelligence testing (defined very broadly) share a common view of the most important components of intelligence, and are convinced that it can be measured with some degree of accuracy." Almost all respondents picked out abstract reasoning, ability to solve problems and ability to acquire knowledge as the most important elements.

There's plenty more on the topic, and as always, Wikipedia is a great place to start your search for sources.

In what way is your blanket dismissal of the scientific consensus different from anti-vaxxers ("the only use of vaccines is support for Illuminati mind-control!!) or flat-earthers ("the only use for a round earth theory is support for, uh, the globe industry!")? Or for that matter, what makes you different from IQ essentialists like neo-Nazis, that take a nuanced scientific concept and flatten it into an all-or-nothing perfect predictor of outcomes? Hell, at least they're _directionally_ in agreement with the scientific establishment about the validity of the concept.

The onus is on those making the claim to provide the evidence. A claim without evidence can be dismissed without evidence.

There is no evidence. Dig into anything that is claimed as evidence and it's clearly invalid, at best. As a statement of the overwhelimingly obvious: the field of Psychology has issues. It knows this. You've heard of the "replication crisis." There are those trying to right it and treat it like it is actually science and rip out all the pseudo-bs that psych is redolent with. Good luck to them. Maybe they'll even remove the utterly discredited stanford prison experiment from every single first year psych textbook? Or keep it as yet another example of collective delusion in the discpline caused by faked research? Yet another one. But in every textbook. Credibility?

"On the whole, scholars with any expertise in the area of intelligence and intelligence testing (defined very broadly) share a common view of the most important components of intelligence, and are convinced that it can be measured with some degree of accuracy." - Anyone who disagrees and asks for the evidence is defined as lacking expertise. It's frigging comical. But it does screw up lives and justify racism so, there's that. Get told you're stupid as a child, there's a good chance that's self-fulfilling.

There is ovewhelming evidence that vaccines work. Seen a polio case, well, ever? There is none that IQ is a useful scientific metric. See Egas Moniz's Nobel prize for how psychology can move as a discipline on mass without evidence. Or maybe butchering brains and getting nobel prizes for it isn't clear enough evidence that you can't take anything in psychology "on trust" anymore than you can physics.

IQ is a disgrace. It is already and will continue to be increasingly sighted as how bad the discpiline of psychology has been for the past 100 years. May they own their shame and do better. Your IQ score being higher than mine means absolutely nothing. My IQ score being higher than yours means nothing. Absolutely nothing. Zero. But yeah, you can convince people it's has meaning and use it mess up lives - even if you don't intend to do that. Like the altruistic motives behind lobotomy and the success they had with the Nobel committee.

Take any large multivariate problem and look for a regressor against some dimension. Say, car speed. You will find that there is a good variable that links that. But that variable won't be explanatory or even correct.

A much better explanation here, from the fairly wonderful blog of cosma shalizi http://bactra.org/weblog/523.html

And most importantly, it won't be predictive.

> And presumably someone who scores 250 on an IQ test is likely to be more intelligent^ than someone who scores 200 on the same test.

Unless the former has taken the same test or some subset of the questions before. Which isn't unusual...

IQ is a silly metric and should be discarded entirely.

And which metric do you propose we replace it with?

Why does it need to be replaced? Get rid of it entirely. Intelligence comes in myriad forms and trying to reduce it to a single three digit number is such a naive, ignorant idea to begin with.

So how do we measure whether someone has an intellectual disability and needs special schooling? How do we decide who we can draft into the military? (It used to be an IQ of at least 83)

It seems like both of those should be individual specific tests, rather than a broad ‘intelligence’ test.

But would the tests be measuring something that a generalized IQ test wouldn’t? It seems better to have one standardized way to measure whatever it is IQ tests are measuring and then use applicable thresholds for your domain.

Is the test for a driver’s license the same as the test for a calculus exam? Of course not. I see no reason why the educational system or military draft is any different. As I said before, intelligence comes in a variety of forms, so the focus should be on fixing the system to account for this, not categorizing certain students with so-called learning disabilities because they don’t fit into the institutionalized definition of intelligence, which is measured on this extremely oversimplified scale known as an IQ test.

IQ tests are perfectly reliable for predicting learning disabilities. If someone scores very low on an IQ test, they will not function well in a normal school. Neither will the function well if they score very high. They’d be bored out of their minds.

I’m struggling to understand your problem with IQ tests. If you have an IQ of between 90 and 110 as per a standard test no one really cares. You’re “normal”. Score higher maybe a bit more intelligent at spacio-temporal problems and it’s probably a good predicator that you’ll do well at mathematics.

If you score below 75 you almost certainly have an intellectual disability and need help. You can give these people any other test you like, it will make no difference. They won’t “function” in a society where the mean IQ is 100 (which it is).

As a previous commenter said Terence Tao is a living genius currently. But also, some people that (somewhat) recently rose to fame in the field of mathematics are:

Andrew Wiles, for providing a proof to Fermat's Last Theorem.

Grigori Perelman (and Richard Hamilton), solver and winner of the Millenium Prize Problem: Poincare's Conjecture.

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