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Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

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Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#381

Post by andrepd »

FabHK wrote: post #374
andrepd wrote: post #347

Earlier quoted context omitted.

> If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. The failure is that mediocre students which come from an environment which helps them (good school, private tutors, stable home life) can be successful, while "naturally gifted" yet disadvantaged students don't. The basic fact that…

> parental income is still the best predictor of educational achievement Is that controlled for genetic influence though? Suppose smart people 1) have high income, 2) have smart kids. Disentangling the various causal factors is substantially harder than your quote above suggests.

I read a study that specifically addressed this by looking separately at adopted kids. I'll try to look for it and post a link when I'm at my computer.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#382

Post by Tainnor »

unsupp0rted wrote: post #251
LudwigNagasena wrote: post #245

Earlier quoted context omitted.

Did those things appear because philosophers talked about them or did philosophers talk about them because they appeared?

I can easily imagine an Earth with no philosophers after say Aristotle that is functionally identical to our current one.

Without philosophy, there is no Hegel, without Hegel there is no Marx, without Marx there is no Lenin, without Lenin, there is no Stalin, without Stalin there is no Cold War, without the Cold War there's probably not a war in Ukraine right now, and without a war in Ukraine I wouldn't be worried about my gas bill. I think that's pretty concrete.

(Just a single, rather obvious example. Easy enough to find others.)

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#383

Post by Tainnor »

LudwigNagasena wrote: post #307
woodruffw wrote: post #252

Earlier quoted context omitted.

Each of the examples I gave have direct origins in philosophy. It’s not even clear what the alternative would be for Hobbes and Popper; for Frege you could call him a mathematician instead, I suppose, if you ignore all of the other philosophy he did.

I don’t see any direct origins. Karl Popper was a small child when Einstein came up with relativity. Hobbes was just a reactionary apologist of absolute monarchy. And Frege’s philosophical contributions were world-changing as long as we can pretend that propositional calculus is philosophy.

You might be interested in the fact that Einstein himself claimed that he might not have stumbled upon relativity if it hadn't been for David Hume:

https://aeon.co/essays/what-albert-einstein-owes-to-david-hu...

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#384

Post by [deleted] »

whytai wrote: post #10
gavagai691 wrote: post #8

Earlier quoted context omitted.

If the proof is right, Zhang is in contention for greatest living mathematician with seven papers total, and on the basis of two of them (and should win all the major prizes he has not won yet and is still eligible for: Abel, Wolf, etc.). Would truly live up to Gauss' motto: "pauca, sed matura!"

Even more incredible is that his own advisor refused to write him letters of recommendation upon graduation [1] After graduation, Zhang had trouble finding an academic position. In a 2013 interview with Nautilus magazine, Zhang said he did not get a job after graduation. "During that period it was difficult to find a job in academics. That was a job market problem. Also, my advisor [Tzuong-Tsieng Moh] did not write m…

[deleted]

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#385

Post by Tainnor »

kbrkbr wrote: post #279
woodruffw wrote: post #252

Earlier quoted context omitted.

Each of the examples I gave have direct origins in philosophy. It’s not even clear what the alternative would be for Hobbes and Popper; for Frege you could call him a mathematician instead, I suppose, if you ignore all of the other philosophy he did.

The causality here is hard to prove, even untangle. I think the French Revolution was largely more influential for the state of governments today. I also think that science was not influenced so much by Popper, but much more by Fisher and Neyman. People tend to use what is a successful tool, and be influenced by power and theatre, not so much by fragile logical constructs without empirical value found sitting in the…

Do you think the French Revolution happened in a vacuum? Without the ideals of Enlightenment philosophy it would have amounted to nothing more than mob violence (if it had even gotten started at all).

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#386

Post by hnthrowaway0315 »

zimpenfish wrote: post #260

Brings to mind Gould's quote - "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." https://www.goodreads.com/quotes/99345-i-am-somehow-less-int...

This is EXACTLY what I'm thinking about. Tons of talents were wasted. To fix this we have to change the global political climate.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#389

Post by yifanl »

bigbacaloa wrote: post #265
forkLding wrote: post #109

Earlier quoted context omitted.

It should be noted that Zhang was a math prodigy when he was young, around 13 years old, however because of the Cultural Revolution in China, school education was stopped for a decade and his parents were purged and he was sent down to the countryside so he could not study at school but was forced to work in the fields and factories as re-education. It was only a decade later that he managed to get into university be…

The professional math world is full of smart but delusionally ambitious people who do things like focus all their energy on the Jacobian conjecture and the Riemann hypothesis. Most crash out never finishing their doctorates (because these problems are too hard and working on them does not provide what it takes to survive professionally). Zhang is an example of such a person. What is very unusual about him is not that…

> people who do things like focus all their energy on the Jacobian conjecture ... Most crash out never finishing their doctorates (because these problems are too hard and working on them does not provide what it takes to survive professionally).

In Zhang's case, I believe his doctoral thesis actually proved the Jacobian conjecture... but his thesis was relying on an incorrect result given by his advisor's own paper (presumably at the guidance of his advisor).

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#390

Post by deepzn »

pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

We will have super advanced AGI exploring the frontiers of Math and Physics. Check out the recent Lex Fridman pod with Andrej Karpathy. Fascinating discussion.
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