Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

news.ycombinator.com

Post reply on HN
Print view View original

281–290 of 439 posts

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

#281

Post by wnkrshm »

deanCommie wrote: post #222
trash3 wrote: post #171

Earlier quoted context omitted.

This sentiment is humorous, as I'm an optimist apparently. More children will learn more quickly. Applying AI to education should supercharge the smartest.

> Applying AI to education should supercharge the smartest. What does that mean?

I don't know but it also fails to disregard that the smartest people (whatever that means) can have executive function issues that are orthogonal to their mental capacity.

Additionally, the belief that intelligence alone will improve the world is misguided imo. You need empathetic, intelligent people.

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

#282

Post by FeepingCreature »

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…

On a similar theme, Scott Alexander's short story Ars Longa, Vita Brevis https://slatestarcodex.com/2017/11/09/ars-longa-vita-brevis/

Analogously, I've heard transhumanists make the argument that as fluid intelligence declines as crystallized intelligence grows, we have yet to see a human mind in its full power.

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

#283

Post by tsimionescu »

abeppu wrote: post #263
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…

I can't pretend to be anywhere near the frontiers of math but aren't some contributions about providing a unifying framework or simplifying re-expression of something that was already known in a way that makes it more comprehensible? Is there not always hope that the right new perspective or innovation in one generation will allow subsequent generations to get up to speed faster?

It's not really plausible that such a process could continue forever. It may be plausible that there are some better foundations to various fields of math that could reduce the size of the proof for Fermat's last theorem by, say, 100 fold - but it's not plausible that it could ever be fitted onto the side of a page with the right abstraction. It's not plausible that, even in the far future, you'll be able to learn the information needed to derive formulas you'd learn in post-graduate maths today after a 1 week course in 5th grade.

On the other hand, it's extremely plausible that math as an abstract idea could build arbitrarily complex structures that would be of interest if we were able to learn to model them - so, almost necessarily, within the limitations of current human cognition and/or lifespan, there will be some structures that it is impossible for a human to learn.

Of course, in some arbitrary future we may find that those limitation of human cognitition/life-span can themselves be overcome - if that's the case, then the argument changes significantly.

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

#285

Post by tsimionescu »

nemothekid wrote: post #221
boringg wrote: post #156

Earlier quoted context omitted.

I haven't spent much time thinking about this but were Einstein's contributions a combination of intellect and "shallow" or relatively quick frontiers. I.e. a very intelligent intellectual working on the problem sets that are approachable without the same level of overhead required these days? I.e. Today's world wouldn't support an individual who could have such an impact on most math/scientific disciplines?

When it comes to physics, I think the issue is more that we are on the limit of what we can reasonably test. It's like trying to figure out how the body works before the invention of the microscope. Newton's Gravity was known to be incomplete for many years, just by looking at Mercury. It took several carefully derived experiments studying light for 100s of years that led us to Maxwell's equations in the 1860s that b…

> good luck running a test in a blackhole

Theoretically speaking, it's not that hard to run a test inside a black hole (getting to one is the hardest part that we know of). It's communicating the results to anyone else that's "slightly" harder.

Jokes aside, in physics we have both a problem with what can be tested, but also one on the theory/mathematics side. Even for a relatively technical problem, we don't have any good way of solving the actual equations of any slightly complex system in either GR, QM, even Newtonian mechanics. We are actually always relying on numerous approximations and simplifying assumptions, and some of these could themselves lead us astray in some cases.

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

#287

Post by data_maan »

wheels wrote: post #239
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…

> [...] 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. That's not really the case here. Zhang spent 10 years out of school working in fields in the cultural revolution, and didn't start college until he was 23. After his PhD, he couldn't get an academic job for 8 yea…

> It seems incredibly likely he'd have been able to proove his big proofs faster had his life gone otherwise.

Why do you think that? It takes sometimes years (!) until you get used tona certain mathematical theory. And how long it takes isa very personal thing.

Remember von Neumann, who that that we don't learn nu mathematics, but only get used to it.

I think the only thing one can say was incredibly likeli is that Zhang, while not formally employed as a mathematician, kept thinking about mathematics (a rather common for people with mathematical training, though many just stick to do occasional problem solving).

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

#288

Post by kbrkbr »

adalacelove wrote: post #244
woodruffw wrote: post #234

Earlier quoted context omitted.

I think we sometimes understate philosophy's progress: it's certainly not measurable in decades, but the world of 2022 looks very different (in terms of philosophical priors and their consequences) than the world of Socrates or Confucius. A handful of examples that come to mind: * (Nearly) everybody on our planet lives under a government whose fundamental structure and right to power comes from modern (meaning 17th c…

We measure philosophy success relative to finding the meaning of life. On the other hand everybody agrees that computers have advanced enormously without achieving yet AGI.

The measure of success is different from school to school, if any exists at all in a given school. And there is no lack of schools.

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

#289

Post by robin_reala »

dctoedt wrote: post #87
dudeinjapan wrote: post #83

Earlier quoted context omitted.

Ironically he didn't patent E=MC^2 and now everyone says it scot-free.

> he didn't patent E=MC^2 and now everyone says it scot-free Laws of nature (and descriptions thereof) aren't patentable. https://www.bitlaw.com/source/mpep/2106_04_b.html#:~:text=Th... .

That’s US law though (no idea if Germany had it any different at the time, but it’s a different jurisdiction).

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

#290

Post by data_maan »

Regarding Zhang's age: Most Fields medalists these days are very close to exceeding 40 years. Wiles himself just a special silver medal, because of that - which I think is outrageous age discrimination. Mind you he didn't get the silver medal because his results were a bit less spectacular than those of the winners, but rather they were so groundbreaking he couldn't be ignored, but because he was just over 40 they had to downgrade thr medal to a silver one (I guess in order to not be in conflict with the rules that the organization that awards the Fields medal has).

This is part of a general trend. As the world population ages, the number of people being able to achieve world-class performance later in life increases. One can see this spectacularly in sports, where older and older people win medals (for example: https://www.npr.org/2022/02/12/1080338798/older-athletes-bre... )

The Fields committee would probably do good updating their statutes, in order to not be so out of step with the times...

Post reply on HN