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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

#191

Post by mlyle »

sillysaurusx wrote: post #127
gavagai691 wrote: post #110

Earlier quoted context omitted.

"The sad part is that as the trend continues we may reach a point where a mathematician's intellectually productive life is not sufficient to contribute anything novel, statistically speaking." People talk about this a lot. While I think it could happen for certain subdisciplines (it already takes essentially an entirely PhD's worth of time to learn all the necessary background to be an algebraic geometer, so most al…

I’m not so sure. The same argument would apply to theoretical physics in 1960. Circa 2023, there are remarkably few shallow parts of physics. Math as a whole may last longer, but this list reminds us how far we’ve come in a mere few millennia: https://usercontent.irccloud-cdn.com/file/SaI50Q1d/166786520... On the timescale of civilization, it seems less and less likely that lone mathematicians can revolutionize the f…

Physics is limited by having to represent phenomena in our physical world simply.

Mathematics is not just a small integer multiple larger than this.

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

#192

Post by computerfriend »

ta988 wrote: post #175
x0x0 wrote: post #161

Earlier quoted context omitted.

An unfortunate parallel: the best physics professor (unfortunately, just an adjunct) I ever had was a Russian immigrant. He quit teaching to go run a blini restaurant because it paid way more :(

This is so true and still the case. I've seen so many highly skilled immigrants passed over for politics and image reasons... Academia is ruthless but for the wrong reasons.

I had so many Russian mathematics professors. They dominate the field, for obvious historical reasons.

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

#193

Post by inamberclad »

maegul wrote: post #169
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. 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 a point where a mathematician's in…

Agreed, it feels like the days of maverick engineers leading huge efforts is mostly over. Will there be any more Kelley Johnsons, or Gene Kranzs in our lifetimes?

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

#194

Post by joshuamorton »

s1artibartfast wrote: post #163
bdhe wrote: post #150

Earlier quoted context omitted.

> It's the old "I'm from the government and I am here to help" joke. What else is the government for? I understand it's a popular Reagan talking point but I don't really grok it. If you assume the govt doesn't work for us, particularly if you're in politics, it becomes a self-fulfilling prophecy.

This is probably not the best thread for a political discussion, but I will take a shot. Nobody disputes that governments should be a force for good. Government's obviously can do both good and bad. Many reason atrocities like the cultural revolution came of under the pretext of trying to help. If you think the government has veered into doing bad, it is natural to want to reform it and make it stop doing that. the t…

> the talking point and metaphor simply conveys a belief that some of the governments work is bad and should be stopped

This is a nuanced and thoughtful position. The statement "The 9 words you never want to hear are I'm from the government and I'm here to help"" is not nuanced and thoughtful, it doesn't suggest governments do good and bad, it positions governments (and their agents) as incapable of doing good. That someone from the government trying to help you must not be, for whatever reason.

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

#195

Post by canadiantim »

dis-sys wrote: post #145
mrybczyn wrote: post #100

Earlier quoted context omitted.

He and his parents were victims of Mao's cultural revolution (like millions of others) - and he was forced into agricultural labour instead of attending high school. Amazing cinderella story. A real academic hero.

> like millions of others Including Xi Jinping.

Unfortunate Xi is repeating past mistakes

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

#196

Post by vlovich123 »

fnordpiglet wrote: post #53
kenjackson wrote: post #29

Earlier quoted context omitted.

Someone needs to make a movie about his life, or at least a documentary.

Good luck finding a movie about Isaac Newton or Einstein, or literally anyone whose value to the world is more than pretending to be someone else or lying a lot, let alone a very interesting mathematician no one recognizes. (Ok I know there’s a few movies about folks like Turing and Nash, but it’s pretty slim pickings).

Einstein is probably a terrible example here because in his day he was regarded as a pop culture icon so there’s plenty about him in film [1]. That’s not even considering that he’s had plenty of excellent biographies written about him. Agora with Rachel Weisz is an excellent one about Hypatia.

Could we do better as a society? Maybe. To do that though you’d have to bring these stories into film classrooms and get students inspired. But first you have to make the stories inspiring and a lot of them aren’t thaaat much except for the advancements they provided to the field and that’s harder to convey. Maybe Leibniz and Newton would be a good rivalry on the screen.

[1] https://www.themoviedb.org/keyword/8689-albert-einstein/movi...

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

#197

Post by nyokodo »

sillysaurusx wrote: post #127
gavagai691 wrote: post #110

Earlier quoted context omitted.

"The sad part is that as the trend continues we may reach a point where a mathematician's intellectually productive life is not sufficient to contribute anything novel, statistically speaking." People talk about this a lot. While I think it could happen for certain subdisciplines (it already takes essentially an entirely PhD's worth of time to learn all the necessary background to be an algebraic geometer, so most al…

I’m not so sure. The same argument would apply to theoretical physics in 1960. Circa 2023, there are remarkably few shallow parts of physics. Math as a whole may last longer, but this list reminds us how far we’ve come in a mere few millennia: https://usercontent.irccloud-cdn.com/file/SaI50Q1d/166786520... On the timescale of civilization, it seems less and less likely that lone mathematicians can revolutionize the f…

> it seems less and less likely that lone mathematicians can revolutionize the field.

Which inspires the question: how much can cutting edge math be parallelized?

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

#198

Post by mhh__ »

xyzzyz wrote: post #25
XCSme wrote: post #11

I am pretty confident that I will never in my lifetime fully understand stuff like this (not the symbols themselves, but the overall meaning of each term and why it is like that): https://i.snipboard.io/by4tsH.jpg

For the meaning, you just have to retrace back to where the things were defined, just like in programming. I am a mathematician, and I do not understand anything in the linked screenshot either (other than big O notation, which many people here should actually know!). FWIW, the author’s preference for Greek letters is rather excessive for my personal taste.

Unless they're deeply ingrained in the literature I find preferences for curly letters quite irritating (especially some older typefaces), dyslexic or not I genuinely cannot read them sometimes; it's a big blocker on my productivity.

I sometimes rewrite them using A, B, C then try to understand them. This procedure should be automatic but unfortunately TeX is ancient.

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

#199

Post by nerdbert »

novalis78 wrote: post #111
Frost1x wrote: post #106

Earlier quoted context omitted.

This is a growing problem in many fields, IMHO. I've been wondering for awhile if it's an inherent flaw in knowledge in that if knowledge can't supplant older knowledge in a high compressed reduced form as things progress, we're just building so much information/knowledge for any given field that at some point, it may be quicker to simply rediscover the process than to search the knowledge for the prior work.

This is where longevity research a la Harold Katcher comes in and allows for super centenarian geniuses to shape the future of humanity.

But what if there are necessary prerequisites for making significant advances in longevity, which themselves are so complex that they require more than a human lifespan to master? We could be at a dead end unless the computers start doing the work. And even then, perhaps the same impediment applies to the development of an AI that can bootstrap other AIs into getting the job done.

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

#200

Post by m_nyongesa »

astrange wrote: post #72
foobarian wrote: post #69

Earlier quoted context omitted.

Hardy may have a point, on average. And it’s probably because of the responsibilities factor, i.e. older people have kids, families, departments to run, etc that takes them out of the game. If I did math with this level of intensity I would not have time for both without a partner willing to make quite some sacrifices.

I remember from articles about his earlier primes work that his wife lived in San Jose i.e. on the other side of the country from him. They didn't really go into it but neither of them seemed upset by this. That house price appreciation must just be that good. (Also, it was reported he "worked at a Subway" but IIRC he was actually the accountant for a friend's Subway franchise.)

He did work behind the counter sometimes.

Source: https://yewtu.be/watch?v=88Q2v6FTSBI 49:03 - 49:56

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