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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

#91

There was a scientist who did his best stuff while he was working as a patent clerk.

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

No, but his image is licensed.

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

#92
post #87

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... .

But he did learn to split the beer atom: https://www.youtube.com/watch?v=Ra7oqFqj9uU

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

#93
post #81

I need a “Explain like I’m 5” for Landau--Siegel zeros. This sounds like a hard task as I couldn’t find anything online that does it :(

Hey, this comment was my attempt at an ELIUndergraduate (5 is probably a little too ambitious for this topic). I hope it may be helpful!

https://old.reddit.com/r/math/comments/y93a86/eliundergradua...

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

#94
post #81

I need a “Explain like I’m 5” for Landau--Siegel zeros. This sounds like a hard task as I couldn’t find anything online that does it :(

Hey, this comment was my attempt at an ELIUndergraduate (5 is probably a little too ambitious for this topic). I hope it may be helpful! https://old.reddit.com/r/math/comments/y93a86/eliundergradua...

Thanks!

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

#95

Is the 2022 in the bound there cause it's sharpest or because he happened to have the freedom to pick it equal to the year of publication?

Not sharpest; he says he thinks it can be improved, but not down to 1 (if it could be improved down to 1, that would prove the nonexistence of Landau--Siegel zeros).

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

#96

Two additional notes: 1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/questions/131221/yitang-zhangs-2007... . But speaking with mathematicians who are intimately familiar with Zhang's previous work, there seems to be good reason to be optimistic nevertheless. First, the idea behind Zhang's proof is similar to the zero-repulsion ideas…

I think Zhang's previous result was good enough to rebuff Hardy's claims. Actually I think Math is more or less a young people's game is because whence someone be super successful and famous it's kinda difficult psychological to retain the previous mental state and push out similar results.

Might come off as political, but Americans need need to throw off the yoke of British intellectual affectations, especially pre WWI ones.

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

#97
post #32

> To give a sense of the scale of this claim: If correct, Zhang's work is the most significant progress towards the Generalized Riemann Hypothesis in a century. Thanks, that totally failed to give any sense of scale.

It's the moral equivalent of making major headway against P!=NP; or, proving that there are no global hidden variables in QM; or, that there's a clear path ("just engineering") to room-temperature semiconductors.

I feel like saying this is similar to making progress on P!=NP is not accurate (extreme disclaimer: I have no formal math training). My understanding of P!=NP is that an answer to that has strong implications for the nature of the concept of determinism _of reality_, let alone most cryptography and lots of other stuff too. From my quick scan of the GRH wikipedia article, it doesn't appear that the GRH has the same widespread almost philosophical implications as P!=NP.

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

#98
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…

>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

>The sad part is that as the trend continues we may reach a point where a mathematician's intellectually productive life is not sufficient

Hmm. I had never thought of it like this. Is it possible for human knowledge to become so advanced in a single subject that it takes a persons entire life to learn just one subject? That's already true of something like the human body, which is why doctors specialize in organs or regions of the body. The more human knowledge expands, the more individuals specialize into increasingly smaller niches.

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

#99
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…

Or we innovate elsewhere.

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

#100

As an older person currently working on a PhD, this guy was and is a something of a hero to me. He has an interesting life story. He was very into math at an early age, so he's different from people like me who got interested in it later in life, but he's also different in that his family was sent down to the countryside in China. I remember reading a lot about him a few years ago and relating to some of the professi…

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.
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