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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

#101

Post by XCSme »

postalrat wrote: post #22
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

Maybe because you haven't tried to understand it? Can't be harder than learning the meaning behind these characters: https://www.pandatree.com/book/DiaryofWorm.jpg

I don't mean the symbols themselves, but how each member was defined and the history behind it.

It's like watching a Marvel movie and not only knowing the plot of the current movie but also the deep history of each character and their relationships with other characters.

I assume the paper didn't come out of nowhere and it's based on "the shoulders of giants".

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

#102

Post by yding »

lordnacho wrote: post #47
gavagai691 wrote: post #13

Earlier quoted context omitted.

Yes, if you want to see something incredible (in both the literal sense and the usual sense), read https://www.math.purdue.edu/~ttm/ZhangYt.pdf (by Moh).

> For some 10 years, I had recommended 100 mainland Chinese students to the department and all accepted by the department. I am always indebt to the trust of my judgements by the department. Only very few of them misbehaved, bit the hands which fed them, none of them intended to murder their parents/friends , almost all of them performed well and became well-liked. No murderers, great success!

It's a reference to Brendt Christensen.

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

#103

Post by gavagai691 »

tschwimmer wrote: post #97
thechao wrote: post #32

Earlier quoted context omitted.

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 wi…

I think P != NP is extremely interesting, but I wouldn't say it has strong implications for the nature of the concept of determinism or reality. I think that the idea of a Turing machine / the notion of computability has deep philosophical implications, but even that I wouldn't say has implications for "the nature of reality."

If you think that prime numbers are interesting, then I can tell you that GRH is the single most central conjecture in the study of prime numbers. Personally, I think prime numbers are some of the most fundamental and intrinsically interesting objects in pure math, but of course, this is subjective!

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

#104

Post by jjgreen »

gradschoolfail wrote: post #96
markus_zhang wrote: post #14

Earlier quoted context omitted.

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.

Huh? Could you expand on this?

Disclosure: a Brit who does not see Americans oppressed by compatriot affectations.

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

#105

Post by XCSme »

gavagai691 wrote: post #28
xyzzyz wrote: post #25

Earlier quoted context omitted.

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.

The Greek characters in the screenshot are standard for the subject. The letters "chi" and "psi" (in that order) are the preferred letters for denoting Dirichlet characters, and zeros of L-functions are always denoted by "rho."

See, this is what I meant. Not only reading in the paper where X was defined but have this in-depth knowledge of why a certain symbol was used and how it came to be, knowledge that probably not even all full-time mathematicians that studied their entire life have.

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

#106

Post by Frost1x »

tsol wrote: post #98
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…

>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…

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.

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

#107

Post by xyzzyz »

gavagai691 wrote: post #28
xyzzyz wrote: post #25

Earlier quoted context omitted.

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.

The Greek characters in the screenshot are standard for the subject. The letters "chi" and "psi" (in that order) are the preferred letters for denoting Dirichlet characters, and zeros of L-functions are always denoted by "rho."

I see, this makes sense. Probably gets easier when one gets used to it.

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

#108

Post by sebg »

m_nyongesa wrote: post #49

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…

Would love to hear your story about getting a PhD as an older person. Have you written anything about it that's public? If not, would it be possible to contact you? Thanks!

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

#109

Post by forkLding »

gavagai691 wrote: post #5

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…

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 because universities re-opened after the Cultural Revolution, by then he was 23 already when he started his bachelors' degree.

Note that, universities could accept people who did not attend school if they passed their university entry exams because so many people were unable to attend schools because they were all closed and teachers purged during the Cultural Revolution.

I would say he "matured" later mainly because he did not have the right opportunities because he could not go to high school and after his university graduation, had no good opportunities because many good professors were purged during the Cultural Revolution so he fled to the US for a better life.

Source: https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

And I quote from the above source which is from a 2015 New Yorker interview with Zhang:

'I asked Zhang, “Are you very smart?” and he said, “Maybe, a little.” He was born in Shanghai in 1955. His mother was a secretary in a government office, and his father was a college professor...As a small boy, he began “trying to know everything in mathematics,” he said. “I became very thirsty for math.”...The [Cultural] revolution had closed the schools. He spent most of his time reading math books that he ordered from a bookstore for less than a dollar.'

As well:

'...when he was fifteen he was sent with his mother to the countryside...where they grew vegetables. His father was sent to a farm in another part of the country. If Zhang was seen reading books on the farm, he was told to stop...After a few years, he returned to Beijing, where he got a job in a factory making locks. He began studying to take the entrance exam for Peking University, China’s most respected school: “I spent several months to learn all the high-school physics and chemistry, and several to learn history. It was a little hurried.” He was admitted when he was twenty-three.'

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

#110

Post by gavagai691 »

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…

"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 algebraic geometry PhD students publish nothing besides their thesis during their PhD studies), it can never happen to mathematics as a whole. If one part of math gets too deep, you can always go somewhere else, where the water is still "shallow."

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