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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

#261
post #233

Quoted post unavailable.

"Cultural Revolution" is actually a very apt name for what happened. One of the core concepts of it was the destruction of the "four olds": old ideas, old culture, old customs, and old habits. They were horrifyingly efficient at it, resulting in what was one of the single-largest destructions of cultural heritage in history, and almost certainly the largest one perpetuated by one's own people (albeit the original ico…

Everyone in Asia did or is doing the same thing.

Meiji did this in Japan, to the point where many B. temples were burnt down (thankfully not as bad as Mao), and the whole of Japan's culture considered obsolete. KMT boys were doing the same thing in China before Mao. Nehru and his Congress cretins who inherited the British state, did the same, and India continues these "destroy Bharata" policies to this day.

In fact, since a lot of Asian culture is tied to India, one might call this an extension of the millennia long war on India from the West, but now on the realm on the realm of ideas. Not surprising that the occidental academia has deep-hatred for India's old-culture and everyone who imbibes it (at the same level as medieval anti-semitism from my own experience). They also have the victim-complex of Islam (and Xtianity to a lesser extent) to their support now.

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

#262
post #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…

Think of it like Rust eventually supplanting C++ once the ecosystem and libraries are complete enough for people to make the change.

The cognitive burden reduces via the new foundations not requiring deep understanding of the old ones to be able to make new steps forward.

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

#263
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?

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

#264
post #169

Earlier quoted context omitted.

> 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?

There is still plenty of amazing engineering going on, for example EUV development at ASML.

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

#265

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 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 he continued to work on such things anyway, rather that he eventually found some measure of success. What I infer from his story is that he is tremendously stubborn and genuinely oblivious to ordinary material feedback. Evidently he has some talent too, but that's not the unusual part of his story.

Said another way - I've known quite a few people like him to a point - with the difference that none of the others ever produced good mathematics, much less solved a major problem.

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

#266
post #263
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?

Point is that the low hanging fruits are finite and are picker continuously, thus sooner or later they run out. Reinventing something I consider low hanging just not recognized for some time.

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

#267
post #161
post #143

Earlier quoted context omitted.

While not common, I know of other Chinese diaspora in North America with similar stories. Many graduates from post Cultural Revolution China left the country in 90's and found the language barrier (and accompanying discrimination) too high to overcome. The man delivering your fried rice might have a PhD.

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 :(

My calculus professor from university in the late '90s had earlier on won a Lottery Visa to the US. As I understood it he took advantage of it, only to find out that while there he could only find very menial jobs.

He came back to Romania and to Bucharest, which was really good for me and for my then colleagues because he was an excellent professor.

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

#268
post #20

Earlier quoted context omitted.

Yeah I started reading that from the Wiki citation. Yikes. Academia is brutal.

Man, it's so weird and pathetic All of these guys are probably a hundred times smarter than me or most of the other code monkeys working for the FANGMAN, but they're all squabbling over little 5-figure scraps of grant money.

Zhang evidently doesn't care about money at all. The same is true for many professonal mathematicians. Caring about money makes it difficult (not impossible) to do anything deep.

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

#269
post #17

Can someone explain the decimal constants that are used throughout the proof? For example, on page 52. It's rare to see these kinds of numbers used in mathematical proofs, but I'm sure they were chosen for good reasons.

Often in math papers there is a series of constants appearing in estimates, each of which depends, sometimes in nonobvious ways, on those appearing earlier. Some authors like to give these constants genuine numerical values in order to help keep track of the dependencies between them and, in particular, to make sure that they aren't accidentally treating two different C's as the same. In delicate analytic proofs this sort of thing is particularly important - subtle missed dependencies are one of the places where serious proof attempts can go wrong in hard to find ways. I'm not saying this is what Zhang is doing, but it's one possibility.

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

#270
post #170

Earlier quoted context omitted.

You’re missing the reference

You've never worked in the private sector... They expect results.

For those of you who don't watch many movies:

https://www.youtube.com/watch?v=RjzC1Dgh17A

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