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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

#111

Post by novalis78 »

Frost1x wrote: post #106
tsol wrote: post #98

Earlier quoted context omitted.

>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.

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

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

#113

Post by XCSme »

amelius wrote: post #44
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.

Ok, but there is a difference between looking up definitions and understanding something.

Agree, same in programming, you could see that f = (a,b) => a ^ (10+ b) , but not understand what it actually means and why 10 is there and not 9.

Another example is the use of commonly known constants, such as pi, i or e. No paper will define those constants and explain indepth what they mean, so you need prior knowledge or to find external resources. I think for such complex papers you will find many such cases where extensive prior knowledge is needed.

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

#114

Post by leemailll »

He first talked about this breakthrough in a Peking Univ alumni meeting, and a preprint circulating in the field before he submitted to arXiv (https://drive.google.com/file/d/1vTLoh_Cpw6Zr436rD7FnjzND6ng...). It's a 111 pages long proof.

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

#115

Post by danuker »

gavagai691 wrote: post #110
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 al…

I suspect computers can also help us get deeper. Stuff like computer algebra systems.

Maybe some CAS-assisted work gets us into feedback loops allowing us to go indefinitely, as in a technological singularity.

But the "shallow" part is also quite wide.

You can teach people what you've learned forever, for instance.

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

#116

Post by ConcernedCoder »

gavagai691 wrote: post #15
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.

"I think Zhang's previous result was good enough to rebuff Hardy's claims." I agree.

age is just a number, some people may have a prejudice against larger numbers, and that to me, seems irrational

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

#117

Post by pencilguin »

Ar-Curunir wrote: post #73
davesque wrote: post #39

Earlier quoted context omitted.

I think it's fair to say that this could lead to certain new things becoming known about the distribution of primes. This could have implications for cryptographic algorithms that depend on prime numbers being hard to find.

Small correction: cryptographic algorithms don't depend on "prime numbers being hard to find", as they are not hard to find. Say you want to sample a 1024-bit prime. Then if you sample a random 1024-bit integer, it will be prime with probability 1/1024, roughly. This is a consequence of the prime number theorem [1] Some crypto (namely, RSA) depends on on composite numbers being hard to factor, which is a different pr…

RSA depends on large prime factors being hard to recover from their product.

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

#118

Post by elefanten »

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…

Regarding population decline vs. extreme dexterity... there's surely a good bit of room to improve our ability to discover and foster the dexterous extremes. If "nurture" plays any fraction of a role in the process, there are too many paths through life in this world that would still deny someone the opportunity to achieve their potential dexterity. As a baseline, I'm just talking about abject poverty / famine / war and other horrors that would easily divert someone from even the opportunity to be spotted as a prodigy.

So even if world population declines for a while, I suspect it'd be possible to enjoy more mathematical talent in the coming decades / centuries.

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

#119

Post by SantalBlush »

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).

And the movies about figures like these that do exist seem to have roughly the same story, relying heavily on the "socially inept genius" trope.

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

#120

Post by daveevad »

keepquestioning wrote: post #16

Is Yitang Zhang this century's Ramanujan?

> While he never went to school at UK, this will not be his first time on campus. Following his graduate work at Purdue University, Zhang lived in Lexington for a few years and managed the finances at a local Subway franchise. During that time he would also spend hours in the mathematics library at UK, reading journals on algebraic geometry and number theory.

A real-life Good Will Hunting, his backstory is incredible.

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