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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

#231

Post by [deleted] »

s1artibartfast wrote: post #224
joshuamorton wrote: post #194

Earlier quoted context omitted.

> 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…

I don't know what to tell you. It's not a literal statement. At Best it is a heuristic and more often, a platitude. It's like don't talk to Cops or corporate HR works for the company and not you. If you were to take it at face value and debate it against it, you would be making the fallacy error of secundum quid. If you want to have a real discussion about how much good and or bad the government does, you need to fin…

[deleted]

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

#232

Post by lawrenceyan »

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…

Definitely a potentially meaningful reason as to why we should invest more heavily into life extension.

I don’t foresee AI overtaking human cognition for at least a decade or two.

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

#233

Post by sb057 »

robomartin wrote: post #140

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 iconoclasts probably give them a run for their money).

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

#234

Post by woodruffw »

earthboundkid wrote: post #227

The “lack of progress” in philosophy comes down to this. By the time of Socrates or Confucius, there had already been a lifetime’s worth of philosophical thought done that you needed to grapple with. Everyone since then has necessarily had to let something slip through in order to move forward at all.

I think we sometimes understate philosophy's progress: it's certainly not measurable in decades, but the world of 2022 looks very different (in terms of philosophical priors and their consequences) than the world of Socrates or Confucius. A handful of examples that come to mind:

* (Nearly) everybody on our planet lives under a government whose fundamental structure and right to power comes from modern (meaning 17th century) political philosophy.

* Everybody posting on this board is using a machine that only existed in the mind games (and works) of math philosophers just over a century ago.

* The philosophical foundations for contemporary science are very young, practically within living memory. Popper died less than 30 years ago!

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

#235

Post by kjellsbells »

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…

That's a very big claim, perhaps true only if human endeavor only ever builds linearly. But I dont think that is true. Certainly not in the arts or music, e.g. the Beatles did not need to ingest the entire corpus of Mozart or even Scott Joplin to be highly productive. Although, it certainly helped that they were extremely open minded to all types of music.

A second example is that of recent advances in virtualization, where the last decade of advances in things like cgroups, namespaces and containers were all done by people who I assert had no training in IBM MVS/zOS and therefore weren't building on what went before (imho, to their detriment).

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

#236

Post by Qtips87 »

canadiantim wrote: post #195
dis-sys wrote: post #145

Earlier quoted context omitted.

> like millions of others Including Xi Jinping.

Unfortunate Xi is repeating past mistakes

At least Xi is much more assertive (not aggressive) in safeguarding his country's territorial integrity whereas Mao didn't give a hoot and let his country land grabbed by its neighbors left and right.

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

#237

Post by joe_the_user »

mlyle wrote: post #191
sillysaurusx wrote: post #127

Earlier quoted context omitted.

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.

This is almost correct.

It's not that math is vastly larger (or more sophisticated) as a field. Both fields are infinitely large in many senses. Rather, the number of respectable starting points where you can do interesting things is much larger, orders larger in math.

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

#238

Post by balsam »

carrolldunham wrote: post #160
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…

Then you spend your whole PhD reinventing a wheel that has a different name in the 30 year old textbook from the next field over, and neither your peers or professor have any awareness of that

Or, as Juergen Schmidhuber likes to point out, in the same field.

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

#239

Post by wheels »

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.

That's not really the case here. Zhang spent 10 years out of school working in fields in the cultural revolution, and didn't start college until he was 23. After his PhD, he couldn't get an academic job for 8 years and ended up delivering food and working as an accountant. He only got a part time lectureship after that. He wasn't made a professor until his big proof at the age of 58.

It seems incredibly likely he'd have been able to proove his big proofs faster had his life gone otherwise.

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

#240

Post by petesergeant »

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).

There's an excellent series in which Newton plays a large part, called The Baroque Cycle. I'd love a TV adaptation of it, although you'd have to gut much of academic stuff in it and just focus on the (excellent) plot
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