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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

#351

Post by kinnth »

zimpenfish wrote: post #260

Brings to mind Gould's quote - "I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." https://www.goodreads.com/quotes/99345-i-am-somehow-less-int...

Very nice quote.

I also like to think that intelligence is everywhere, but the persistent pursuit of truth is difficult. Zhang embodies a man determined to work on his particular pursuit.

I hope I can be as persistent over time.

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

#352

Post by sniperjoe360 »

Cheeky of him to use -2022 in the exponent reflecting the year of publication

> It is possible to replace the exponent −2022 in Theorem 1 by a larger (negative) value if the current arguments are modified, but we will not discuss it in this paper.

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

#353

Post by vecter »

hoseja wrote: post #293
maegul wrote: 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…

It's also a major failure in didactics. It feels like very little of the new knowledge since twentieth century has been truly digested for easy teaching. Why isn't general relativity taught in elementary school? It should be possible.

I see no reason to believe that general relativity could be taught in elementary school. It requires advanced undergraduate or graduate mathematics, not to mention that the physics itself is quite difficult (to put it mildly).

To put the blame on didactically seems to miss the more important factor that humans just aren’t that intelligent, save the one in a million genius who might have the intellectual capacity to learn something so difficult at such a young age.

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

#354

Post by woodruffw »

pmontra wrote: post #344
woodruffw wrote: post #234

Earlier quoted context omitted.

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 c…

I second your other two points but I think this one is inaccurate: > * (Nearly) everybody on our planet lives under a government whose fundamental structure and right to power comes from modern (meaning 17th century) political philosophy. A large number of countries are ruled by dictators and their close supporters. Sometimes they position themselves within the boundaries of a more or less modern ideology but ultimat…

I meant more the structure of and justification for the state and sovereign, not liberal ideology. You’re absolutely right that a large number of people don’t live under the latter.

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

#355

Post by dublin »

fredley wrote: post #295
zimpenfish wrote: post #260

Brings to mind Gould's quote - "I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." https://www.goodreads.com/quotes/99345-i-am-somehow-less-int...

I think about this often. Having studied mathematics, it's a field where there is a huge range of talents, even at 18 (and younger). There are genuinely gifted people who stride ahead, but the sad reality is that even at top institutions most of the undergraduate cohort will be merely averagely clever people who have received great (often private) tuition. In a field where finding every genius really matters because…

Given that even our first-tier colleges and universities still have no real idea how to teach math in a way that ensures that students will internalize and understand it, this isn't surprising. I think one of the most curious things about the modern world is that centuries into working with higher math, we still do not have good ways to teach it.

Most students with creative insights that could help advance the field tend to wind up one of two ways: (We need to create a viable, replicable third way - today it seems to require exceptional personalities for both student and teacher...) 1) They slog through the existing math education system, but it crushes their creativity and insight, leaving them mostly useless husks (this pit catches most mathemeticians, IMO), or, 2) They become disgusted by the incomprehensibility of higher mathematics and abandon the field entirely (this is a huge chasm of a pit, that prevents most all engineers and scientists from ever becoming more than moderately competent in mathematics and methods.)

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

#356

Post by woodruffw »

LudwigNagasena wrote: post #307
woodruffw wrote: post #252

Earlier quoted context omitted.

Each of the examples I gave have direct origins in philosophy. It’s not even clear what the alternative would be for Hobbes and Popper; for Frege you could call him a mathematician instead, I suppose, if you ignore all of the other philosophy he did.

I don’t see any direct origins. Karl Popper was a small child when Einstein came up with relativity. Hobbes was just a reactionary apologist of absolute monarchy. And Frege’s philosophical contributions were world-changing as long as we can pretend that propositional calculus is philosophy.

I don’t think this is going to be productive, but to be clear: the claim isn’t that science didn’t exist before Popper, or that Popper somehow gets credit for all of science. It’s that Popper has produced the best description of science’s epistemic underpinnings thus far, allowing science to progress without imploding under the demands of positivism. In other words: when we “do” science, the epistemic model we use is less than a century old.

The claim that propositional calculus is in the domain of philosophy and mathematics is not controversial in either domain. Nor is it unusual: the history of philosophy is the history of discharging subjects once they develop a field of their own.

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

#357

Post by dublin »

andrepd wrote: post #346
LudwigNagasena wrote: post #306

Earlier quoted context omitted.

Might as well attribute all of that to Christianity. That claim probably holds as much water.

Attributing science and freedom of religion to Christianity? That's a bold thought.

And a correct one. There is a reason these things did not develop until when and where they did...

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

#358

Post by ConceptJunkie »

unsupp0rted wrote: post #251
LudwigNagasena wrote: post #245

Earlier quoted context omitted.

Did those things appear because philosophers talked about them or did philosophers talk about them because they appeared?

I can easily imagine an Earth with no philosophers after say Aristotle that is functionally identical to our current one.

Wow. I guess you're not familiar with any philosophers other than Aristotle, otherwise you could never make such a statement.

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

#359

Post by ConceptJunkie »

trash3 wrote: post #171
maegul wrote: 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…

This sentiment is humorous, as I'm an optimist apparently. More children will learn more quickly. Applying AI to education should supercharge the smartest.

You must be an optimist if you think what passes for AI right now could in any way help education. It's an incredibly useful tool, but not in the way you almost certainly are thinking.

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

#360

Post by pbronez »

novalis78 wrote: post #111
Frost1x wrote: post #106

Earlier quoted context omitted.

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.

If you could live two or three lifetimes, would you really want to spend them all on the same thing?

Feels like attention would become the limiting factor.

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