Just a cultural observation: I wonder how many Chinese geniuses are behind the iron firewall of China. With the number of Chinese population and STEM focus, it's likely that in two decades Chinese dominance of sciences, technology, and later culture (language, art etc) is ensured.
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
#272Math 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…
There's also occasionally realignments where the deep stuff gets shallower. It takes a lot of rickety scaffolding to get to a new place, and occasionally the finished product stands fine on its own.
The simplest example that comes to mind is that you can learn group theory without really needing to know anything about Galois theory. I also imagine there's a lot of good math that has shed vestigial physics...
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#273Math 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…
Another approach to the finite-mathematician-lifespan problem might be to develop new foundations that are closer to the edge. I expect there's a logical universe in which sets are bizarre and hard to construct but objects which would take a modern mathematician years to grok are convenient and simple to work with.
My favorite thought game along these lines is imagining an alien civilization where permutations are the fundamental object instead of the natural numbers.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#274Two 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…
That rejoinder has not been true for a while now. Laszlo Babai's graph isomorphism work is another recent example.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#275Wow, from the 2015 article: [A journal reviewer of his famous paper says]: "you should be careful. This guy posted a paper once, and it was wrong. He never published it, but he didn’t take it down, either.’ ” The reader meant a paper that Zhang posted on the Web site arxiv.org, where mathematicians often post results before submitting them to a journal, in order to have them seen quickly. Zhang posted a paper in 2007…
One can't really take papers down from arXiv anyway.
Well, you can update them with a disclaimer that points out known issues.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#276Add Comment
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#277I 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
Pretty sure it's much harder than Chinese. The depth and abstraction of the concepts involved and the density of these concepts in these lines vastly eclipses anything in any natural language
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#278Math 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…
Maths always used to be an entertainment for aristocrats and philosophers.
Only in very few exceptional times in history it was been used for something else, being the largest exceptions the industrial and scientific revolution, and these usually did not require breakthroughs: just apply existing knowledge.
It’s never been a young person game.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#279Earlier quoted context omitted.
Did those things appear because philosophers talked about them or did philosophers talk about them because they appeared?
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.
The causality here is hard to prove, even untangle. I think the French Revolution was largely more influential for the state of governments today. I also think that science was not influenced so much by Popper, but much more by Fisher and Neyman.
People tend to use what is a successful tool, and be influenced by power and theatre, not so much by fragile logical constructs without empirical value found sitting in the armchair.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#280Earlier 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…
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.
This is not a good example, as Rust does not build on C++, it simply replaces it as the foundation. Of course, the development of Rust is built upon lessons learned from C++.
But there is no universal law that says that the foundations of a field must be simple enough for one human to understand them in 70 years. It may well be that the simplest possible statement of a field of knowledge is still too complex for a single human to understand it in a normal life-span (not to mention that our capacity for storing information is limited - you can't actually continually learn new things for 70 years without forgetting much of what you learned initially).
Even today, you could spend literally your entire life trying to learn everything we know about the human body and you would almost certainly die before having learned everything. Now, fortunately, there is plenty of real work, both as a doctor and as a researcher, that can be done by focusing on just one aspect of the body (say, the circulatory system) and having only relatively shallow knowledge about the rest. Still, there is the possibility already that a mind that could build on all of the deep knowledge we have could come up with new ideas in medicine and biotech that we are unable to because of this silo-ing.