Earlier quoted context omitted.
Ironically he didn't patent E=MC^2 and now everyone says it scot-free.
I'm sorry for the others, friend. I am here to laugh with you.
Hakuna matata! Downvotes are just a karma payment coming due.
Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
301–310 of 439 posts
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#302Earlier quoted context omitted.
> he didn't patent E=MC^2 and now everyone says it scot-free Laws of nature (and descriptions thereof) aren't patentable. https://www.bitlaw.com/source/mpep/2106_04_b.html#:~:text=Th... .
That’s US law though (no idea if Germany had it any different at the time, but it’s a different jurisdiction).
Germany outlawed Einstein.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#303Brings 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…
I don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society.
However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed at a very high level? If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. We might focus more on making sure a wider group of 'averagely clever people' get such good tuition, rather than on the finding and promotion of undiscovered geniuses.
Two examples that I often think about in this context: firstly the Budapest school of mathematics in the early 20th century. A hugely disproportionate number of the world-class mathematicians from that era were directly taught by Fejer and/or part of his seminar and mentee group. (He stands out as a supervisor to a far greater extent than any mathematician stands out from the pack for his own achievements.) Is it possible that while one or two of this group might have been 'born geniuses', it also includes several who might otherwise have been second-rate, but who became world-class because of the influence both of Fejer and of their high-performing colleagues?
Secondly, George Harrison of the Beatles. In the second half of the Beatles' recording career, he wrote some of their best-loved songs, several of which are regarded as absolute classics. Did the Beatles happen to contain three inherently gifted songwriters, by sheer coincidence? Or is it more likely that working for a decade alongside two extremely talented and successful songwriters nurtured and elevated Harrison far beyond what might otherwise have been expected?
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#304Earlier 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.
Minus evidence-based science, free markets, government of the people, freedom of religion and the end of slavery. Yep, exactly the same.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#305I need a “Explain like I’m 5” for Landau--Siegel zeros. This sounds like a hard task as I couldn’t find anything online that does it :(
There are moments I'm pretty proud of my intellect and what I have achieved with it. Reading and not comprehending even the very basics of proofs like Zhang's are a good reality check in that regard.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#306Earlier quoted context omitted.
I can easily imagine an Earth with no philosophers after say Aristotle that is functionally identical to our current one.
Minus evidence-based science, free markets, government of the people, freedom of religion and the end of slavery. Yep, exactly the same.
Might as well attribute all of that to Christianity. That claim probably holds as much water.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#307Earlier 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.
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.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#308Earlier 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…
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…
But you can manufacture new areas of mathematics. For example, Conway's Game of Life, and then prove theorems on it.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#309Earlier quoted context omitted.
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…
I don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society. However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed…
I think the Beatles included three inherently gifted songwriters by sheer coincidence. No doubt the apprenticeship helped, but Harrison was writing songs like Taxman and experimenting with Indian classical music on Love You Too in 1966.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#310Two 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…
I'd like to think that there's much more socioeconomic diversity among present day scientists, compared to those back in the day of Hardy.
Not to mention that up until 1910s, life expectancy was under 50.
Being able to work in academia as a tenured professor/researcher probably resulted in drastically different life expectancy, compared to being forced to do something else. I think it's safe to say that Zhang would been forced to live as a peasant, had he been born 120 years ago.