Earlier quoted context omitted.
Do you know how much a patent clerk makes?
You’re missing the reference
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Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
151–160 of 439 posts
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#152Earlier quoted context omitted.
Plenty of counterexamples to the claim https://mathoverflow.net/questions/25630/major-mathematical-...
Just curious how many examples that show FIRST major discovery after say 40? I think I spotted a few.
Marjorie Rice. Housewife.
https://www.quantamagazine.org/marjorie-rices-secret-pentago...
Her discoveries first mentioned in a 1988 magazine when she was 65.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#153Two 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…
True. I am wondering whether this trend would make Fields Medal ( https://en.wikipedia.org/wiki/Fields_Medal ), the most prestigious award in mathematics, to change its requirement of that recipients must be of age 40 or less.
They didn't break the rule for Andrew Wiles after he proved Fermat's Last Theorem, which was arguably the most notorious unsolved problem in all of mathematics.
So I expect them to stick to their rule.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#154Math 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…
>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…
I think we're kind of becoming multi a cell organism.
There's limit to human knowledge, but we are getting more and more efficient at communication, both with other humans and with machines.
Even without something like Neuralink we are creating abstractions and interfaces allowing us to quickly connect our work with others. E.g. especially with ML you can lazy load all necessary context.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#155Earlier 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 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.
do you have experience with CAS?
i would love to learn how to use CAS to write proof more effectively
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#156Math 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…
I haven't spent much time thinking about this but were Einstein's contributions a combination of intellect and "shallow" or relatively quick frontiers. I.e. a very intelligent intellectual working on the problem sets that are approachable without the same level of overhead required these days?
I.e. Today's world wouldn't support an individual who could have such an impact on most math/scientific disciplines?
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#157Math 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.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#158Quoted post unavailable.
It's not really remarkable because governments rarely come up with nasty names. Even then the cultural revolution isn't an inherently positive. Culture can be good or bad and so can revolutions
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#159Earlier quoted context omitted.
>room-temperature semiconductors I suppose superconductors. Semiconductors are well in the room temperature regions :)
the path is just really, really clear
I can't decide if this is my favorite autocorrect, or least favorite. I'll let it stand — mostly because it's too late to edit!
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#160Math 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…
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