211–220 of 439 posts
Part of the translation is not so perfect and you have to use your best guess sometimes. The Chinese version is a masterpiece.
In addition, here is an article from Yitang Zhang's PhD advisor. Not so nice: https://www.math.purdue.edu/~ttm/ZhangYt.pdf
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…
Agreed, it feels like the days of maverick engineers leading huge efforts is mostly over. Will there be any more Kelley Johnsons, or Gene Kranzs in our lifetimes?
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…
Agreed, it feels like the days of maverick engineers leading huge efforts is mostly over. Will there be any more Kelley Johnsons, or Gene Kranzs in our lifetimes?
Is this something a proof assistant could be used to help validate?
[1]: https://leanprover-community.github.io/blog/posts/lte-final/
Earlier quoted context omitted.
While not common, I know of other Chinese diaspora in North America with similar stories. Many graduates from post Cultural Revolution China left the country in 90's and found the language barrier (and accompanying discrimination) too high to overcome. The man delivering your fried rice might have a PhD.
An unfortunate parallel: the best physics professor (unfortunately, just an adjunct) I ever had was a Russian immigrant. He quit teaching to go run a blini restaurant because it paid way more :(
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…
I first found out his story from new yorker https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty when the issue came out. I almost busted in tears. I just wish he continue to enjoy mathematics, no matter if this paper is flawed or not.
It's a fantastic piece. New Yorker has some really in depth writing.
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…
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?
General relativity was much more difficult. It took Einstein about a decade to develop it and he had to learn differential geometry in order to do so. This work was undoubtedly more profound and required much more advanced mathematics merged with deep insights such as the equivalence principle [0]. This was what made Einstein so successful: the combination of mathematics with physical insights that no one else had put together at the time.
Two 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…
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…