|
|
|
|
|
|
by xanderlewis
814 days ago
|
|
|
I didn’t claim it was incorrect. I was just observing that it sounded like an echo of the past, which it does. …however, surely if we’re reaching some sort of plateau in mathematical understanding, it’s the end of all research — and that is slightly hard to believe. Do you think we’re nearing a proof of the Collatz conjecture? Or is the theory we have just totally inadequate? |
|
|
Well, Terrence Tao made a recent advance towards it. It's hard no doubt, but I don't think recent theory is inadequate, except maybe that no one has found any structural link to a body of more advanced math like it was done with Fermat's last theorem, which is why some people think we need new theory to solve it.
Also, I definitely didn't mean to imply we are reaching a plateau of mathematical understanding: there's still a long way to go in proof theory, K-theory, Langlands (a better understanding of orbital integerals, how to compute them symbolically...), nonabelian cohomology even (lots of stuff there seems ad-hoc like definitions of higher nonabelian cohomoogy groups).
What I do mean to imply is that it is getting to the point where none of the discovers at that level really lead BACK to anything that the vast majority of scientists or even math graduate students have much interest in. That's different in cases like evolutionary biology: even the advanced discoveries can still be tied back to things that are interesting for the "every day scientist".
Math has lost that link. It's not running out of problems, but it's running out of interesting problems IMO.