Comment by thereitgoes456
21 hours ago
I am asking about approaches, not results.
Nobody serious would deny this is incredible progress, but GP is making an unmotivated leap to RSI, so I respond to that framing. It’s an interesting argument to be had but I suspect few of us have standing to say one way or the other.
(Gesturing at the number of problems solved, or the number of years the problem was open for, isn’t an argument.)
Sorry for the delayed reply - it's taking some time for people to digest these!
Yes there are some extremely novel approaches. Scott Aaronson highlights[1] some of ones he's interested in, and I'd highlight:
> Matrix multiplication in O(n9/4) time—a rational exponent for once (!), and via a completely different approach than was used for O(n2.373) and so forth
And in his wife's comments on USG (which she worked on):
> The UGC proof invents a completely new bizarre code with a noise test. It’s some crazy recursive construction. It’s not the long code, not the short code – some alien craziness
[1] https://scottaaronson.blog/?p=10169
Those Theorists are arguing whether the QR Hypothesis result is the biggest Number Theory Advance in 1 or 2 centuries because there was zero progress on it whatsoever and many believed that would remain the case in our lifetime. Any approach there would be surprising as no-one had the faintest clue how to begin this at all. There are like at least a dozen of these results that would have catapulted a human to instant fame and the highest accolades in the field. If you think about it, it would be impossible for there to be no surprising approaches.