> The sub O(nlogn) proof for DFT for example violated very old human assumptions.

btw people has massively improved the lower bound (from 1-2^-182 to about 1-2^-10) in the past couple of days: https://github.com/CrocSwap/integer-mult-bounds

Looking at this I'm reminded of https://en.wikipedia.org/wiki/Polymath_Project, in particular "Yitang Zhang's 2013 breakthrough on bounded prime gaps, eventually lowering the upper bound on the gap between consecutive primes from 70,000,000 down to 246".