A.I. e la matematica @ThManfredi @gianlucac1bis con il prof Giuseppe Mingione @grmvader : stiamo entrando nei dieci anni più trasformativi della storia umana? Non promettiamo di rassicurarvi... Una puntata imperdibile! youtu.be/ilG2bxcoIrQ #crosswords

What does a superhuman level of mathematics look like? Here is one elementary example I could give to nonexperts. Daniel Kane and Terence Tao showed (arxiv.org/abs/1702.00912) that, given a collection X of sets, the total number of ways to write A as a disjoint union of B and C, with A, B, C from X (disjoint means non-overlapping), is at most cardinality of X to the power 1.72598…, and this power is sharp. To show this, they came up with an innocent-looking function B(x,y,z) = (xyz)^c of three variables, satisfying a certain arithmetic inequality and having prescribed boundary conditions. Proving that arithmetic inequality was really a headache. There was a question whether one could improve this bound, i.e., maybe add some logarithmic correction terms, and one could kind of imagine what should be done (see comments on terrytao.wordpress.com/2017/…), but it was not clear whether it would be easy to do. Now superintelligence improves this bound by introducing a certain monster function of three variables (see screenshot). Even if I had seen this function in my dreams, I would never have dared to verify that main arithmetic inequality. The candidate function produced by SI gives a bound matching the known lower-bound examples up to a constant factor, including the sharp logarithmic correction. All the details are here paatai.github.io/ai-proofs/b…

New math slop coming in a few hours. Pretty impressive result by Astra.

My dream had always been to prove beautiful theorems as the AI agents unloaded my dishwasher. Well, it went the wrong way... 😂