Is the quasi-Riemann Hypothesis Proof a New Idea?
Alex Kontorovich says the quasi Riemann Hypothesis case is not a genuinely new idea. It is a beautiful combination of things that were already very well known. A lot of people are kicking themselves because they had some idea in that direction 20 years ago.
Two years ago, a big breakthrough on cubic theta functions and cubic Gauss sums became the path the AI took to the solution. He pictures a semigroup as tiles on a board: from one tile you may place another to the left, the right, the front, or the back, and keep going. Existing ideas, pushed that way, might prove a whole lot more than humans have explored. Deep problems in mathematics sometimes fall to a three page solution that is elementary, could be explained to an undergrad, and could have been discovered 20 years before the problem was posed. Found that early, it would be a textbook exercise. When the short solution stays hidden, bright people work a long time, make incremental progress, and the problem grows famous, so the eventual answer looks like a big deal.
A year ago he wrote proceedings for the International Congress of Mathematicians, text they wanted 10 months in advance, and he stands by it. One claim is that many more problems thought unreachable by current technology are reachable by current technology when the pieces are put together in just the right way. AI is amazing at that assembly. Calling the solutions combinations already inside the convex hull is not invalid, and he likes the balloon metaphor too.
#503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory ·