https://en.wikipedia.org/wiki/Computer-assisted_proof#Theorems_proved_with_the_help_of_computer_programs

Most (all?) problems in the list can be reduced to/is equivalent to discrete mathematics problems where there exists subproblems that can be checked rigorously by a computer. That doesn't seem to be the case for any Millennium Prize problem.

@meiqian The ideal view I have is that a perhaps one day we have an AI where Andrew Wiles could submit his first good but incomplete attempt to Fermat's Last Theorem and some sort of LLM for math would correct it. Perhaps they would do some back and forth.

@MP I don't think we are even close to formalizing Andrew Wile's proof of Fermat's last theorem in any proof assistant, which I think is substantially easier than having a computer suggesting proof ideas.

@meiqian yeah, I hold no view

Guys, when I created this market, there weren't loans, so I didn't want to put a long end date. I think it's fair to extend for at least a decade the solution of this question. What people betting NO think?

@MP I think extending it is fine. 2025 is already in the realms of long term bets by my standards.

@MP I'm confused why the end date matters at all? I thought this market closed once the next Millennium Problem is solved.

@IsaacKing Me too. But past me added an end date and Manifold doesn't support perpetual markets.

"Some sort of brute force algorithm obviously doesn't count" so if a sort of ML4TP Alpha Go - style agent which does RL on the proof search space by searching billions of possible lines of argument finds a solution, does that count as brute force?

@BoltonBailey I am not familiar with this particular algo, but you bet I will be if I ever need to adjudicate this question.

That said, if you search the solution universe without any clever way to avoid testing all the solutions, I don't think I'll consider that to be an AI.

But there are nuances. One of the steps of your brute force can be an AI. If you have an oracle that uses AI and is able to say whether for all numbers bettewn two consecutive integer numbers the Riemman Hypothesis is valid or not and then you run it in a super computer for decades testing every two numbers and then you discover that between Googol and Googol +1 the Riemann Hypothesis isn't valid, I guess you can say you used AI, even though there was brute force envolved.

Very interesting question, so I made a twist on it. https://manifold.markets/FutureOwl/will-artificial-intelligence-be-par-d434ff7690c1

@FutureOwl Very interesting market, sir! ty for sharing