Motivation
AI can clearly solve some impressive problems in mathematics. However, an interesting observation is that most major conjectures resolved by AI are by finding a (counter)example. This question asks if and when an AI will prove a conjecture.
This is a sequel to the following market:
Resolution Criteria
To qualify, an AI has to resolve one of the remaining 128 unsolved conjectures, with the two following additional constraints:
The resolution has to go the way mathematicians expect.
The proof cannot boil down to "here is an (counter)example".
As example to point 1: disproving the Riemann hypothesis would not count for this market, proving it would count. If it's close/unclear, I'll do my best to find out the consensus under mathematicians. If I cannot determine a consensus (not even a weak one), then this constraint is automatically satisfied.
Point 2 tries to capture that the proof has to be an mathematical argument that something always/never holds, not a construction that exhibits some properties. This is not trying to be a gotcha, and parts of the proof can definitely be constructions. Also, the proof does not have to elegant/understandable/short. This constraint can be checked by asking "would a proof or a disproof of this conjecture feel more like providing an example?". If it's unclear, this constraint is automatically satisfied. In most cases this constraint will agree with constraint 1 (definitely for P=NP, Collatz, Riemann hypothesis, twin prime, and all others I can think of on the top of my head).
Each of these criteria individually would disqualify both the resolution of the Jacobian conjecture and the Erdős unit distance conjecture (the latter is furthermore disqualified by not being on the list).
The resolution criteria of the original market still apply.
In the (highly unlikely) situation that all 128 conjectures are resolved, but disqualified by the two constraints above, then all answers will resolve NO.
Disclaimer
This is not intended to move the goal posts. AI can make impressive contributions to mathematics today. I am just curious how big the gap is for AI from finding novel counterexamples to finding novel proofs.
I might add new answers as needed.
I will not bet on this market.
1,000