I think that’s an opportunity, not a problem. If prompt + hint generates a verifiable solution then you can build systems that propose hints, either randomly or by exploring a search space, and keep trying combinations until you hit on something that works.

Maybe you could do it with math research?

First, give it the abstract for a fresh paper that it couldn’t have been trained on, then see if it can come up with the same proofs to see if it can replicate the logic knowing the conclusion.

Second, you could give it all the papers cited in the intro and ask a series of leading questions like “based on this work, what new results can you derive”?

Honestly, that's still far too much help in lots of cases.

Finding a set of papers, whose results can be combined in a reasonable amount of time to make a new interesting result is itself a hard problem. This is often a thing Professors do for PhD students -- give them a general area to research and some papers to start reading.

It's still a contribution, but so much easier than just asking "Hey, choose a set of papers from which you can derive new interesting results"

AlphaProof is among the most relevant methods here. And because it trains by self-play, instead of historical human data - it has a much better chances of being able to solve novel problems, or come up with solutions that humans have not. It did pretty good at the 2024 Olympiad. Will be interesting to see how 2025 goes.

exactly. hindsight bias makes it really hard to separate genuine inference from subtle prompt leakage. even framing the question can accidentally steer it toward the right answer. would be interesting to try with completely synthetic problems first just to test the method.