It’s a noble goal to change the incentives, but how will you prevent the headlines from this event being “students prove Collatz conjecture with Claude” and instead be “students give great explanation of Collatz conjecture proof”?
You're right that we can't. We'll be responsible in our press releases and award prizes based on explanation, but we don't control the headlines.
However, this is already an improvement over the current state, where results are announced by headlines alone.
As I've commented elsewhere in this thread - if your goal is really to have people use LLMs to further mathematical understanding for humanity, instead of to brag about "solving" open problems, then why is there an explicit push for the Marathon to involve open problems at all? The whole thing could explicitly be about generating pedagogical content, or writing mathematical theories that simplify known results (example project idea: Kevin Buzzard wrote a lovely article on the issues that he had formalizing Grothendieck's definition of a scheme. They have since been wildly successful using AI to do formalization all the way to FLT, but no one has gone back and written a new Hartshorne that takes the insights from the formalism into account, and writes a clearer introduction to schemes that is simultaneously formally rigorous in ZFC. Using an LLM to attempt this would certainly contribute far more to human understanding of math than writing a new arxiv paper would).
I suspect you will find there is less appetite at the funding level for this kind of thing though, because what your funders really care about is generating headlines in front of their IPOs, and this kind of thing wouldn't generate the same headlines. I would be pleasantly surprised to be proved wrong of course.
EDIT: A more cynical point that I should add - I also suspect your funders would have less appetite for this kind of marathon because LLMs don't seem to be very good at this yet, which kind of points to the whole problem: so far, LLMs seem good at producing Lean proofs but not very good at the rest, but that fact is being lost in the media narrative, and "the rest" is actually the part that matters.
