Won't deny that this is an interesting idea, but I feel like waiting on the output of an LLM for 40 hours feels like it is completely antithetical to what makes classic Hackathons appealing / educative. More generally, I don't think the shape of a hackathon (intensely working for a short timespan) maps at all onto the way LLM Math progress has seemingly been made so far; AFAIK it mostly involves picking out something…
Have you done any math hacking with sol/astra or fable? It’s more fun than using them for coding. The models are great at the monotony, like constructing a Gröbner-basis, etc. But they’re all still absolutely awful at coming up with new ideas, new proof methods, or new constructive forms. So you spend all your time on coming up with novel hypotheses yourself and handing off the rote work to an agent.
It’s also quite fun to get instant results by finding isomorphisms into unfamiliar areas of mathematics that previously would’ve required some networking in order to build a collaborative relationship.