This does seem like one math domain where there's some potential for program synthesis approaches like the recent AlphaEvolve and others. I say that because some of these problems you could feasibly write automatic evaluation code and solve them by the LLM spitting out a constructor for solutions and then doing hill climbing. That's not true in many areas of math though. There's also problems here that require a proof and maybe would be approachable eventually using automated theorem proving. But there's also problems that don't obviously fit into either of those categories.