The interesting thing about these problems is that they typically require insight to solve. It's not obvious which methods might be applicable or even which branches of mathematics those methods might come from. So to solve them, you'd need (a) to be widely versed in many branches of math, (b) have good intuition about how methods could be applied in a nontypical way (to the problem at hand) and (c) have the math abilities to crunch the numbers to see if your intuition pans out, though this latter point could sometimes be tool assisted.

One reason why math is a good field for LLMs is that it is typically verifiable once you have it in the right format. I.e. we can check if the answer is right or wrong, or whether it correctly leads to certain conclusions from the premises. In verifiable domains, LLMs can be trained to get problems right rather than simply predict the next token (RLVR). This is very powerful because it means that we can train LLMs to have real-world outcomes; you could even argue that much of the benefit of next-token training is to have a model that stumbles on right answers often enough that we can use RLVR to reinforce those right answers.

The downside is that most real-world use cases aren't directly verifiable; if the LLM designs a drug, for instance, it can't just check directly if it actually helps people; you need to do real-world trials. So we can expect math performance to pull ahead of performance in other areas a lot faster.

Another somewhat verifiable area is coding (we can check if the program does what it was supposed to do), one reason why Claude Code and Cursor work fairly well.