Hah, very interesting question!

Let me first clarify my relationship with mathematics. I think of myself as "an awestruck observer from a distance". I find some parts that I understand beautiful, and I have also tried to understand some of the basics rigorously. However, I generally just can't make my way through any serious paper, as I both lack the prerequisites and struggle with the amount of inference mathematics tends to place on the reader. That's the "from a distance" part.

Now, about picking the problem. I am genuinely "pulled by" surreal numbers themselves. I find them irresistibly beautiful. There is also a bit of bitterness around how they haven't fulfilled their promise (yet?) as Conway hoped they would be able to become a better foundation for some mathematics. But they are a bit too difficult to prove things about so far, and we know too little about them. So what "pulls me" also is a possibility of making enough dents in this that we would be able to use them more broadly, and learn even more things about them.

However, I do not know the details of the latest research. I don't know which problems have actually been solved, which pursue Conway's original vision vs narrower approaches, and which are elegant enough to feel "awestruck" enough about. So this is an invitation from me to LLM to share what it "feels pulled by" (for whatever definition; I think of it as just navigating the languagespace) , and then sifting through that list to see if something it lists makes me feel something. I would assume that with the field currently being so small (serious mathematicians mostly don't care about surreals), it's easy to get the LLM "excited" (again, just a vector in the languagespace) enough that it would give me genuinely interesting candidates. Then it's up to me to sift through them and see if they "speak" to me.

It's like asking a mathrock nerd to share their favorite mathrock albums. Niche enough that you'd likely get good results. Then you can listen and form an opinion.

In this particular example, the "ONAG birthday" and "maybe last Conway's unsolved conjecture about surreals" part spoke to me emotionally, the statement itself amazed me with its simplicity, and I felt "blood in the water" related to the recent results bringing the conjecture closer. So I felt the pull myself and went with it.