I have always felt that mathematics begins before proof. Long before a statement is settled, there is a quieter stage of choosing what to notice, what to distrust, and what deserves another look. Kodaira once compared logic in mathematics to grammar in literature, and that image has stayed with me: rigor gives thought its final form, while intuition decides where thought should go.

I had followed AI in mathematics for years, and OpenAI’s recent work on ten research-level problems finally pushed me to try AI for Math seriously. I chose an open problem close to my interests in mathematical physics and worked through it in five rounds.

My own thinking changed more than the problem did: first I looked for an entry point, then for patterns, then for the first place an argument lost something essential; after that I began to treat failure as evidence, tracing each broken approach back to the piece of structure it had forgotten, and finally trying to preserve those pieces long enough for them to interact. Somewhere in that process, exploration started to feel less like searching for a proof and more like learning the shape of the problem.

I was also fortunate to exchange ideas with James Sud, one of the authors of the original conjecture. His comments often arrived at the same place my own thoughts were heading, especially the idea that proofs become loose when interacting pieces are separated too early. There is a rare pleasure in meeting someone who understands why a failed argument can still be worth keeping.

What began as a small experiment has now grown into a manuscript and, perhaps, a few genuine mathematical ideas. I still do not know what they will amount to. For now, I am simply glad that the path kept opening.