In this talk, I will discuss some ways in which AI can be used in mathematical research. Through a series of examples, I will illustrate how AI can help explore problems, suggest ideas, test conjectures, and sometimes obtain partial results. I will also describe several instances where these methods contributed to ongoing work, including partial progress that eventually appeared in a paper.

Part of the talk will be conducted in a live, experimental format. I will demonstrate how one can use AI in real tim by selecting a mathematical paper and attempting to engage with it on the spot. By this, I mean using AI to investigate the paper, explore related questions, and try to prove partial results inspired by it. The goal is not to present AI as a replacement for mathematical thinking, but rather as a new kind of experimental tool that may assist with exploration and discovery.