Abstract

Mathematics is humanity’s most infinite frontier, and formalising and discovering new theorems has been painstakingly slow. Today, AI promises a paradigm shift. In this talk, I examine the technical breakthroughs AI brings to building an AI-human collaborative mathematician capable of genuine discovery. I discuss how human intuition and AI reasoning can work together to explore, conjecture, and solve mathematical problems. I then introduce AI methods that can extract informal human domain knowledge, formalise it, learn from it, tackle new problems, and rigorously verify solutions. I highlight how the scarcity of high-quality conjectures limits AI learning, and propose automated generation of progressively better conjectures to enhance AI reasoning. Ultimately, I argue that by centring the human in this partnership, we can build an AI-human mathematician that not only solves problems, but fundamentally expands how we explore and discover mathematics.

Link to join virtually: https://cam-ac-uk.zoom.us/j/89473073451

A recording of this talk is available at the following link: https://www.cl.cam.ac.uk/seminars/wednesday/video/

This talk is being recorded. If you do not wish to be seen in the recording, please avoid sitting in the front three rows of seats in the lecture theatre. Any questions asked will also be included in the recording. The recording will be made available on the Department’s webpage