AI in Science

People from around campus talk about how they use AI.  Two 20 minute talks. The audience is mostly physics, math, CS.   This week features Tao Tao  (Physics) and the second speaker is Todd Rowland (Math).

Title: Can Transformers Predict Pseudorandom Numbers?

Abstract:
Pseudorandom number generators are deterministic algorithms designed to produce sequences that appear random, making them a useful setting for studying what Transformers can learn from seemingly unpredictable data. In this talk, I will present our work on training Transformers to predict several families of PRNGs. I will discuss when Transformers can learn these algorithms, how curriculum learning enables generalization to more challenging generators, and what these results reveal about the computational mechanisms learned by Transformers.

Second talk title  

 Exploring Open Math Problems with AI: A Journey Through Gauss’s Class Number One Problem.

Abstract

How can a human and an AI collaborate in a meaningful way on an open mathematical problem? This talk follows one such journey, by a nonexpert in number theory working with Claude, an AI assistant, on Gauss’s class number one problem for real quadratic fields. Numbers of the form a + b√d can fail to have unique factorization into primes, and the class number measures the failure, with class number 1 meaning it holds. Gauss conjectured that this happens for infinitely many square-free d > 0. Over two hundred years later the question is still open, in contrast with negative d, where exactly nine values work.

The journey includes human experiments, AI explanations, mistakes from both, misunderstandings between us, and the checks that caught them. I will describe what worked, what did not, and what this suggests for how humans and AI can do mathematics together, including how a nonexpert can test an AI’s claims.