2025 Distinguished Lecture Series in Mathematics

University of Hawai’i at Mānoa, March 28 — April 2,  2025

Jordan Ellenberg

John D. MacArthur Professor of Mathematics, Guggenheim Fellow, NYTimes Best-selling author of “How Not to be Wrong” and “Shape”.

Colloquium:  Friday, March 28, 3:30pm (PSB 217)

What does artificial intelligence have to offer mathematics?

The interaction of machine learning with math has attracted a lot of attention, because mathematics is in some respects a closed world with well-defined rules (like chess, and unlike poetry-writing) but also a domain where success is ultimately judged by human assessments of ingenuity and importance, not rigid criteria (like poetry-writing, and unlike chess). Can machines prove theorems? Can they generate mathematical ideas?  I'll talk about some of my own work with collaborators from DeepMind, using a protocol called FunSearch, and what I've learned from this work about the current and near-future relevance of AI to mathematical practice. 

Two relevant papers:

https://www.nature.com/articles/s41586-023-06924-6

https://www.arxiv.org/abs/2503.11061

Public Lecture:  Monday, March 31, 5:30pm (PSB 217)

From malaria to ChatGPT: the birth and strange life of the random walk

Between 1905 and 1910 the idea of the random walk, now a major topic in applied math, was invented simultaneously and independently by multiple people in multiple countries for completely different purposes, from mosquito control to physics to finance to winning a theological argument (really!) I’ll tell some part of this story and also gesture at ways that random walks (or Markov processes, named after the theological arguer) underlie current approaches artificial intelligence, and what this tells us about the capabilities of those systems now and in the future.

Seminar: Wednesday, April 2, 3:30pm (Keller 303)

Smyth's conjecture and a non-deterministic Hasse principle

The matrix

3     -3    4     -4    5     -5    0     0

4     -4    -3    3     0     0     5     -5

-5    5     0     0     -3    3     -4    4

has an interesting property.  Can you see what it is?

In case this puzzle is not enough information about the talk:  I will explain how to prove a conjecture of Smyth from 1986 about linear relations between Galois conjugates, and explain what this has to do with linear combinations of permutation matrices,  Brianchon's theorem on ellipses inscribed in hexagons, weightings on the edges of directed hypergraphs, and the study of Diophantine equations where the equation is to be solved with probability distributions instead of with numbers.  This is joint work with Will Hardt.