Episode 1: On the Erdös unit distance problem and the role of AI in research mathematics
Guests: Daniel Litt and Melanie Matchett Wood

Listen to Episode 1.
Listen to Episode 1 on YouTube.

This interview was recorded on June 18, 2026.
Podcast release date: July 1, 2026.

See more episodes at academiaontheline.com.
Podcast abstract
OpenAI's recent disproof of Erdös' unit distance conjecture surprised much of the mathematics community and prompted many researchers to reconsider the capabilities of modern reasoning models. In our inaugural episode, Melanie Matchett Wood and Daniel Litt join us to discuss the mathematics behind the result, the nine author companion paper written by leading mathematicians, and the broader implications of AI for mathematical research and graduate education.

Podcast timeline
00:00 Introduction
04:17 Guests Melanie Matchett Wood and Daniel Litt come on the line.
17:05 What is the unit distance problem?
24:41 OpenAI's disproof of Erdös' conjecture.
58:25 Do we still need professional mathematicians? How will we evaluate them?
1:13:40 How else will research mathematics change in the age of AI?
1:19:56 Preserving humanity's understanding of mathematics, human capital, and education.
1:32:50 Who pays for AI tools in research mathematics?
1:45:25 Final thoughts and credits.

Theme Music: Ophelia's Blues by Jason Shaw (Audionautix.com), licensed under Creative Commons.
Related materials

0. OpenAI's announcement on May 20, 2026.
1. OpenAI's research paper with the disproof of Erdös' unit distance conjecture.
2. The nine author companion paper.
3. Twitter source for the projected lattice image that Daniel mentions in the episode.
4. Find your Erdös number, or collaboration distance more generally.


   

About our Guests

Daniel Litt is an assistant professor of mathematics at the University of Toronto, working at the intersection of algebraic geometry, number theory, and topology. After receiving his PhD in 2015 from Stanford, he held positions at the University of Georgia, the Institute for Advanced Study, and Columbia University. He is a Sloan Research Fellow, a Fellow of the AMS, a recipient of the Ontario Early Researcher Award, and a recipient of the 2025 Cathleen Synge Morawetz Prize. In the fall, he'll be the Benedict H. Gross distinguished visitor at Harvard University.

Melanie Matchett Wood is the William Caspar Graustein Professor of Mathematics at Harvard University. She received her BS in Mathematics from Duke University and her PhD in Mathematics from Princeton University. Following an American Institute of Mathematics Five-Year Fellowship and a Szëgo Assistant Professorship at Stanford University, she held faculty appointments at the University of Wisconsin–Madison and the University of California, Berkeley before joining Harvard in 2020. Wood has received a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, a Presidential Early Career Award for Scientists and Engineers, the National Science Foundation's Alan T. Waterman Award, and a MacArthur Fellowship. She is a Fellow of the American Mathematical Society, an Honorary Member of the London Mathematical Society, a member of the American Academy of Arts & Sciences, and a member of the National Academy of Sciences.