In this episode, Lauren Williams, professor of mathematics at Harvard University and a 2025 MacArthur Fellow, speaks about the surprising and often messy reality of mathematical research. The conversation begins with a turbulent moment in academia, when federal grants supporting her work were suddenly canceled—only months before she received the MacArthur “Genius Grant,” an unexpected recognition that allowed her to continue her research. Williams explains her work in algebraic combinatorics, illustrating how abstract mathematics can connect to real-world systems. The discussion also explores the human side of discovery, from collaborations that span continents to the strange coincidence of research papers and babies arriving the same week. Finally, the episode dives into one of the most intriguing experiments in modern mathematics: the First Proof project, which tests whether artificial intelligence can produce genuine mathematical proofs, revealing both the promise and the current limitations of AI-generated reasoning.

Chapters

01:27 Winning the MacArthur Genius Grant

01:43 Becoming a Woman in Mathematics at Harvard

04:25 Research Applications

10:04 The Human Side of Research

12:20 The First Proof Project

18:29 Advice for Young Mathematicians

22:51 The Intersection of Mathematics and AI

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