Lauren Williams

Also known as Lauren K. Williams, Lauren Kiyomi Williams

Lauren Williams is a Harvard mathematician who helps test AI systems on research-level mathematics as an editor of the First Proof project. Trained at Harvard, Cambridge and MIT, where she earned her PhD under Richard Stanley in 2005, she built much of her research around the positive Grassmannian, connecting it to interacting soliton waves and to the amplituhedron of particle physics. She taught at Berkeley from 2009 to 2018 and returned to Harvard in 2018 as the second tenured woman in its mathematics department. Her honours include a 2022 Guggenheim Fellowship, election to the American Academy of Arts and Sciences in 2025 and a 2025 MacArthur Fellowship. In February 2026, she and ten other mathematicians shared First Proof, ten unpublished research problems for testing AI systems; she is the Dwight Parker Robinson Professor of Mathematics at Harvard.

Now at: Harvard University
Born: 1978
Badges: Boomerang

Years link to their sources.

Timeline

1994–2005

Harvard, Cambridge and an MIT PhD

She attends the 1994 Research Science Institute at MIT as a high school student, working with Satomi Okazaki, a student of Richard P. Stanley. She earns an A.B. in mathematics from Harvard in 2000 and completes Part III of the Mathematical Tripos at Cambridge in 2001. At MIT, she devises a formula in 2003 for counting the cells of positive Grassmannians of any dimension and earns her PhD under Stanley in 2005 with the thesis Combinatorial aspects of total positivity.
2005–2009

Postdocs at Berkeley and Harvard

After her 2005 doctorate, she is a National Science Foundation postdoctoral fellow at the University of California, Berkeley, and a Benjamin Peirce Fellow at Harvard, where she spends three years. Right after graduate school, she writes a series of papers with Sylvie Corteel linking the combinatorics of the positive Grassmannian to statistical physics.
2009–2018

Professor at Berkeley

She rejoins Berkeley’s mathematics department as an assistant professor in 2009, becomes a full professor in 2016 and stays on the faculty until 2018. In 2009, she notices that Ohio State physicist Yuji Kodama has cited her work in his research on shallow water waves; together they show how the positive Grassmannian describes interacting soliton waves, in papers on KP solitons published in 2011 and 2014. The American Mathematical Society names her one of its inaugural fellows in 2012, and she wins the Association for Women in Mathematics–Microsoft Research Prize in Algebra and Number Theory in 2016.
2018–2021

Full professor at Harvard

With Sylvie Corteel and Olya Mandelshtam, she develops a new characterization of Macdonald polynomials through the exclusion process in 2018, and in fall 2018 she rejoins Harvard’s mathematics department as a full professor, the second tenured woman in its history. In fall 2019, she and physicist Nima Arkani-Hamed co-organize a semester-long Harvard program on the link between the positive Grassmannian and the amplituhedron, a shape whose volume gives the amplitude of a particle collision. As a 2020–2021 Radcliffe Institute fellow, she works with Sergey Fomin and Andrei Zelevinsky on the book Introduction to Cluster Algebras.
2022–2023

Guggenheim Fellowship and IHES visit

In 2022, she wins a Guggenheim Fellowship for a project on the combinatorics of hopping particles and statistical physics, and she is an invited speaker at the 2022 International Congress of Mathematicians. From August 2022 to July 2023, she spends almost a year as a visiting professor at the Institut des Hautes Études Scientifiques (IHES) in Bures-sur-Yvette, France, with funding from the ENGIE Foundation.
2024–2025

A MacArthur Fellowship

As a 2024–2025 Radcliffe Institute fellow, she works on interacting particle systems, mirror symmetry and the amplituhedron. In April 2025, she is elected to the American Academy of Arts and Sciences. The MacArthur Foundation names her a 2025 Fellow for connecting algebraic combinatorics with problems in other areas of math and physics, including her proof that the positive Grassmannian can be used to triangulate the amplituhedron.
February–June 2026

First Proof’s first two batches

In February 2026, she and ten other mathematicians, including Mohammed Abouzaid and Fields medalist Martin Hairer, share First Proof, ten unpublished research problems for testing whether AI systems can solve research-level mathematics. In June 2026, she coauthors the Second Batch report with Abouzaid, Nikhil Srivastava and Rachel Ward, and at least one AI system answers six to seven of the ten new problems essentially correctly. She faults the AI answers for their many missing citations, which she says one might call plagiarism in a human.
As of October 2026

First Proof editorial board

She is the Dwight Parker Robinson Professor of Mathematics at Harvard, where she teaches a freshman seminar on the alternating sign matrix conjecture in fall 2026. She serves on First Proof’s editorial board with Mohammed Abouzaid, Nikhil Srivastava and Rachel Ward, and the project publishes its Third Batch results in October 2026.

Career

Since 2005Harvard UniversityBenjamin Peirce Fellow, Full Professor
2022–2023Institute of Advanced Scientific StudiesVisiting Professor
2005–2018University of California, BerkeleyNational Science Foundation Postdoctoral Fellow, Assistant Professor