PeopleofSuperintelligence

Researcher

Grant Barkley

Also known as Grant T. Barkley, Grant Thurman Barkley

Grant Barkley is a mathematician at the University of Michigan who studies Coxeter groups and Kazhdan–Lusztig polynomials, and whose work meets AI through benchmarks and machine-learning conjectures. He co-authored FrontierMath, a 2024 benchmark of hundreds of original, exceptionally challenging mathematics problems on which state-of-the-art AI models solved under 2%. With Christian Gaetz, he proved for lower intervals a Kazhdan–Lusztig recurrence that Blundell, Buesing, Davies, Veličković and Williamson had conjectured with the help of machine learning. After undergraduate study at NC State University, he earned a Harvard PhD under Lauren Williams in 2025, and in 2026 he, Gaetz and Thomas Lam proved combinatorial invariance for the coefficient of q in Kazhdan–Lusztig polynomials. Since late 2025, he is an NSF Research Fellow and IBL Research Assistant Professor at Michigan.

Timeline

  1. 2019–2021

    Domino tilings and billiard paths

    He is an undergraduate at NC State University before his Harvard doctorate. In November 2019, he and Ricky Ini Liu post "Channels, Billiards, and Perfect Matching 2-Divisibility," which links channels in planar graphs to billiard paths to bound the power of 2 dividing the number of perfect matchings; the paper appears in the Electronic Journal of Combinatorics in 2021.

  2. 2022–2026

    Kazhdan–Lusztig work with Christian Gaetz

    In 2022, while both are at Harvard, he and Christian Gaetz begin working on the Combinatorial Invariance Conjecture, drawn by a new conjectural approach from Geordie Williamson and collaborators at DeepMind. Their 2025 paper in Mathematische Annalen uses hypercube decompositions that Blundell, Buesing, Davies, Veličković and Williamson discovered with machine-learning techniques. A 2026 paper in International Mathematics Research Notices proves those authors' machine-learning-assisted recurrence for lower intervals.

  3. November 2022

    Extended weak order with David Speyer

    In November 2022, representing Harvard University, he speaks at Cornell's Discrete Geometry and Combinatorics seminar on extending the weak Bruhat order. With David Speyer, he proves the conjecture that Matthew Dyer's extended weak order is a lattice for affine Coxeter groups.

  4. November 2024

    Co-authoring FrontierMath

    He is among the co-authors of FrontierMath, first posted in November 2024, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. Its problems span most major branches of modern mathematics, and state-of-the-art AI models at release solve under 2% of them.

  5. 2025

    A Harvard PhD on root systems

    He completes his PhD at Harvard University in 2025 under Lauren Williams, with the dissertation "Infinite Root Systems In Algebra And Geometry." He is one of four Williams students who defend their theses in April 2025.

  6. 2025–2026

    The coefficient of q

    In 2025, he and Gaetz visit the Sydney Mathematical Research Institute during its special semester "Modern perspectives in representation theory" to work with organizers Thomas Lam and Geordie Williamson. In 2026, Barkley, Gaetz and Lam prove the combinatorial invariance conjecture for the coefficient of q in Kazhdan–Lusztig polynomials, which also settles the conjecture for Bruhat intervals of length 5 or 6.

  7. Since 2025

    NSF fellow at Michigan

    He starts a postdoc at the University of Michigan in late 2025, where he is an NSF Research Fellow and IBL Research Assistant Professor. In 2026, he teaches the undergraduate mini-course "Bruhat orders and applications" at Notre Dame's Center for Mathematics and co-organizes a Fall 2026 learning seminar on solvable lattice models with Thomas Lam, Yelena Mandelshtam and Rui Xiong.

  1. Google had the most people shaping AI every year from 2014 to 2025Our estimates of which organizations employed the most people shaping AI from 1961 to 2025, with a year-by-year chart.
  2. The United States employs an estimated 53% of people in our data with a known employment countryOur estimates of where AI careers are concentrated now and how countries’ shares of dated positions changed over time.
  3. 46% of living people in our data with known birth and employment countries work outside their birth countryOur estimate of cross-border careers in AI, from country of birth and the country of each current organization.
  4. More people shaping AI studied at Massachusetts Institute of Technology than at any other institutionOur estimates of where the people shaping AI studied and where their careers led, from education records in cited biographies.

Sources and credits

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  1. Grant T. Barkley gtbarkley.org. Checked 19 October 2026.
  2. Channels, Billiards, and Perfect Matching 2-Divisibility arxiv.org. Checked 19 October 2026.
  3. An interview with Christian Gaetz: Cracking Combinatorial Invariance for the Coefficient of q mathematical-research-institute.sydney.edu.au. Checked 19 October 2026.
  4. Abstracts for the Seminar: Discrete Geometry and Combinatorics, Fall 2022 pi.math.cornell.edu. Checked 19 October 2026.
  5. FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI arxiv.org. Checked 19 October 2026.
  6. Grant Barkley - The Mathematics Genealogy Project mathgenealogy.org. Checked 19 October 2026.
  7. Graduate students and postdocs (Lauren Williams) people.math.harvard.edu. Checked 19 October 2026.
  8. CMND 2026 Thematic Program: Algebraic Combinatorics and Applications sites.nd.edu. Checked 19 October 2026.
  9. Algebraic combinatorics learning seminar: Solvable lattice models in combinatorics gtbarkley.org. Checked 19 October 2026.