About

Michael R. Douglas received his bachelor’s degree in Physics from Harvard University in 1983 and his PhD from Caltech in 1988 under the supervision of John Schwarz. He is a string theorist, best known for his part in the development of matrix models, and for his work on noncommutative geometry in string theory, on Dirichlet branes and their relation to derived categories, and on the statistical approach to string phenomenology. Before coming to help start the Simons Center in 2008, Douglas was at Rutgers University where he was Professor of Physics and Director of the New High Energy Theory Center. He has been awarded the Sackler Prize in Physical Sciences, and has held positions as a Louis Michel Visiting Professor at the IHES and a Clay Mathematical Institute Mathematical Emissary. He is a fellow of the American Mathematical Society and a member of the American Physical Society, and has served as the editor of the Journal of High Energy Physics and of Communications in Mathematical Physics. His research focuses on theoretical physics, string theory, machine learning, and symbolic computation.

Research topics

• Physics
• Theoretical physics
• Mathematics
• Mathematical physics
• Pure mathematics

Selected publications

• Mathematical data science

  Advances in Theoretical and Mathematical Physics · 2026-01-01

  preprintOpen access1st authorCorresponding

  This article explores how machine learning, through a paradigm of mathematical data science, can enable the discovery of new mathematical structures by analyzing datasets of mathematical objects, illustrated by case studies on murmurations in number theory and partition loadings related to Kronecker coefficients.

  PublisherOA PDFDOI

• Formalization of QFT

  ArXiv.org · 2026-03-16

  articleOpen access1st authorCorresponding

  A foundational result in constructive quantum field theory is the construction of the free bosonic quantum field theory in four-dimensional Euclidean spacetime and the proof that it satisfies the Glimm-Jaffe axioms, a variant of the Osterwalder-Schrader axioms. We present a formalization of this result in the Lean 4 interactive theorem prover. The project is intended as a proof of concept that extended arguments in mathematical physics can be translated into machine-checked proofs using existing AI tools. We begin by introducing interactive theorem proving and constructive quantum field theory, then describe our formalization and the design decisions that shaped it. We also explain the methods we used, including coding assistants, and conclude by considering how AI assisted formalization may influence the future of theoretical physics. Our original release assumed three results, Minlos' theorem, the nuclear property of Schwartz space, and Goursat's theorem. In subsequent releases from our group and from contributors from the Lean community, these assumptions have been proven (or avoided), so that the OS/GJ axioms are now proven using only Lean and its library Mathlib.

  PublisherOA PDF

• The Yang–Mills Millennium problem

  Nature Reviews Physics · 2026-01-12

  article1st authorCorresponding
  PublisherDOI

• Mathematics and machine learning program

  Advances in Theoretical and Mathematical Physics · 2026-01-01

  articleOpen access1st authorCorresponding

  over 80 participants from many subfields of mathematics, physics and computer science.For eight weeks we explored the new opportunities created by applying the most recent developments in machine learning to mathematical problems old and new, proposed problems and formed working groups, and began in-depth studies.Our work continued after the program, and many of the results are reported in the articles here.Let us briefly outline the contents by subtopic.First come papers on methods and new software developed specifically for mathematical applications.A noteworthy feature of the program was the close collaboration between mathematical and machine learning experts, and much was learned on both sides.These papers include "Int2int -a Transformer Model for Integer Sequences" by Charton on a new transformer model and "Generative Modeling for Mathematical Discovery" by Sutherland et al. on a new implementation of the funsearch method, "Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization" by Barth et al., "Kolmogorov-Arnold stability" by Dzhenzher and Freedman, and "Mathematical Data Science" by Douglas and Lee, which surveyed this broad area with case studies such as the discovery of murmurations.Going the other direction, there were many talks and discussions on studying machine learning using ideas and methods from mathematics and physics.This topic is represented in the issue by "Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models" by Atanasov et al., and by work to appear in later issues of ATMP.Two program weeks focused on number theory, leading to many papers: "Learning Euler factors of elliptic curves" by Babei et al., "Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves" by Banwait

  PublisherOA PDFDOI

• Formalization of QFT

  arXiv (Cornell University) · 2026-03-16

  preprintOpen access1st authorCorresponding

  A foundational result in constructive quantum field theory is the construction of the free bosonic quantum field theory in four-dimensional Euclidean spacetime and the proof that it satisfies the Glimm-Jaffe axioms, a variant of the Osterwalder-Schrader axioms. We present a formalization of this result in the Lean 4 interactive theorem prover. The project is intended as a proof of concept that extended arguments in mathematical physics can be translated into machine-checked proofs using existing AI tools. We begin by introducing interactive theorem proving and constructive quantum field theory, then describe our formalization and the design decisions that shaped it. We also explain the methods we used, including coding assistants, and conclude by considering how AI assisted formalization may influence the future of theoretical physics. Our original release assumed three results, Minlos' theorem, the nuclear property of Schwartz space, and Goursat's theorem. In subsequent releases from our group and from contributors from the Lean community, these assumptions have been proven (or avoided), so that the OS/GJ axioms are now proven using only Lean and its library Mathlib.

  PublisherDOI

• Mathematics and machine learning program

  Advances in Theoretical and Mathematical Physics · 2026-01-01

  article1st authorCorresponding
  PublisherDOI

• Compactification of Superstring Theory

  Encyclopedia of Mathematical Physics · 2024-10-03

  book-chapter1st authorCorresponding
  PublisherDOI

• Point-of-Care Ultrasound in Obstetrics

  2024-01-01

  book-chapterSenior author
  PublisherDOI

• Harmonic $1$-forms on real loci of Calabi-Yau manifolds

  arXiv (Cornell University) · 2024-05-29

  preprintOpen access1st authorCorresponding

  We numerically study whether there exist nowhere vanishing harmonic $1$-forms on the real locus of some carefully constructed examples of Calabi-Yau manifolds, which would then give rise to potentially new examples of $G_2$-manifolds and an explicit description of their metrics. We do this in two steps: first, we use a neural network to compute an approximate Calabi-Yau metric on each manifold. Second, we use another neural network to compute an approximately harmonic $1$-form with respect to the approximate metric, and then inspect the found solution. On two manifolds existence of a nowhere vanishing harmonic $1$-form can be ruled out using differential geometry. The real locus of a third manifold is diffeomorphic to $S^1 \times S^2$, and our numerics suggest that when the Calabi-Yau metric is close to a singular limit, then it admits a nowhere vanishing harmonic $1$-form. We explain how such an approximate solution could potentially be used in a numerically verified proof for the fact that our example manifold must admit a nowhere vanishing harmonic $1$-form.

  PublisherOA PDFDOI

• Random Algebraic Geometry, Attractors and Flux Vacua

  Encyclopedia of Mathematical Physics · 2024-10-03

  book-chapter1st authorCorresponding
  PublisherDOI

Frequent coauthors

• Frederik Denef

  Columbia University

  20 shared

• Albert Schwarz

  18 shared

• Constantin P. Bachas

  16 shared

• Inga Hofmann

  15 shared

• Willem H. Ouwehand

  University of Cambridge

  15 shared

• Corinne Pondarré

  Hôpital Intercommunal de Créteil

  15 shared

• Henrik Johansson

  Uppsala University

  13 shared

• Nathan Seiberg

  Institute for Advanced Study

  13 shared

Education

• Ph.D., Physics

  Caltech

  1988

Awards & honors

• Sackler Prize in Physical Sciences
• Louis Michel Visiting Professor at the IHES
• Clay Mathematical Institute Mathematical Emissary
• Fellow of the American Mathematical Society
• Member of the American Physical Society