Matthew D. Foreman
Distinguished Professor of Mathematics, University of California, Irvine
Biography
Matthew D. Foreman is a Distinguished Professor in the Department of Mathematics at the University of California, Irvine. He earned his Ph.D. in Mathematics from UC Berkeley in 1980 under the supervision of Robert Solovay, his B.A. in Mathematics and Philosophy from the University of Colorado, Boulder in 1975, and an MBA from Harvard in 2013. Foreman joined UCI in 1992 as a Professor of Mathematics and Philosophy, was promoted to Distinguished Professor in 2011, and previously held faculty positions at Ohio State University from 1986 to 1993.
Foreman's research spans set theory and foundations of mathematics, ergodic theory and dynamical systems, paradoxical decompositions and amenability, and mathematical finance. He has authored over 60 peer-reviewed articles in journals including Annals of Mathematics, Journal of the American Mathematical Society, and Transactions of the American Mathematical Society. His work has been supported by continuous National Science Foundation funding since 1980, including current grants totaling over $487,000. Foreman has received numerous honors, including the 2021 Gödel Lecture from the Association for Symbolic Logic, election as a Fellow of the American Mathematical Society in 2022, and an invited address at the International Congress of Mathematicians in Berlin in 1998. He has served as a plenary speaker at major international conferences and maintains active collaborations with researchers worldwide.
At UCI, Foreman teaches undergraduate and graduate courses in mathematics and has mentored numerous doctoral students. He co-organizes the Mathematical Logic Seminar and the Mathematical Ergodic Theory and Dynamical Systems Seminar. Foreman contributes extensively to professional service, reviewing grants for multiple national and international funding agencies including the NSF, Israel Science Foundation, and German Research Foundation. He has served on various university committees, including the UC Systemwide Committee on Affirmative Action, Diversity and Equity, and has been instrumental in diversity initiatives, including initiating a $450,000 UCOP grant for advancing faculty diversity in the School of Physical Sciences.
Return to topEducation
- Ph.D. in Mathematics, UC Berkeley, 1980
- MBA in Business Administration, Harvard, 2013
- B.A. in Mathematics and Philosophy, University of Colorado, Boulder, 1975
Distinctions
- Celebrating von Neumann, 120 (Plenary Speaker), Renyi Institute of Mathematics, Budapest, 2023
- Karp Prize Lecture, Logic Colloquium, 2014
- 32nd Annual Gödel Lecture, Association for Symbolic Logic, 2021
- American Mathematical Society Fellow, 2022
- Invited 45 minute address, International Congress of Mathematicians, 1998
- Distinguished Scholar, Ohio State University, 1993
- Outstanding Undergraduate in the College of Arts and Sciences, University of Colorado, 1975
Areas of Expertise
- Set Theory Foundations
- Ergodic Theory Applications
- Large Cardinal Properties
- Descriptive Set Theory
- Measure Preserving Transformations
- Borel Equivalence Relations
- Diffeomorphism Classification Problems
- Forcing Axioms Methods
- Paradoxical Decomposition Theory
- Mathematical Finance Applications
Recent Publications
- M. Magidor, M. Zeman, “Games with Filters” (opens in new tab), Journal of Mathematical Logic, vol. 24, 2023.
- S. Gao, A. Hill, C.E. Silva, B. Weiss, “Rank-one transformations, odometers, and finite factors” (opens in new tab), Israel Journal of Mathematics, vol. 255, no. 1, pp. 231-249, 2023.
- B. Weiss, “Odometer Based Systems” (opens in new tab), Israel Journal of Mathematics, vol. 251, no. 1, pp. 327-364, 2022.
- B. Weiss, “Measure Preserving Diffeomorphisms of the Torus are Unclassifiable” (opens in new tab), Journal of the European Mathematical Society, vol. 24, no. 8, pp. 2605-2690, 2022.
Most Cited Publications
- Matthew Foreman, M. Magidor, S. Shelah, “Martin's maximum, saturated ideals, and nonregular ultrafilters. I.” (opens in new tab), Annals of Mathematics (2), vol. 127, no. 2, pp. 175-196, 1988.
- Matthew Foreman, J. Cummings, M. Magidor, “Squares, scales and stationary reflection.” (opens in new tab), Journal of Mathematical Logic 1 , vol. 76, pp. 35-98, (2001).
- Matthew Foreman, “Ideals and generic elementary embeddings” (opens in new tab), Handbook of set theory, Springer, Dordrecht, vol. 2, pp. 885–1147, 2010.
- Matthew Foreman, M. Magidor, “Large cardinals and definable counterexamples to the continuum hypothesis” (opens in new tab), Annals of Pure and Applied Logic, vol. 76, no. 1, pp. 47-97, 1995.
- Matthew Foreman, M. Magidor, “A Very Weak Square Principal” (opens in new tab), Journal of Symbolic Logic, vol. 62, no. 1, pp. 175-196, 1997.
- Matthew Foreman, B. Weiss, “An anti-classification theorem for ergodic measure preserving transformations.” (opens in new tab), Journal of the European Mathematics Society, vol. 6, no. 3, pp. 277-292, 2004.
- Matthew Foreman, J. Cummings, “The Tree Property” (opens in new tab), Advances of Mathematics, vol. 133, no. 1, pp. 1-32, 1998.
- Matthew Foreman, W. H. Woodin, “The generalized continuum hypothesis can fail everywhere” (opens in new tab), Annals of Mathematics (2), vol. 133, no. 1, pp. 1–35 , 1991.
- Matthew Foreman, D. Rudolph, B. Weiss, “The conjugacy problem in ergodic theory” (opens in new tab), Annals of Mathematics (2), vol. 173, no. 3, pp. 1529-1586, 2011.
- Matthew Foreman, M. Magidor, “Mutually Stationary Sequences of Sets and the non-saturation of the Non-Stationary Ideal on P_\kappa(\lambda)” (opens in new tab), Acta Mathematica, vol. 186, no. 2, pp. 271-300, 2001.
Contact Information
Email: mdforema@ad.uci.edu
Phone: (949) 824-5244
Address: Department of Mathematics, UC Irvine, Irvine, CA 92697
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Last updated on 7/30/2025.