Jeremy Avigad

Jeremy Avigad
Name	Jeremy Avigad
Birth date	1968
Birth place	Pittsburgh, Pennsylvania
Nationality	American
Fields	Logic; Philosophy of Mathematics; Formal Verification; Computer Science; Mathematics
Workplaces	Carnegie Mellon University; University of California, Berkeley; Harvard University; Institute for Advanced Study
Alma mater	Harvard University; Carnegie Mellon University
Doctoral advisor	Michael O. Rabin; Gerald Sacks

Jeremy Avigad Jeremy Avigad is an American philosopher, logician, and mathematician known for work at the intersection of mathematical logic, philosophy of mathematics, and formal methods. He has held faculty positions at major research institutions and contributed to the development of proof assistants and the formalization of classical mathematics. Avigad's research spans foundational studies related to Kurt Gödel, David Hilbert, and Bertrand Russell as well as practical collaborations with computer scientists working on systems such as Isabelle (proof assistant), Coq, and Lean (proof assistant).

Early life and education

Avigad was born in Pittsburgh, Pennsylvania and grew up in a family engaged with the intellectual communities of the Northeastern United States. He completed undergraduate studies at Carnegie Mellon University before pursuing graduate work at Harvard University, where he studied under scholars in logic and recursion theory. His doctoral work addressed topics influenced by recursive function theory and proof theory, drawing on traditions associated with Alonzo Church, Alan Turing, and Kurt Gödel. During graduate school he interacted with faculty from institutions such as Massachusetts Institute of Technology, Princeton University, and the University of California, Berkeley.

Academic career and positions

After earning his doctorate, Avigad held postdoctoral and visiting appointments at institutions including the Institute for Advanced Study and collaborative research centers tied to Harvard University and Carnegie Mellon University. He joined the faculty at Carnegie Mellon University as an assistant professor before accepting a position at University of California, Berkeley where he worked with colleagues from departments connected to Berkeley Lab and interdisciplinary programs linking computer science and philosophy. Later he returned to Harvard University as a professor, contributing to both the Department of Philosophy and the Department of Mathematics. He has served on advisory boards and editorial committees for journals affiliated with Association for Symbolic Logic, American Mathematical Society, and conferences sponsored by ACM and IEEE.

Research and contributions

Avigad's research program addresses foundational questions about the nature of mathematical proof and the formalization of mathematical practice. He has published work on proof theory that engages with the legacies of Hilbert's program, Gentzen, and Gerhard Gentzen, analyzing consistency proofs and the role of induction in arithmetic. His philosophical contributions examine themes from Wittgenstein and Ludwig Wittgenstein-inspired critiques of formalism, juxtaposing those views with constructive approaches associated with Brouwer and L. E. J. Brouwer. In mathematical logic, Avigad has developed results connecting reverse mathematics—a field influenced by Stephen Simpson—with computational interpretations derived from Kurt Gödel’s functional interpretation and concepts tied to Turing machine computability.

A prominent thread in Avigad's work is the formal verification of mathematical proofs using proof assistants. He has collaborated with developers of systems related to Isabelle (proof assistant), Coq, HOL Light, and notably Lean (proof assistant), advancing libraries that formalize classical results in analysis, algebra, and number theory. These efforts intersect with projects launched at Microsoft Research and initiatives like the Polymath Project, bringing together mathematicians and computer scientists from institutions such as Princeton University, University of Cambridge, and University of Oxford. Avigad has contributed to methodology for encoding informal mathematical arguments into machine-checkable form, drawing on work by Gerard Huet, Robin Milner, and John McCarthy regarding programming language theory and logical frameworks.

He has also worked on semantic and syntactic issues in the foundations of arithmetic and set theory, engaging literature stemming from Paul Cohen’s forcing techniques and Kurt Gödel’s constructible universe. His interdisciplinary collaborations often involve researchers from Stanford University, Yale University, Columbia University, and national labs, addressing both theoretical questions and tool development for education and research reproducibility.

Awards and honors

Avigad has received recognition from professional societies including fellowships and awards from organizations such as the National Science Foundation, the American Philosophical Society, and the Association for Symbolic Logic. He has been invited to deliver named lectures at venues like Princeton University’s Institute for Advanced Study, the European Summer School in Logic, Language and Information, and colloquia at Massachusetts Institute of Technology. His work has been supported by grants from agencies and foundations associated with computational and philosophical research, with collaborative funding involving Microsoft Research and national funding bodies in the United States.

Selected publications

- Avigad, J., & Feferman, S. — papers on proof theory and the logical foundations connected to Solomon Feferman’s work. - Avigad, J., et al. — formalization projects documenting mechanized proofs in systems like Lean (proof assistant), Coq, and Isabelle (proof assistant). - Avigad, J. — articles on reverse mathematics referencing results of Stephen Simpson and analyses of Peano arithmetic. - Avigad, J. & Harrison, J. — collaborative work on formalizing analysis with connections to John Harrison’s contributions to HOL Light. - Avigad, J. — essays on the philosophy of mathematics discussing figures such as Bertrand Russell, David Hilbert, and Kurt Gödel.

Category:American mathematicians Category:Philosophers of mathematics Category:Logicians Category:Harvard University faculty