Welcome to my home page. I am a professor in the Department of Philosophy and the Department of Mathematical Sciences at Carnegie Mellon University. I am the director of the Charles C. Hoskinson Center for Formal Mathematics, and I am associated with Carnegie Mellon's interdisciplinary program in Pure and Applied Logic. You can read my CV.
Mathematical logic, philosophy of mathematics, formal verification, automated reasoning, history of mathematics.
Office: Baker Hall 135E
Department of Philosophy
Baker Hall 161
Carnegie Mellon University
Pittsburgh, PA 15213
The Hoskinson Center has been announced! You can read the press release and watch Charles Hoskinson talk about the center on YouTube. You can also watch Charles' presentation and my presentation from the inauguration of the center. The slides that went with my talk are here.
My book, Mathematical Logic and Computation, will be published by Cambridge University Press. You can read the table of contents and preface: pdf.
Seul Baek, Alex Bentkamp, Marijn Heule, Wojciech Nawrocki, and I discovered an inconsistency in a logic puzzle by Raymond Smullyan: arXiv.
An essay I have written, Varieties of mathematical understanding, just appeared in the Bulletin of the American Mathematical Society.
I gave a talk, "Formal mathematics, dependent type theory, and the Topos Institute," in the Topos Institute Colloquium. You can see the slides and the video.
I have been working on verification of blockchain protocols with colleagues at StarkWare. There is a preprint here, a Lean formalization here, and an informal discussion here. The paper has been accepted to Certified Proofs and Programs (CPP) 2022.
Marijn Heule, Wojciech Nawrocki, and I just taught a new course, Logic and Mechanized Reasoning. You can see the course page, the textbook (still a work in progress), a PDF version of the textbook, and the course repository. You can also see the slides and video from an associated talk.
I have put online a draft of a chapter on mathematical language, written for the forthcoming Handbook for the Philosophy of Mathematical Practice.
Alexander Bentkamp and I have presented joint work in progress on verified optimization.
I have written a draft of a chapter on logic and foundations for the Handbook of Proof Assistants and their Applications in Mathematics and Computer Science.
Kevin Buzzard, Johan Commelin, Yury Kudryashov, Heather Macbeth, Scott Morrison, and I are co-organizing Lean for the Curious Mathematician, which will be held at ICERM in the summer of 2022.
Heather Macbeth, Patrick Massot, and I are organizing a summer school on the formalization of mathematics, which will be held at MSRI in the summer of 2023.
Erika Abraham, Kevin Buzzard, Jordan Ellenberg, Timothy Gowers, Marijn Heule, and Terence Tao and I are organizing an IPAM workshop on machine assisted proofs, which will probably be scheduled for early 2023.
Kevin Buzzard, Robert Lewis, Patrick Massot, and I have started working on a tutorial, Mathematics in Lean. You can learn about some of the interesting things going on with Lean and mathlib on the Lean community web pages.
Good news from some of my recent and current students:
- Robert Y. Lewis joined the Department of Computer Science at Brown University.
- Floris van Doorn started a postdoctoral position in Paris.
- Mario Carneiro and Seul Baek (with Marijn Heule) have had a paper accepted to TACAS and then to a special issue of the Journal of Automated Reasoning.
- Wojciech Nawrocki (with Zhenjun Liu, Andreas Fröhlich, Marijn Heule and Armin Biere) has had a paper accepted at SAT.
- Mario's work on Metamath Zero is coming along (see also his YouTube tutorial).
- Seul's work on TESC, a proof format for first-order theorem provers, is coming along. His paper on a formal verifier for it was accepted at ITP.
- Paula Neeley defended her MS thesis on a formalization of dynamic epistemic logic. She gave a talk about it at Lean Together 2021.
An old paper of mine, Forcing in proof theory, has been selected as one of the winners of the Bulletin of Symbolic Logic's 25th Anniversary Prize.
I am on the editorial boards of the Journal of Automated Reasoning and Logical Methods in Computer Science.