Joel David Hamkins

Hamkins received a B.S. in mathematics from the California Institute of Technology in May 1988.⁠[1]

He recalls that as a Caltech freshman, taking his first genuine logic course, he learned that logic was an entire field of study and decided it would be his future; the incompleteness theorems and the independence phenomenon fascinated him early on.⁠[2]

He received a C.Phil. in mathematics from the University of California, BerkeleyUniversity of California, BerkeleyThe University of California, Berkeley (UC Berkeley) is a campus of the University of California system; the University of California was founded in 1868 through a merger of two institutions and moved to Berkeley, California, in 1873.Open the full entry, in December 1991 and a PhD in mathematics in May 1994.⁠[3]

After his PhD he held a postdoctoral visiting assistant professorship at Berkeley in the 1994–1995 academic year; he had already been offered his position at the City University of New York and deferred its start from 1994 to 1995.⁠[4]

In 1995 he joined the mathematics faculty of the CUNY College of Staten Island, serving as assistant professor 1995–1998 and associate professor 1999–2002, receiving tenure in 2000 and becoming full professor in 2003.⁠[5]

From January to December 1998 he held a fellowship from the Japan Society for the Promotion of Science at the Graduate School of Kobe University, as part of its logic group, with Philip Welch as his official mentor.⁠[6]

On August 21, 1998, he and Andy Lewis submitted “Infinite Time Turing Machines” to arXiv, extending the operation of Turing machines to infinite ordinal time and investigating the resulting supertask theory of computability and decidability on the reals; the paper was noted as forthcoming in the Journal of Symbolic Logic.⁠[7]

He was visiting associate professor of mathematics at Carnegie Mellon UniversityCarnegie Mellon UniversityCarnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. It grew out of the Carnegie Technical Schools, founded with funding from Andrew Carnegie in 1900, which were renamed the Carnegie Institute of Technology in 1912 and took the present name after merging with the Mellon Institute in 1967. The university is known for computer science, robotics, engineering, and the arts, and has campuses in Qatar, Silicon Valley, and Rwanda. As of September 2025, it enrolled 16,582 students. Its current president is Farnam Jahanian. On September 30, 2026, the university announced a $3 billion gift from Ken Griffin and plans to build a new campus in Miami.Open the full entry in 2000–2001, associate professor of mathematics and statistics at Georgia State University in 2002–2003, and Mercator guest professor at the Institute for Mathematical Logic of the Universität Münster from May to August 2004.⁠[8]

On September 27, 2005, he and Benedikt Löwe submitted “The modal logic of forcing” to arXiv, using modal logic to capture the general principles relating forceability and truth in set theory and proving that, if ZFC is consistent, the ZFC-provable principles of forcing are exactly the modal theory S4.2.⁠[9]

The paper later appeared in the Transactions of the American Mathematical Society, volume 360, issue 4 (2008).⁠[1]

On August 22, 2011, he submitted “The set-theoretic multiverse” to arXiv, introducing and defending the multiverse view that there are many distinct concepts of set, each instantiated in its own set-theoretic universe; he argued that on this view the continuum hypothesis is settled by our extensive knowledge of how it behaves in the multiverse and can no longer be settled in the manner formerly hoped for.⁠[10]

The paper was published in the Review of Symbolic Logic, volume 5 (2012).⁠[3]

On February 18, 2013, he and C. D. A. Evans submitted “Transfinite game values in infinite chess” to arXiv, studying the transfinite game values in chess on an infinite board and proving that every countable ordinal arises as the game value of a position in infinite three-dimensional chess.⁠[11]

He has said that while visiting the philosophy department at New York University he posted one of his infinite chess positions as a puzzle on his office door, where graduate students and postdocs gradually added proposed solutions.⁠[2]

In September 2018 he became Professor of Logic in the Faculty of Philosophy at the University of OxfordUniversity of OxfordThe University of Oxford is a university in Oxford, England, where teaching existed in some form by 1096; it describes itself as the oldest university in the English-speaking world and is organised as a federal system of the university and dozens of self-governing colleges.Open the full entry and Sir Peter Strawson Fellow in Philosophy at University College, Oxford.⁠[12]

While at Oxford he said that much of his work concerned potentialism in the philosophy of mathematics and that his research often followed a cycle in which philosophical inquiry and mathematical analysis drive each other.⁠[13]

In 2020 he was named Distinguished Professor at the CUNY College of Staten Island; he had been on the CUNY Graduate Center’s doctoral faculty in mathematics since 1997, computer science since 2002 and philosophy since 2013.⁠[14]

He was a founding co-organizer of the weekly CUNY Logic Workshop and founded the CUNY Set Theory Seminar.⁠[14]

MIT Press published his Proof and the Art of Mathematics in 2020 and Lectures on the Philosophy of Mathematics in 2021.⁠[3]

Reviewer Danny Yee noted that the latter is based on lectures for an Oxford honours course and is written mainly for mathematicians, and said Hamkins “writes exceptionally clearly.”⁠[15]

In January 2022 he took up a position at the University of Notre Dame, appointed in the Department of Philosophy with an affiliation with the Department of Mathematics; he said he expected to work with students in both philosophy and mathematics.⁠[16]

As of November 2023 he was working on The Book of Infinity and exploring set theory, potentialism and modal model theory with students and faculty at Notre Dame.⁠[17]

His Proof and the Art of Mathematics received the Mathematical Association of America’s 2024 Daniel Solow Author’s Award; in his response he said that the book’s theorems are all amenable to elementary proof, making it suited to teaching the craft of proof writing.⁠[18]

He appeared on episode 488 of the Lex FridmanLex FridmanLex Fridman is a Soviet-born, US-raised computer scientist and podcast host who works as an MIT research scientist on human-AI interaction and autonomous driving. His Lex Fridman Podcast is known for hours-long conversations with guests including heads of state and technology leaders.Open the full entry Podcast, whose description calls him a mathematician and philosopher specializing in set theory, the foundations of mathematics and the nature of infinity; topics included infinity and paradoxes, Russell’s paradox, Gödel’s incompleteness theorems, the halting problem, the continuum hypothesis, the mathematical multiverse, surreal numbers, P vs NP and infinite chess.⁠[19]

In August 2026 he announced that he had been awarded the Alternative Fields Medal in recognition of “Excellence in exposition of mathematics to a popular audience”; he said the citation mentions his books and his nearly 2,000 posts on MathOverflow since 2010, reaching 5.8 million viewers.⁠[20]

On August 25, 2026, the MIT Press published his 400-page The Book of Infinity; the publisher describes its 25 chapters as moving from classical paradoxes such as Zeno and Hilbert’s hotel to Cantor’s transfinite arithmetic, the continuum hypothesis, surreal numbers and debates about potential versus actual infinity.⁠[21]

As of October 2026 his MathOverflow reputation stood at 251,569, with 1,982 answers reaching about 6.0 million people.⁠[22]

On his website he states that his MathOverflow contributions have earned the site’s top-rated reputation score.⁠[8]

On his Substack newsletter Infinitely More he serializes The Book of Infinity, A Panorama of Logic and a new book on infinite games, and writes a series of essays on the surreal numbers.⁠[23]

Personal website: Public link: https://jdh.hamkins.org/ (opens in a new window)⁠[19]

X: Public account: https://x.com/JDHamkins (opens in a new window)⁠[19]

YouTubeYouTubeYouTube is Google’s video-sharing and creator platform, founded in 2005 by Steve Chen, Chad Hurley, and Jawed Karim and acquired by Google in 2006. Built around video uploading, viewing, and creator earnings, the platform has developed Shorts, YouTube Music, Premium, YouTube TV, and products for children, and is headquartered in San Bruno, California, United States.Open the full entry: Public channel: https://www.youtube.com/@joeldavidhamkins5484 (opens in a new window)⁠[23]

University of California, Berkeley: Official website: https://www.berkeley.edu/ (opens in a new window)⁠[4]

City University of New York: Official website: https://www.cuny.edu/ (opens in a new window)⁠[5]

University of Oxford: Official website: https://www.ox.ac.uk/ (opens in a new window)⁠[12]

University of Notre Dame: Official website: https://www.nd.edu/ (opens in a new window)⁠[16]