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Boston, MA, MAA Mathfest, August 2026
Invited Guest Lecture: Juliet Floyd
At the Mathfest 2026 in Boston, MA, August 5, 2026, Time TBA, Juliet Floyd, Boston University, Department of Philosophy, will give the POMSIGMAA Invited Address, "On the Autonomy of Mathematics"
In this talk I will discuss a number of different ways in which the philosophical concept of “autonomy” is important for philosophy of mathematics. We will explore some of the philosophical aspects of autonomy in mathematics and suggest future paths of research. We have traditional philosophical notions of autonomy – spontaneity of individual choice and interest (Descartes, Hume); selfdetermination according to (self-given) laws (Leibniz and Kant); rational self-determination within a civil state or set of institutions that is ordered, historically stable, and allows for selfrecognition (Hegel); a listing of specific freedoms (Rawls, first amendment issues). Each of these notions receives an interesting inflection today, when the heretofore protected autonomy of universities and the choices of researchers and educators within them have come under threat from a variety of forces, political, economic, and research-driven (AI). Groups of mathematicians are concerned about the human aspects of mathematics – pure and applied -- in the face of AI and machine learning, and are attempting to draw up research declarations to avoid the distortion and suppression of certain forms of research and teaching by corporate interests.
G.H. Hardy argued for the purity of mathematics, its independence from demands of e.g. military and empirical research; Wittgenstein questioned the ability of mathematicians to divorce their research interests from wider problems of history, meaning and culture, while doubting that either metaphysical or social-constructivist views of mathematical truth would prove viable. Franks stressed the ideal of “autonomy” in connection with Hilbert’s program, i.e., its freedom from metaphysical and philosophical demands, as have certain constructivists and intuitionists, though there remain philosophical questions about the role of “intuition” in mathematics in a world where research is driven by AI (Friedman and Kish). Arana has explored both the idea of "purity of proof” and its relation to wider social and cultural structures (such as the phenomenon of “linguistic hygiene” in Newton and Descartes as they inserted mathematics into the wider issue of the social construction of bourgeois subjects). Others (e.g. Juliette Kennedy) have argued that finding mathematically invariant structures allows for the avoidance of metaphysical speculation and the lure of a return to everyday language alongside future research in the most abstract areas of set theory.
We will explore some of the philosophical aspects of autonomy in mathematics and suggest future paths of research.
Boston, MA, MAA Mathfest, August 2026
Invited Paper Session
The philosophy of mathematics is an interdisciplinary subject, requiring background in mathematics and philosophy. As an area of research within philosophy, it serves as a test for theories of existence, knowledge, and language, but many mathematicians have not had the chance to keep up with recent developments. The holding of a national meeting in Boston offers an opportunity to bring together many of those involved with recent developments in the philosophy of mathematics, both inside and outside the mathematical community. Many questions from a century ago remain alive in a philosophical setting, but technical results have a role to play. From the time of Zeno’s paradoxes onward, mathematicians have had to look at philosophical issues. The objective of the proposed session is not to ignore technical details but to explain how the various currents of mathematics and mathematical practice interact with philosophical issues.
Each talk will be 35 minutes in length beginning at the time listed, followed by 20 minutes for questions and discussion.
| Time | Presenter | Title |
|---|---|---|
| 8:00 a.m. | Peter Koellner | On the Question of Whether the Mind Can be Mechanized: From Gödel to Penrose . |
| 9:00 a.m. | Arthur Jaffe | Some Remarks on Mathematical Picture Language . |
| 10:00 a.m. | Jody Azzouni | Why are Professional Mathematical Proofs More Robust than Formal Derivations? . |
| 11:00 a.m. | Don Fallis | Is it Safe for Mathematicians to Consume Fugu? . |
Each talk will be 25 minutes in length beginning at the time listed, followed by 10 minutes for questions and discussion.
| Time | Presenter | Title |
|---|---|---|
| 10:15 a.m. | Steven Deckelman | Dialectical Paradigms in the Philosophy of Mathematics: Epistemology and Axiology . |
| 10:45 a.m. | Dan Sloughter | Numerology and Mathematics: From Plato to Procluss to I. J. Good . |
| 11:15 a.m. | Thomas Drucker | A Timely Golden Braid: A Look Back at Gödel, Escher Bach . |
| 11:45 a.m. | Bonnie Gold | What is the 'Philosophy of Mathematical Practice'? . |
Spring Wisconsin section MAA meeting at the University of Wisconsin-River Falls.
On April 10, 2026, at the Spring Wisconsin Section MAA Meeting at the University of Wisconsin-River Falls, Steven M. Deckelman gave a talk, "The Philosophy of Mathematics for Mathematicians" Abstract