Professor of logic wins award for textbook re-examining the art of proof-writing

Author: Mary Kinney

Joel David Hamkins is the John Cardinal O'Hara Professor of Logic in the Department of Philosophy.

University of Notre Dame mathematician and philosopher Joel David Hamkins was recently recognized for his ability to give readers “a look behind the curtain at the workings of the mind” of a mathematician through his work, Proof and the Art of Mathematics.

Hamkins, the John Cardinal O'Hara Professor of Logic in the Department of Philosophy, is the recipient of the 2024 Daniel Solow Author’s Award. The award — given by the Mathematical Association of America — recognizes authors of “outstanding undergraduate mathematics teaching materials,” such as textbooks, lecture notes, and other learning resources.

In his textbook, Hamkins re-examines the art of proof-writing and structures it around surprising and interesting mathematical topics rather than simply teaching proof methods. This innovative approach provides students and readers an opportunity to learn how to write proofs while understanding the subject in an engaging and inspiring way.

“The main audience for the book is aspiring mathematicians who want to learn how to write proofs,” Hamkins said. “But — because of the playful topics and inherent interest of the mathematics in the book — it has found a secondary audience amongst people who are not aspiring mathematicians, but just want to partake in the fascinating wonder of it all.”

According to the association, instructors who have integrated the book into their curriculum have praised it for showcasing the diverse and multifaceted nature of mathematics to their students.

“Students had not realized that math had so many different faces,” wrote one instructor. “They were amazed to discover the various ways of thinking involved.”

Previously a faculty member at Oxford University, Hamkins’ research focuses on mathematics and philosophy of the infinite, working on a broad spectrum of topics in logic and the philosophy of mathematics. He also explores set theory, potentialism, and modal model theory.

Hamkins is currently working on a new book project, tentatively titled “The Book of Infinity.” His other work includes Lectures on the Philosophy of Mathematics and journal articles on the set-theoretic multiverse, the modal logic of forcing, the dream solution of the continuum hypothesis, and transfinite game values in infinite chess.

“One of the great pleasures for any mathematician is to share the fascination and wonder of mathematics with those who are eager to learn it — to teach aspiring mathematical minds the art of mathematics, watching as they bend the logical universe to their purpose for the first time,” Hamkins said. “What a joy it has been for me to experience these moments with my students using my book Proof and the Art of Mathematics, and I am truly honored by the recognition of the Daniel Solow Award for this book. I am so glad to learn that others have understood so well what I was trying to do with the book and that they also have benefitted from it.”