BOOK REVIEW 1690 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 66, NUMBER 10 John C. Baez is a professor of mathematics at University of California Riv- erside who also works at the Centre for Quantum Technologies. His email address is baez@math.ucr.edu. Communicated by Notices Book Review Editor Stephan Ramon Garcia. For permission to reprint this article, please contact: reprint-permission @ams.org. DOI: https://dx.doi.org/10.1090/noti1964 This volume, however, focuses mainly on the founda- tions of physics. In recent decades fundamental physics has entered a winter of discontent. The great triumphs of the twentieth century—general relativity and the Standard Model of particle physics—continue to fit almost all data from terrestrial experiments, except perhaps some anoma- lies here and there. On the other hand, nobody knows how to reconcile these theories, nor do we know if the Standard Model is mathematically consistent. Worse, these theories are insufficient to explain what we see in the heavens: for example, we need something new to account for the for- mation and structure of galaxies. But the problem is not that physics is unfinished: it has always been that way. The problem is that progress, extremely rapid during most of the twentieth century, has greatly slowed since the 1970s. While theories developed since then have yielded a huge harvest of exciting math- ematics, their predictions have not been confirmed by experiment. The discovery of the Higgs boson, for example, merely confirms a theory that particle physicists proposed in the 1960s. So far the Large Hadron Collider has not found anything new. Thus, it is fascinating to see Joseph Kouneiher’s attempt to bring together some of the best mathematicians and physicists and let them speak on what has happened in the last century. The result illustrates the frustrating situation in which fundamental physics finds itself now. The elephant in the room is string theory. After the rise of the Standard Model, some of the best minds in physics turned to the project of unifying all particles and Foundations of Mathematics and Physics One Century After Hilbert New Perspectives Edited by Joseph Kouneiher The title of this book recalls Hil- bert’s attempts to provide founda- tions for mathematics and physics and raises the question of how far we have come since then—and what we should do now. This is a good time to think about those questions. The foundations of mathematics are growing happily. Higher category theory and homotopy type theory are boldly expanding the scope of traditional set-theoretic foundations. The connection between logic and compu- tation is growing ever deeper, and significant proofs are starting to be fully formalized using software. There is a lot of ferment, but there are clear payoffs in sight and a clear strategy to achieve them, so the mood is optimistic. Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives edited by Joseph Kouneiher John C. Baez