BOOKSHELF New and Noteworthy Titles on our Bookshelf January 2020 Lost in Math: How Beauty track positions, and a system that rewards work in “pop- Leads Physics Astray ular” areas at the expense of innovation and risk-taking. by Sabine Hossenfelder There is no question that this book is interesting and eye opening. Despite its intense focus on the pursuit of The pursuit of mathematical mathematical elegance in foundational physics and the beauty has derailed modern phys- ramifications of this search, this is definitely not a “math ics and ushered in an existential book.” Nevertheless, it should be a light and enjoyable read crisis that threatens to reshape the for any mathematician with a sincere interest in founda- field. This is the opinion of Sabine tional physics. Hossenfelder, a theoretical physi- cist who is deeply frustrated with On Gravity: A Brief Tour the current state of affairs. Some Basic Books, 2018, 304 pages 304 2018, Basic Books, of a Weighty Subject aesthetically appealing theories, by A. Zee such as the existence of multiverses, appear difficult or impossible to verify experimentally. If it cannot be tested Gravitational waves have received a and has no hope of being falsified, is it really science? lot of attention in the popular sci- Shouldn’t the discipline honor definitive experiments over ence media in recent years. There are untestable theories? These are the sorts of questions that probably a great many mathemati- Hossenfelder grapples with. cians who are curious about these Although the book is non-technical, the reader should exciting developments but who probably have a healthy interest in modern physics. For are unsure where to start. Mathe- a book with “math” in the title, its mathematical content maticians with no background in may leave the typical Notices reader disappointed, since the 192 pages 2018, Press, Princeton University physics should find this book an mathematics is discussed mostly at a vague and superficial appealing introduction to gravity. Zee describes its level as level. Nevertheless, there is no shortage of familiar names. “slightly above a popular physics book and somewhat below For example, Alain Connes, Henri Poincaré, David Hilbert, a physics textbook.” This is an entirely accurate description. Richard Borcherds, and Edward Witten make very brief The book is light on mathematics, although a short appen- appearances, as do Calabi–Yau manifolds, E8, and the dix entitled “What Does Curved Spacetime Mean?” involves Monster Group. However, the book’s main focus is physics, some multivariable calculus. not mathematics. Many of the key players in particle phys- Zee is well known in the theoretical physics community ics and cosmology play prominent roles. Readers who are for his “…in a Nutshell” books. He approaches gravity with casual watchers of popular science programs will recognize his signature conversational and humorous style. The title Max Tegmark, Nima Arkani-Hamed, Steven Hawking, and sums up the book perfectly. It is a whirlwind tour of gravity several others. from Newton and Einstein to Hawking radiation, gravitons, Hossenfelder observes a few disturbing trends in her and LIGO. These are covered in nineteen chapters, each discipline that should resonate with mathematicians: punctuated by short sections with thought-provoking titles increased specialization, lack of communication between such as “Gravity is absurdly weak,” “Let there be light! But subfields, the focus on grant writing, the rise in non-tenure- wait, what is light?” and “Are inertial mass and gravitational mass really the same mass?” The book ends with the imag- The Bookshelf is prepared monthly by Notices Associate Editor Stephan Ramon Garcia. ined responses of Aristotle, Newton, Einstein, and a yet-to-be Appearance of a book in the Notices Bookshelf does not represent an en- determined quantum theorist of gravity to the question dorsement by the Notices or by the AMS. “Why do we all fall down?” Although mathematical physi- Suggestions for the Bookshelf can be sent to notices-booklist cists will find this book too lightweight, most Notices readers @ams.org. will find this book engaging, informative, and entertaining. 72 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 67, NUMBER 1.