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BOOKSHELF New and Noteworthy Titles on our Bookshelf May 2020

The Shape of a Life 99 Variations on a Proof One ’s Search by Philip Ording for the Universe’s Hidden Geometry by Shing-Tung Yau and Steve Nadis This entire book is de- voted to 99 proofs, lib- The Shape of a Life is an autobiogra- erally interpreted, of the phy of Shing-Tung Yau, winner of following statement: “If the 1982 Fields Medal and many x3-6x2+ 11 x-6 = 2x-2, then other prestigious awards. The x=1 or x=4.” It seems im- book is coauthored with science probable that one could writer and Discover contributing write more than a few editor Steve Nadis, who previously pages on such a modest Yale, 2019, 328 pages 2019, Yale, collaborated with Yau in 2010 on 272 pages Princeton, 2019, topic, but Ording has the popular science book The Shape of Inner Space: String managed to parlay this simple question into a perceptive Theory and the Geometry of the Universe’s Hidden Dimensions. reflection on and its culture. Students and Although there is no explicit mathematics in the book, the professors alike will enjoy this unusual book. writing style is clear enough that the mathematically literate The inspiration for 99 Variations on a Proof comes from reader will be able to understand, at an intuitive level, the Raymond Queneau’s Exercises in Style, a 1947 work that stunning breakthroughs and remarkable discoveries that retells the same story in 99 strikingly different ways. The Yau and his collaborators contributed to. book is divided into 99 short chapters, each of which ex- The Shape of a Life is an interesting and engaging read, plores a different “proof” of the main result. The word written in a detailed yet lively style. The book vividly docu- “proof” here appears in quotes since most would not pass ments Yau’s trials as a desperately poor child in Hong Kong; muster in an undergraduate course. Each comes with a short his unlikely path to the UC Berkeley graduate program; parenthetical description. For example, Proof 36 (Social his deteriorating relationship with his doctoral advisor, Media) appears in the form of a fictitious tweet by Girol- Shiing-Shen Chern; the development of geometric analysis; amo Cardano: “Cube & 9 times first power equals 6 times the discovery of Calabi-Yau manifolds; and more. square & 4 solved by reduction to @delferro’s equation The Shape of a Life maintains an appropriate pace, never .org/abs/4307.1160 #cubic #tartaglia”. Some ap- dragging its feet nor skipping important details. Yau is proaches seem uncomfortably familiar, such as Proof 44 always frank and forthright. He has strong opinions and (Omitted with Condescension): “There is a simply beauti- does not hesitate to share them. Whether one agrees with ful theorem which provides all solutions of the equation him or not, one must conclude that The Shape of a Life is a x3-6x2+ 11 x-6 = 2x-2. Alas, any further explanation would deeply personal reflection that provides a keen insight into deny you the satisfaction of discovering it on your own…” the life and mind of one of the world’s top . and Proof 94 (Authority): “Of course, if x3-6x2+ 11 x-6 = 2x-2, then it follows from Euler that the real number in question must be 1 or 4.” There are also some serious mathematical proofs, graphical proofs, proofs by experiment, and several unique expositions that demonstrate a great deal of artistry. For example, there are proofs in dialogue form and dog- The Bookshelf is prepared monthly by Notices Associate Editor Stephan gerel, along with screenplays and blog entries. Fittingly, the Ramon Garcia. book ends with Proof 99 (Prescribed): “The proof is left to Appearance of a book in the Notices Bookshelf does not represent an en- the reader.” dorsement by the Notices or by the AMS. Suggestions for the Bookshelf can be sent to notices-booklist @ams.org.

706 Notices of the American Mathematical Society Volume 67, Number 5