The Marvels of Math

lovemath The Marvels of MathFrenkel, Edward. Love and Math: The Heart of Hidden Reality. Basic Bks: Perseus. Oct. 2013. 288p. illus. notes. index. ISBN 9780465050741. $27.99. MATH

“Math” and “love” seldom go together, but the title here fits this book. Frenkel (mathematics, Univ. of California, Berkeley) has had a lifetime love affair with uncovering mathematical secrets. The autobiographical portion of this book proves to be fascinating. As a Jew in Soviet-era Russia, where he was born in 1968, Frenkel fought against prejudice to receive a topflight mathematical education, much of it outside the traditional path. Frenkel’s early work was so well received that he was invited to be a visiting professor at Harvard while still finishing his undergraduate degree in Russia. All the while, his passion to understand the mysteries of math drove him, enabling him to immerse himself so completely in his research as to facilitate the complex discoveries that brought him prestige. Intertwined with his memoir is information that will help readers see the beauty of mathematics. By using analogies, he describes concepts such as symmetries, dimensions, and Riemann surfaces in a way that will enable nonmathematicians to understand them. VERDICT Whether or not readers develop a love for math, they will get a glimpse of the love that Frenkel has for the subject. Recommended for all readers, math whizzes or not, inclined to be interested in the subject.—William Baer, Georgia Inst. of Technology Lib., Atlanta

Pask, Colin. Magnificent Principia: Exploring Isaac Newton’s Masterpiece. Prometheus. Aug. 2013. 500p. illus. index. notes. ISBN 9781616147457. $27.50; ebk. ISBN 9781616147464. MATH

Isaac Newton’s Principia (1687)—fully titled Philosophiae Naturalis Principia Mathematica—is widely considered the single most influential book describing the natural and mechanical basis for the physical sciences and mathematics, but how accessible is it today? Pask (matheamatics, emeritus, Univ. of New South Wales; Math for the Frightened: Facing Scary Symbols and Everything Else That Freaks You Out About Mathematics ) has broken down the concepts, historical background, and key components of the Principia into one accessible volume. It serves as a rough guide to the work and succinctly explains each concept, and rationale, with references at the end of each section for those wishing to delve more deeply. Pask successfully takes the reader into Newton’s thought process, pointing out areas of debate and discussion as well as weaknesses in the work and technical details (the casual reader may want to skip over those). VERDICT A summary of this type is overdue, as previous works are dated and less accessible. Niccolò Guicciardini’s Reading the Principia and I. Bernard Cohen’s guide to the Principia , preceding his and Anne Whitman’s translation, accomplish the same goals but with less elegance and simplicity. Highly recommended for all science and mathematics enthusiasts, instructors, and readers.—Elizabeth A. Brown, Binghamton Univ. Libs., NY

Posamentier, Alfred S. & Ingmar Lehmann. Magnificent Mistakes in Mathematics. Prometheus. Aug. 2013. 300p. illus. bibliog. notes. ISBN 9781616147471. $24; ebk. ISBN 9781616147488. MATH

Posamentier (mathematics education, Mercy Coll.) and Lehmann (formerly, mathematics, Humboldt Univ., Berlin), coauthors of several math books, present a compendium of mathematical errors, arranged by topic into five chapters. Only the first, on errors made by eminent mathematicians, has much narrative. Here, we see number-theoretic conjectures that were based upon a few examples and a lot of wishful thinking. In Chapter Two, the authors address errors in arithmetic based mostly upon misunderstandings of notations. Chapter Three deals with algebraic errors primarily caused by inadvertent division by zero or the introduction of extraneous roots. In Chapter Four we have errors in geometric proofs, mostly arising from deliberately misleading diagrams. The final chapter deals with probability, showing mistakes made by confusing the concepts of conditionality, independence, and mutual exclusivity of events. Many of the errors are clever and instructive, some are repetitive and uninteresting; only a few should be designated as “magnificent.” VERDICT This volume could be useful to a teacher of mathematics as a source of examples that can hammer home important concepts. Beyond that, it will have a limited readership.—Harold D. Shane, Mathematics, Emeritus, Baruch Coll., CUNY

OrangeReviewStar The Marvels of MathTammet, Daniel. Thinking in Numbers: On Life, Love, Meaning, and Math. Little, Brown. Aug. 2013. 288p. ISBN 9780316187374. $26; ebk. ISBN 9780316250801. MATH

Autistic savant Daniel Tammet ( Born on a Blue Day: Inside the Extraordinary Mind of an Autistic Savant ) talks numbers, and he does so with evident inspiration and awe. Whether or not readers consider themselves mathematically inclined, they will be enthralled. In somewhat autobiographical essays that are conversational in tone Tammet examines topics as disparate as the complexity of snowflakes, the nuances of counting in Icelandic, how big is big, and how Ann Boleyn leaned to count on her eleven fingers. He regales us with discussions that incorporate references to ancient societies, insights into modern usage of language, and sprinkle in the ideas of a wide range of scientists, mathematicians, poets, and novelists. His narration about the time he enumerated the number pi to over 22,000 decimal places is riveting. Tammet enlivens his discussion of numbers with engaging personal components, including a chapter about his mother, an approach that renders his book a delightful read for a broad audience. VERDICT This book will charm just about anyone, but will absolutely captivate sci-tech readers with an interest in mathematics.—Margaret F. Dominy, Drexel Univ. Lib., Philadelphia

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