What's Happening in the Mathematical Sciences, Volume 7

Since 1993, the AMS has been publishing ""What's Happening in the Mathematical Sciences"", a series of lively and highly readable accounts of the latest developments in mathematics. This seventh volume describes some genuine surprises, such as the recent discovery that coin tosses are inherently unfair; a mathematical theory of invisibility that was soon followed by the creation of a prototype 'invisibility cloak'; and, an ultra-efficient approach to image sensing that led to the development of a single-pixel camera. The past few years have also seen deep results on some classical mathematics problems. For example, this volume describes a proof of the Sato-Tate Conjecture in number theory and a major advance in the Minimal Model Program of algebraic geometry. The computation of the character table of the exceptional Lie group $E_8$ brings 'the most beautiful structure in mathematics' to public attention, and proves that human persistence is just as important as gigabytes of RAM. The amazing story of the Archimedes Palimpsest shows how the modern tools of high-energy physics uncovered the centuries-old secrets of the mathematical writings of Archimedes. Dana Mackenzie, a science writer specializing in mathematics, makes each of these topics accessible to all readers, with a style that is friendly and at the same time attentive to the nuances that make mathematics fascinating. Anyone with an interest in mathematics, from high school teachers and college students to engineers and computer scientists, will find something of interest here. The stories are well told and the mathematics is compelling.