Cloth | December 2012 | ISBN: 9780691152714
320 pp. | 6 x 9 | 13 halftones. 26 line illus.
Henri Poincare (1854-1912) was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincare explores all the fields that Poincare touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today.
Math historian Jeremy Gray shows that Poincare's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincare conjecture. And Poincare's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincare the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France.
Richly informed by letters and documents, Henri Poincare demonstrates how one man's work revolutionized math, science, and the greater world.
Jeremy Gray is professor of the history of mathematics at the Open University, and an honorary professor at the University of Warwick. His most recent book is Plato's Ghost: The Modernist Transformation of Mathematics (Princeton).
"Poincare was much more than a mathematician: he was a public intellectual, and a rare scientist who enthusiastically rose to the challenge of explaining and interpreting science for the public. With amazingly lucid explanations of Poincare's ideas, this book is one that any reader who wants to understand the context and content of Poincare's work will want to have on hand."--Dana Mackenzie, author of The Universe in Zero Words
"This engaging book recounts the achievements of Henri Poincare, covering his mathematics, physics, and philosophy, and his activities as a public intellectual. He is an eminently worthy subject for an intellectual biography of this kind."--Benjamin Wardhaugh, University of Oxford
"This comprehensive scientific biography of Poincare situates the scientist's life and work in the sociopolitical context of his era. Covering his varied and wide-spanning work--from the most philosophical to the most technical--this book gives the general reader a clear historical sense of the man's voluminous accomplishments."--Jimena Canales, Harvard University
Foreword by David Mumford
Paper | November 2012 | ISBN: 9780691156552
376 pp. | 5 1/2 x 8 1/2 | 37 halftones. 15 line illus. 3 tables.
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more.
In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
Mircea Pitici, a PhD candidate in mathematics education at Cornell University, teaches math and writing at Cornell and Ithaca College. He also edited the 2010 and 2011 editions of The Best Writing on Mathematics (both Princeton).
Praise for The Best Writing on Mathematics 2011: "Mathematics instructor Pitici turns out a second volume of unexpectedly fascinating mathematical research, musings, and studies that explore subjects from art to medicine. . . . From a discussion of the utility of mathematics in stone and bronze sculptures to a study of computing and its interaction with the sciences, readers from many disciplines will find much to pique their interest."--Publishers Weekly
Praise for The Best Writing on Mathematics 2011: "[E]ntertaining and informative."--Ian D. Gordon, Library Journal
Praise for The Best Writing on Mathematics 2011: "This wonderful book is not just a collection of essays; there are also references including a list of notable texts, links to mathematics websites, and biographies of the contributors, which may prove to be as valuable to the reader as the essays themselves. The Best Writing on Mathematics 2011 cannot be recommended highly enough!"--Robert Schaefer, New York Journal of Books
Paper | November 2012 | ISBN: 9780691155920
Cloth | November 2012 | ISBN: 9780691155913
272 pp. | 6 x 9
This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations.
The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas.
The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.
Xinyi Yuan is assistant professor of mathematics at Princeton University. Shou-wu Zhang is professor of mathematics at Princeton University and Columbia University. Wei Zhang is assistant professor of mathematics at Columbia University.
Paper | January 2013 | ISBN: 9780691147338
368 pp. | 5 1/2 x 8 1/2 | 5 halftones. 48 line illus.
Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses and Complexity offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity.
This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into--and modify--this framework. It then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling.
Providing an essential overview of the history, science, and growing significance of this exciting field, Spin Glasses and Complexity also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.
Daniel L. Stein is professor of physics and mathematics at New York University's Courant Institute of Mathematical Sciences. His books include Spin Glasses and Biology. Charles M. Newman is professor of mathematics at NYU's Courant Institute of Mathematical Sciences. His books include Topics in Disordered Systems.
"This excellent book fills a unique and valuable niche. It is a great introduction to some fascinating physics, emphasizing the fundamental concepts and the connections to other complex systems. There are lots of technical volumes on spin glasses, but no other book works at this nonmathematical level, certainly not while still being so accurate and insightful."--Cosma Shalizi, Carnegie Mellon University
"This primer builds the theory of spin glasses, starting with the real physical systems and experiments that inspired the theory. Stein and Newman work hard to make this material accessible to nonphysicists, and they write in an entertaining and friendly way. Even as a physicist I learned a fair amount."--Cris Moore, University of New Mexico