Saturday, September 22, 2007

Pg. 99: Ian Stewart's "Why Beauty Is Truth"

The current feature at the Page 99 Test: Ian Stewart's Why Beauty Is Truth: The History of Symmetry.

About the book, from the publisher:
At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered “Lie groups” with 14, 52, 78, 133, and 248 dimensions-groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the “octonionic” symmetries that may explain the very existence of the universe.
Among the praise for Why Beauty Is Truth:
Anyone who thinks math is dull will be delightfully surprised by this history of the concept of symmetry. Stewart, a professor of mathematics at the University of Warwick (Does God Play Dice?), presents a time line of discovery that begins in ancient Babylon and travels forward to today's cutting-edge theoretical physics. He defines basic symmetry as a transformation, "a way to move an object" that leaves the object essentially unchanged in appearance. And while the math behind symmetry is important, the heart of this history lies in its characters, from a hypothetical Babylonian scribe with a serious case of math anxiety, through √Čvariste Galois (inventor of "group theory"), killed at 21 in a duel, and William Hamilton, whose eureka moment came in "a flash of intuition that caused him to vandalize a bridge," to Albert Einstein and the quantum physicists who used group theory and symmetry to describe the universe. Stewart does use equations, but nothing too scary; a suggested reading list is offered for more rigorous details. Stewart does a fine job of balancing history and mathematical theory in a book as easy to enjoy as it is to understand.
--Publishers Weekly

Werner Heisenberg recognized the numerical harmonies at the heart of the universe: "I am strongly attracted by the simplicity and beauty of the mathematical schemes which nature presents us." An accomplished mathematician, Stewart here delves into these harmonies as he explores the way that the search for symmetry has revolutionized science. Beginning with the early struggles of the Babylonians to solve quadratics, Stewart guides his readers through the often-tangled history of symmetry, illuminating for nonspecialists how a concept easily recognized in geometry acquired new meanings in algebra. Embedded in a narrative that piquantly contrasts the clean elegance of mathematical theory with the messy lives of gambling, cheating, and dueling mathematicians, the principles of symmetry emerge in radiant clarity. Readers contemplate in particular how the daunting algebra of quintics finally opened a conceptual door for Evaniste Galois, the French genius who laid the foundations for group theory, so empowering scientists with a new calculus of symmetry. Readers will marvel at how much this calculus has done to advance research in quantum mechanics, relativity, and cosmology, even inspiring hope that the supersymmetries of string theory will combine all of astrophysics into one elegant paradigm. An exciting foray for any armchair physicist!

Stewart’s book is a good-humoured, panoramic history of the development of mathematics from Babylonian times to the present. He discusses the big ideas and the often unconventional characters who shaped them. Much of this will be unfamiliar and surprising to non-mathematicians.... Stewart tackles the problem of accessibility by spicing his account with stories of some of the greatest eccentrics ever to have solved a quadratic equation. Why Beauty is Truth is worth reading for these alone.
--Financial Times

Ian Stewart has been publishing good popular accounts of math and mathematicians for several years. With this new book, he is completely comfortable with his subject and at the height of his powers. This tale takes us through the remarkably sordid history of group theory, a somewhat abstract branch of mathematics that has fostered the notion that symmetry and beauty are paramount to our understanding of the world. The result is a surprising intellectual romp that is itself quite beautiful.
--SEED Magazine

Learn more about Why Beauty Is Truth at the author's website and in Stewart's brief essay about the book at Britannica Blog.

Ian Stewart is Professor of Mathematics at the University of Warwick and Director of its Mathematics Awareness Centre. His many books include From Here to Infinity, Nature’s Numbers, Does God Play Dice?, The Problems of Mathematics, and Letters to a Young Mathematician. His writing has appeared in New Scientist, Discover, Scientific American, and many newspapers in the U.K. and U.S.

The Page 99 Test: Why Beauty Is Truth.

--Marshal Zeringue