Symmetry: a journey into the patterns of nature

Symmetry is all around us. Our eyes and minds are drawn to symmetrical objects, from the pyramid to the pentagon. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. In chemistry and physics, the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; and symmetry—and the breaking of it—is central to ideas in art, architecture, and music.

Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry’s elusive qualities. He explores what is perhaps the most exciting discovery to date—the summit of mathematicians’ mastery in the field—the Monster, a huge snowflake that exists in 196,883-dimensional space with more symmetries than there are atoms in the sun.

What is it like to solve an ancient mathematical problem in a flash of inspiration? What is it like to be shown, ten minutes later, that you’ve made a mistake? What is it like to see the world in mathematical terms, and what can that tell us about life itself? In Symmetry, Marcus du Sautoy investigates these questions and shows mathematical novices what it feels like to grapple with some of the most complex ideas the human mind can comprehend.

The Barnes & Noble Review

Mathematicians are not like the rest of us. This becomes instantly clear in Chapter 1 of Marcus du Sautoy’s Symmetry, where we are introduced to his two early mentors, John Horton Conway and Simon Norton. Sautoy’s admiring yet frankly boggled description of these famed savants confirms every suspicion ever levied against the breed. Norton has a hobby of memorizing train schedules and plotting out optimal routes, while Conway can rattle off from memory a 54-digit number that represents the symmetries of a multi-dimensional construct known as the Monster. Thanks to du Sautoy’s sharp portraits, we get to know these men and others like them, souls most at home in a Platonic realm of sheer abstraction, where mathematical concepts assume a shining, epiphanical lucidity seldom attainable from earthly objects. And yet, the miracle of du Sautoy’s book is that by the end, we are affirming the essential humanity of such rarefied mathematical pursuits and identifying emotionally with these tangle-haired, mad-eyed explorers of the numerical realm. Du Sautoy moves quickly into the purely mathematical aspects of the term: Symmetry should be thought of as something active rather than passive. A symmetry of an object is what you can do to an object to leave it essentially looking like it did before you touched it. (He returns to the natural world briefly at the climax with a discussion of symmetry in viruses.) All the abstruse implications of this definition took 2,000 years to fully unravel, one advance building on another, resulting ultimately in the Atlas of Finite Groups, a landmark publication that effectively capped exploration in the field. Cannily weaving in autobiographical details, du Sautoy conveys the allure of his chosen field but also agreeably stretches the minds of his readers, until we too can experience at least faintly the excitement that accompanies hard-won insight into the fine structure of the cosmos. —Paul DiFilippo