Why Beauty is Truth by Ian Stewart, a mathematician at the University of Warwick in the UK, is a historical account of the evolution of mathematics into modern physics right up to the era of superstrings. It traces the development of the mathematical conceptualization of symmetry and even provides some new and intriguing interpretations of historical events, such as the death of French mathematician Evariste Galois in a duel in 1832.

Stewart begins with the ancients: the Babylonian development of a modern (base six) number system; and early treatments of the algebraic problem of solving quadratic equations. As the historical tour unfolds, we see both the bizarre cult of Pythagoras and the Persian mathematician Omar Khayyam’s development of the solution of a cubic equation. Then we move on to the Renaissance and the Enlightenment, as we trace the quest for mathematical solutions to higher-order algebraic equations, before arriving at the problem of solving quintic (i.e. fifth-order) equations.

Thus begins the tale of the young Frenchman Galois. He was a radical, revolutionary and energetic man – one can visualize Tom Hulse’s portrayal of Mozart in the film Amadeus to capture a glimpse of what might have been Galois’ energized persona. Galois evolved sophisticated new methods for solving quintic equations by “thinking outside the box” and for the first time introducing symmetry to analyse an algebraic problem. Stewart gives a succinct account of who Galois was before going on to speculate about how he came to meet his tragic end at the age of just 21.

According to folklore, the radical Republican Galois was shot by Pescheux d’Herbinville, who may have been an assassin hired by the French Crown. Allegedly, Galois had been entrapped into a love triangle with d’Herbinville’s wife, which led to the duel. However, Stewart largely debunks this interpretation. While a romantic impetus for the event persists, he suggest that the opponent in the duel may in fact have been an old friend of Galois’, perhaps Vincent Duchatelet, a young compatriot in love with the same woman. The event was gruesome – a single bullet to the stomach, usually fatal in those days. Contrary to the legend, Galois did not succumb on the field of honour in a matter of hours, but instead died the next day in a Paris hospital due to peritonitis, and refusing the last rites.

Galois left behind notes on his solutions to the quintic equations, incorporating symmetry, which spawned a revolution in mathematics. The material made its way to the great Joseph Liouville and was presented to the French Academy of Sciences. Thus emerged the conceptual foundation of symmetry as an algebraic system: the codification of symmetry into what mathematicians call group theory, which now envelops almost all branches of mathematics, from number theory to topology. The book then tracks the further expansion of modern mathematical thought through William Rowan Hamilton, Niels Abel, Sophus Lie and Elie Cartan. Finally, at the dawn of the 20th century, symmetry and group theory became part of modern physics.

Albert Einstein was the first physicist to think in the modern style of symmetry, and Stewart covers the development and implications of special and general relativity through their underlying symmetry principles. Today, group theory underlies the Standard Model of particle physics through the concept of local gauge invariance. However, the book underplays the famous theorem of the German mathematician Emmy Noether that connects symmetry to conservation laws, and which Einstein and David Hilbert so championed. The author handles well a vignette of quantum theory and the first proposal of hidden extra dimensions of space–time by Theodor Kaluza and Oscar Klein.

Finally we are brought up to date with today’s speculative ideas of supersymmetry and superstring theory. Stewart gives us a personal view of the towering figure of modern theoretical physics, Edward Witten. Interestingly, Stewart hints that George McGovern’s failed US presidential campaign and the subsequent election of Richard Nixon in 1972 led Witten to abandon a career as a political journalist and instead to go to Princeton University to obtain a doctorate in physics. Witten has been the clear leader of theoretical physics for 25 years (often compared to Einstein) and is a recipient of the Fields Medal for his contributions to knot theory.

String theory awaits definitive test by experiment. Such a test will come soon with the discovery of (or failure to discover) supersymmetry at the Large Hadron Collider at CERN, due to switch on next year, although some will dissent with that view. It is disappointing that Stewart fails to connect to this timely enterprise by which physicists will take their next step into the depths of physical reality. Indeed, the book loses its focus somewhat at the end.

The format of history intermeshed with mathematical concepts is a popular approach nowadays. Why Beauty is Truth requires some prior interest in the subject, and it lacks the edge of Simon Singh’s Fermat’s Last Theorem. However, it will be a satisfying read for anyone who wants to delve into the historical development and conceptual foundations of modern mathematics and physics.