From Publishers Weekly
The title of astrophysicist Livio's latest wide-ranging science survey is a teaser since God rarely makes an appearance; along with the French astronomer Laplace, Livio has no need of that hypothesis. Rather, Livio (The Golden Ratio
) is concerned with the contentious question: is mathematics a human invention? Or is it the intricate design of the universe that we are slowly discovering? Scientists in past centuries have argued for the latter, Platonist position. In the last 50 years, however, many scientists, calling into question the whole idea of scientific discovery, maintain that we have invented mathematics. Livio gives as one example the famous golden ratio, which has fascinated Western mathematicians for millennia and was originally emphasized for its mystical symbolism. But Chinese mathematicians, not sharing that outlook, didn't discover it—or maybe they just didn't need to invent it. Livio hedges his bets, unsatisfyingly arguing that mathematics is partly discovered and partly invented. But Livio is a smooth writer. His fans will enjoy this book, and new ones may discover him. B&w illus. (Jan. 6)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
*Starred Review* Four centuries after church inquisitors accused Galileo of dangerous skepticism, a modern astrophysicist hails the Italian scientist as the embodiment of bold faith: namely, faith that God himself inscribed the heavens in mathematics. Because mathematics now empowers research communities investigating everything from deep-space pulsars to genetic proteins, a secularized version of Galileo’s credo now defines the new orthodoxy of science. But Livio recognizes a profound mystery inherent in the formulas his colleagues employ so sedulously: Why does the universe harmonize so well with numbers accessible to human minds? Probing this mystery, Livio traces the evolution of mathematical reasoning from the ritual symbolism of the ancient Pythagoreans to the multilayered analyses of twenty-first-century string theorists. In the impressive parade of intellectual explorers, we encounter Archimedes pondering geometrical figures at the very moment of his death, Descartes overthrowing all of medieval philosophy with one audacious thought, and Gödel quashing the ambitions of system-building logicians. This wide-ranging inquiry, however, ultimately highlights far more than personalities. A sharp conflict emerges between platonically minded philosophers who view mathematical breakthroughs as transcendent discoveries and psychologically inclined thinkers who interpret these breakthroughs as merely human inventions. Testing the tensions between these views, Livio delivers an exhilarating foray into the founding premises of mathematical science. --Bryce Christensen