Fermat's Enigma

by Simon Singh

With a few minor manipulations imaginary numbers turn out to be the ideal way to analyze the natural swinging motion of objects such as pendula. This motion, technically called a sinusoidal oscillation, is found throughout nature, and so imaginary numbers have become an integral part of many physical calculations. Nowadays electrical engineers conjure up i to analyze oscillating currents, and theoretical physicists calculate the consequences of oscillating quantum mechanical wave functions by summoning up the powers of imaginary numbers. Pure mathematicians have also exploited imaginary numbers, using them to find answers to previously impenetrable problems. Imaginary numbers literally add a new dimension to mathematics, and Euler hoped to exploit this extra degree of freedom to attack Fermat’s Last Theorem.