Fermat's Enigma

by Simon Singh

Mathematicians studying elliptic equations might not be well versed in things modular, and conversely. Then along comes the Taniyama-Shimura conjecture, which is the grand surmise that there’s a bridge between these two completely different worlds. Mathematicians love to build bridges.” The value of mathematical bridges is enormous. They enable communities of mathematicians who have been living on separate islands to exchange ideas and explore each other’s creations. Mathematics consists of islands of knowledge in a sea of ignorance. For example, there is the island occupied by geometers who study shape and form, and then there is the island of probability where mathematicians discuss risk and chance. There are dozens of such islands, each one with its own unique language, incomprehensible to the inhabitants of other islands. The language of geometry is quite different from the language of probability, and the slang of calculus is meaningless to those who speak only statistics. The great potential of the Taniyama-Shimura conjecture was that it would connect two islands and allow them to speak to each other for the first time.