# FERMAT'S LAST THEOREM: Unlocking the Secret of an Ancient Mathematical Problem

By

## KIRKUS REVIEW

For more than three centuries, Fermat's Last Theorem was the most famous unsolved problem in mathematics; here's the story of how it was solved. To begin with, Aczel (Statistics/Bentley College) sketches the essential problem: to prove that the deceptively simple equation A x + B x = C x does not hold true except where x=2. Pierre de Fermat, one of the most prolific mathematicians of the 17th century, formulated the problem in a marginal note to a mathematics text, claiming to have proved it. But he never published a proof, and later mathematicians failed to find a comprehensive proof. After laying the groundwork for an understanding of the basic concept, Aczel jumps back in time to the Babylonian era, when the foundations of mathematics were just being discovered. We follow the history of mathematics through various steps, growing ever closer to the time of Fermat. Aczel makes a special point of showing how mathematics continually builds upon the discoveries of earlier scholars, and he gives a lively sense of the personalities of the great mathematicians of the past. He does not overload the reader with equations and other mathematical expressions but gives enough to indicate the complexity of the concepts at issue. The modern assault on the problem began with an obscure Japanese conference on algebraic number theory in 1955. Two of the participants, Y. Taniyama and G. Shimura, offered a conjecture that an American theorist, Ken Ribet, recognized as equivalent to Fermat's theorem; if the one could be proven, the other would follow. It fell to Andrew Wiles, of Princeton, to connect the two after seven years of secret research. His dramatic announcement of the solution in 1993 was followed by the discovery of a flaw, which he retired to his study to repair, eventually publishing a perfected proof of the theorem. An excellent short history of mathematics, viewed through the lens of one of its great problems--and achievements.

Pub Date: Oct. 21st, 1996
Page count: 200pp
Publisher: Four Walls Eight Windows