What it argues
In 1637, Pierre de Fermat scrawled a note in the margin of a mathematics book claiming to have found a proof that no three positive integers can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2 — but that the margin was too narrow to contain it. That marginal note became the most famous unsolved problem in the history of mathematics, and it remained unsolved for 358 years. Simon Singh tells the story of how it was finally resolved in 1994, when Princeton mathematician Andrew Wiles completed a seven-year secret project to produce a proof spanning more than 100 pages.
The book works on two levels simultaneously. On one level it is intellectual history: Singh traces three and a half centuries of mathematicians who devoted their careers to the problem, from Euler and Gauss to Kummer, Mordell, and finally Wiles. He explains the mathematics with rare clarity — elliptic curves, modular forms, the Taniyama-Shimura conjecture, and the Galois representations that Wiles used to bridge them — in ways that a reader with no formal mathematics training can follow. On another level it is a human drama: Wiles spent seven years working in secret, avoiding conferences and declining to mention his work for fear of competition, and his announcement in June 1993 — followed by the discovery of a flaw, the 14 months of despair, and finally the fix — is one of the great scientific narratives of the 20th century.
What it gets right
- 1.
Fermat's Last Theorem states that a^n + b^n = c^n has no integer solutions when n is greater than 2. Fermat claimed a proof; no proof was found for 358 years.
- 2.
Andrew Wiles's proof works by establishing the Taniyama-Shimura conjecture for semistable elliptic curves, which had been shown to imply Fermat's Last Theorem by Ribet in 1986.
- 3.
Elliptic curves and modular forms are two apparently unrelated areas of mathematics that Taniyama and Shimura conjectured were secretly the same objects — a bridge between two mathematical worlds.
What it covers
Who wrote it
Simon Singh is a British science writer and former BBC television producer. He has a doctorate in particle physics from Emmanuel College, Cambridge, and worked on the BBC documentary Fermat's Last Theorem before writing the book. He has written several other popular science books including The Code Book (1999), Big Bang (2004), and Trick or Treatment (2008), which examined the evidence for alternative medicine. He is a Fellow of the Royal Society of Arts and has been involved in legal cases defending science journalism.
