Part 2

Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem
By Amir D. Aczel

(Page 2 of 2)

The next day, Wednesday, June 23, 1993, was his last talk. As he neared the lecture hall, Wiles found it necessary to push his way in. People stood outside blocking the entrance and the room was overflowing. Many carried cameras. As Wiles again wrote seemingly endless formulas and theorems on the board, the tension increased. "There was only one possible climax, only one possible end to Wiles' presentation," Professor Ken Ribet of the University of California at Berkeley later told me. Wiles was finishing the last few lines of his proof of an enigmatic and complicated conjecture in mathematics, the Shimura-Taniyama Conjecture. Then suddenly he added one final line, a restatement of a centuries-old equation, one which Ken Ribet had proved seven years earlier would be a consequence of the conjecture. "And this proves Fermat's Last Theorem," he said, almost offhandedly. "I think I'll stop here."

There was a moment of stunned silence in the room. Then the audience erupted in spontaneous applause. Cameras flashed as everyone stood up to congratulate a beaming Wiles. Within minutes, electronic mail flashed and faxes rolled out of machines around the world. The most celebrated mathematical problem of all time appeared to have been solved.

"What was so unexpected was that the next day we were deluged by the world press," recalled Professor John Coates, who organized the conference without having the slightest idea that it would become the launching ground for one of the greatest mathematical achievements. Headlines in the world's newspapers hailed the unexpected breakthrough. "At Last, Shout of 'Eureka!' In Age-Old Math Mystery" announced the front page of the New York Times on June 24, 1993. The Washington Post called Wiles in a major article "The Math Dragon-Slayer," and news stories everywhere described the person who apparently solved the most persistent problem in all of mathematics, one that had defied resolution for over 350 years. Overnight, the quiet and very private Andrew Wiles became a household name.

Pierre de Fermat

Pierre de Fermat was a seventeenth-century French jurist who was also an amateur mathematician. But while he was technically an "amateur" since he had a day job as a jurist, the leading historian of mathematics E. T. Bell, writing in the early part of the twentieth century, aptly called Fermat the "Prince of Amateurs." Bell believed Fermat to have achieved more important mathematical results than most "professional" mathematicians of his day. Bell argued that Fermat was the most prolific mathematician of the seventeenth century, a century that witnessed the work of some of the greatest mathematical brains of all time.

One of Fermat's most stunning achievements was to develop the main ideas of calculus, which he did thirteen years before the birth of Sir Isaac Newton. Newton and his contemporary Gottfried Wilhelm von Leibniz are jointly credited in the popular tradition with having conceived the mathematical theory of motion, acceleration, forces, orbits, and other applied mathematical concepts of continuous change we call calculus.

Fermat was fascinated with the mathematical works of ancient Greece. Possibly he was led to his conception of calculus ideas by the work of the classical Greek mathematicians Archimedes and Eudoxus, who lived in the third and fourth centuries B.C., respectively. Fermat studied the works of the ancients - which were translated into Latin in his day - in every spare moment. He had a full-time job as an important jurist, but his hobby - his passion - was to try to generalize the work of the ancients and to find new beauty in their longburied discoveries. "I have found a great number of exceedingly beautiful theorems," he once said. These theorems he would jot down in the margins of the translated copies of ancient books he possessed.

Fermat was the son of a leather merchant, Dominique Fermat, who was Second Consul in the town of Beaumont-de-Lomagne, and of Claire de Long, the daughter of a family of parliamentary judges. The young Fermat was born in August 1601 (baptized August 20 in Beaumont-de-Lomagne), and was raised by his parents to be a magistrate. He went to school in Toulouse, and was installed in the same city as Commissioner of Requests at the age of thirty. He married Louise Long, his mother's cousin, that same year, 1631. Pierre and Louise had three sons and two daughters. One of their sons, Clement Samuel, became his father's scientific executor and published his father's works after his death. In fact, it is the book containing Fermat's work, published by his son, that has come down to us and from which we know his famous Last Theorem.

Copyright © 1997 by Amir D. Aczel.

About the Author

Amir D. Aczel is the author of many research articles on mathematics, two textbooks, and nine nonfiction books, including the international bestseller Fermat's Last Theorem, which was nominated for a Los Angeles Times Book Award. Aczel has appeared on over thirty television programs, including nationwide appearances on CNN, CNBC, and Nightline, and on over a hundred radio programs, including NPR's Weekend Edition and Morning Edition. Aczel is a Fellow of the John Simon Guggenheim Memorial Foundation.