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Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem - Softcover

Singh, Simon

 
9780385493628: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
Softcover
ISBN 10: 0385493622 ISBN 13: 9780385493628
Verlag: Knopf Doubleday Publishing Group, 1998

Inhaltsangabe

xn + yn = zn, where n represents 3, 4, 5, ...no solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

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Über die Autorin bzw. den Autor

Simon Singh received his Ph.D. in physics from the University of Cambridge. A BBC producer, he directed and coproduced an award-winning documentary film on Fermat's Last Theorem that aired on PBS's "Nova" series. He is also the author of the bestselling The Code Book:  The Science of Secrecy from Ancient Egypt to Quantum Cryptography.  He lives in London, England.

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xn + yn = zn, where n represents 3, 4, 5, ...no solution
"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In "Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

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"I Think I'll Stop Here"

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
--G. H. Hardy
June 23, 1993, Cambridge

It was the most important mathematics lecture of the century. Two hundred mathematicians were transfixed. Only a quarter of them fully understood the dense mixture of Greek symbols and algebra that covered the blackboard. The rest were there merely to witness what they hoped would be a truly historic occasion.

The rumors had started the previous day. Electronic mail over the Internet had hinted that the lecture would culminate in a solution to Fermat's Last Theorem, the world's most famous mathematical problem. Such gossip was not uncommon. The subject of the Last Theorem would often crop up over tea, and mathematicians would speculate as to who might be doing what. Sometimes mathematical mutterings in the senior common room would turn the speculation into rumors of a breakthrough, but nothing had ever materialized.

This time the rumor was different. When the three blackboards became full, the lecturer paused. The first board was erased and the algebra continued. Each line of mathematics appeared to be one tiny step closer to the solution, but after thirty minutes the lecturer had still not announced the proof. The professors crammed into the front rows waited eagerly for the conclusion. The students standing at the back looked to their seniors for hints of what the conclusion might be. Were they watching a complete proof to Fermat's Last Theorem, or was the lecturer merely outlining an incomplete and anticlimactic argument?

The lecturer was Andrew Wiles, a reserved Englishman who had emigrated to America in the 1980s and taken up a professorship at Princeton University, where he had earned a reputation as one of the most talented mathematicians of his generation. However, in recent years he had almost vanished from the annual round of conferences and seminars, and colleagues had begun to assume that Wiles was finished. It is not unusual for brilliant young minds to burn out, a point noted by the mathematician Alfred Adler: "The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished."

"Young men should prove theorems, old men should write books," observed G. H. Hardy in his book A Mathematician's Apology. "No mathematician should ever forget that mathematics, more than any other art or science, is a young man's game. To take a simple illustration, the average age of election to the Royal Society is lowest in mathematics." His own most brilliant student, Srinivasa Ramanujan, was elected a Fellow of the Royal Society at the age of just thirty-one, having made a series of outstanding breakthroughs during his youth. Despite having received very little formal education in his home village of Kumbakonam in South India, Ramanujan was able to create theorems and solutions that had evaded mathematicians in the West. ln mathematics the experience that comes with age seems less important than the intuition and daring of youth.

Many mathematicians have had brilliant but short careers. The nineteenth-century Norwegian Niels Henrik Abel made his greatest contribution to mathematics at the age of nineteen and died in poverty, just eight years later, of tuberculosis. Charles Hermite said of him, "He has left mathematicians something to keep them busy for five hundred years," and it is certainly true that Abel's discoveries still have a profound influence on today's number theorists. Abel's equally gifted contemporary *variste Galois also made his breakthroughs while still a teenager.

Hardy once said, "I do not know an instance of a major mathematical advance initiated by a man past fifty." Middle-aged mathematicians often fade into the background and occupy their remaining years teaching or administrating rather than researching. In the case of Andrew Wiles nothing could be further from the truth. Although he had reached the grand old age of forty he had spent the last seven years working in complete secrecy, attempting to solve the single greatest problem in mathematics. While others suspected he had dried up, Wiles was making fantastic progress, inventing new techniques and tools that he was now ready to reveal. His decision to work in absolute isolation was a high-risk strategy and one that was unheard of in the world of mathematics.

Without inventions to patent, the mathematics department of any university is the least secretive of all. The community prides itself in an open and free exchange of ideas and afternoon breaks have evolved into daily rituals during which concepts are shared and explored over tea or coffee. As a result it is increasingly common to find papers being published by coauthors or teams of mathematicians, and consequently the glory is shared out equally. However, if Professor Wiles had genuinely discovered a complete and accurate proof of Fermat's Last Theorem then the most wanted prize in mathematics was his and his alone. The price he had to pay for his secrecy was that since he had not previously discussed or tested any of his ideas with the mathematics community, there was a significant chance that he had made some fundamental error.

Ideally Wiles had wanted to spend more time going over his work and checking fully his final manuscript. But when the unique opportunity arose to announce his discovery at the Isaac Newton Institute in Cambridge he abandoned caution. The sole aim of the institute's existence is to bring together the world's greatest intellects for a few weeks in order to hold seminars on a cutting-edge research topic of their choice. Situated on the outskirts of the university, away from students and other distractions, the building is especially designed to encourage the academics to concentrate on collaboration and brainstorming. There are no dead-end corridors in which to hide and every office faces a central forum. The mathematicians are supposed to spend time in this open area, and are discouraged from keeping their office doors closed. Collaboration while moving around the institute is also encouraged--even the elevator, which travels only three floors, contains a blackboard. In fact every room in the building has at least one blackboard, including the bathrooms. On this occasion the seminars at the Newton Institute came under the heading of "L-functions and Arithmetic." All the world's top number theorists had been gathered together in order to discuss problems relating to this highly specialized area of pure mathematics, but only Wiles realized that L-functions might hold the key to solving Fermat's Last Theorem.

Although he had been attracted by having the opportunity to reveal his work to such an eminent audience, the main reason for making the announcement at the Newton Institute was that it was in his hometown, Cambridge. This was where Wiles had been born, it was here he grew up and developed his passion for numbers, and it was in Cambridge that he had alighted on the problem that was to dominate the rest of his life.

The Last Problem

In 1963, when he was ten years old, Andrew Wiles was already fascinated by mathematics. "I loved doing the problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found I discovered in my local library."

One day, while wandering home from school, young Wiles decided to visit the library in Milton Road. It was rather small, but it had a generous collection of puzzle books, and this is what often...

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Verlag
Knopf Doubleday Publishing Group
Erscheinungsdatum
1998
Sprache
Englisch
ISBN 10 
0385493622
ISBN 13 
9780385493628
Einband
Taschenbuch
Anzahl der Seiten
336
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Verantwortliche Person
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