History
Fermat left no proof of the conjecture for all n, but he did prove the special case n = 4. This reduced the problem to proving the theorem for exponents n that are prime numbers. Over the next two centuries (1637–1839), the conjecture was proven for only the primes 3, 5, and 7, although Sophie Germain proved a special case for all primes less than 100. In the mid-19th century, Ernst Kummer proved the theorem for regular primes. Building on Kummer's work and using sophisticated computer studies, other mathematicians were able to prove the conjecture for all odd primes up to four million.
The final proof of the conjecture for all n came in the late 20th century. In 1984, Gerhard Frey suggested the approach of proving the conjecture through a proof of the modularity theorem for elliptic curves. Building on work of Ken Ribet, Andrew Wiles succeeded in proving enough of the modularity theorem to prove Fermat's Last Theorem, with the assistance of Richard Taylor. Wiles's achievement was reported widely in the popular press, and has been popularized in books and television programs.
Read more about this topic: Fermat's Last Theorem
Famous quotes containing the word history:
“A great proportion of the inhabitants of the Cape are always thus abroad about their teaming on some ocean highway or other, and the history of one of their ordinary trips would cast the Argonautic expedition into the shade.”
—Henry David Thoreau (1817–1862)
“Postmodernism is, almost by definition, a transitional cusp of social, cultural, economic and ideological history when modernism’s high-minded principles and preoccupations have ceased to function, but before they have been replaced with a totally new system of values. It represents a moment of suspension before the batteries are recharged for the new millennium, an acknowledgment that preceding the future is a strange and hybrid interregnum that might be called the last gasp of the past.”
—Gilbert Adair, British author, critic. Sunday Times: Books (London, April 21, 1991)
“A people without history
Is not redeemed from time, for history is a pattern
Of timeless moments.”
—T.S. (Thomas Stearns)