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There is a seemingly reliable report that Fermat was born at Beaumont de
Lomagne, near Toulouse, on August 17, 1601. It is known that he died at
Castres or Toulouse on January 12, 1665. His tombstone, originally in the
church of the Augustines in Toulouse and later moved to the local museum,
gives the preceding date of death and Fermat's age at death as fifty-seven
years. Because of this conflicting data, Fermat's dates are usually listed as
(1601?-1665). Indeed, for various reasons, Fermat's birth year, as given by
different writers, ranges from 1590 to 1608.
Fermat was the son of a leather
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merchant
and received his early education
at home. At the age of thirty, he obtained the post of councilor for the local
parliament at Toulouse and there discharged his duties with modesty and punctiliousness.
Working as a humble and retiring lawver. He devoted the bulk of his
leisure time to the study of mathenatics. Although he published very little
during his lifetimel, he was in scientific correspondence with many leading
mathematicians of his day and, in this way, considerably influenced his contemporaries.
He enriched so many branches of mathematics with so many
important contributions that he has been called the greatest French mathematician
of the seventeenth century.
Of Fermat's varied contributions to mathematics, the most outstanding is
the founding of the modern theory of numbers. In this field, Fermat possessd
extraordinary intuition and ability. It was probably the Latin translation of
Doiphantus Arithmetica, made by Bachet de Meziriac in 1621, that first dirdcted
Fermat's attention to number theory. Many of Fermat's contributions to
the field occur as marginal statements made in his copy of Bachet's work.
There do not exist positive integers £ø, y, z, n such that x©ú£«y©ú=z©ú,
when n > 2.
This famous conjecture is known as Fernat's last "theorem."
It was stated by Fermat in the margin of his copy of Bachet's
translation of Diophantus, at the side of Problem 8 of Book ¥±:"To
divide a given square number into two squares." Fermat's marginal
note reads. "To divide a cube into two cubes, a fourth power, or in
general any power whatever onto two powers of the same denomination
above the second is impossible, and I have assuredly found an
adnirable proof of this, but the margin is too narrow to contain it."
Whether Fermat really possessed a sound demonstration of this problem
will probably forever remain an eafima. Many of the most prominent
mathematicians since his have tried their skill on the prolem,
but the general conjecture still remains open. There is a proof
given elsewhere by Fermat for the case n = 4, and Euler supplied a
proof (later perfected by others) for n = 3. About 1825, independent
proofs for the case n = 5 were by Legendre and Dirichlt, in
1839, Lame proved the theorem for n =7. Very significant advances in
the study of the problem were made by the German mathematician E.
Kummrt (1810-1893). In 1843, Kummer subnitted a purported proof
to Dirichlet, who pointed out an error in the reasoning. Kummer then
returned to the problem with renewed vigor,and a few years later,
after developing an important allied subject in higher algebra called the
theory of ideals, derived very general conditions for the insolubiliy of
the Fermat relation.
Almost all important subsequent progress on the
problem has been based on Kummer's investigations. It is now known
that Fermat's last "theorem" is certainly true for all n < 125,000,©÷and
for many other special values of n. In 1908, the German mathematician
Paul Wolfskehl bequeathed 100,000 marks to the Academy of Science
at Gottingen as a prize for the first complete proof of the "theorem."
The result was a deluge of alleged proofs by golry-and money-seeking
laymen; ever since then, the proplem has haunted amateurs, as does
the trisection of an arbitrary angle and the squaring of the circle.
Fermat's last "theorem" has the peculiar distinction of being the
mathematical problem for which the greatest number of incorrect
proofs have been publlshed.
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