17 August 1601 or 1607/812 January 1665 Lived & Died
Slide 4
was a French lawyer at the Parlement of Toulouse, France, and
an amateur mathematician who is given credit for early developments
that led to infinitesimal calculus, including his adequality. In
particular, he is recognized for his discovery of an original
method of finding the greatest and the smallest ordinates of curved
lines, which is analogous to that of the then unknown differential
calculus, and his research into number theory. He made notable
contributions to analytic geometry, probability, and optics. He is
best known for Fermat's Last Theorem, which he described in a note
at the margin of a copy of Diophantus' Arithmetica. Pierre
Slide 5
Together with Ren Descartes, Fermat was one of the two leading
mathematicians of the first half of the 17th century. According to
Peter L. Bernstein, in his book Against the Gods, Fermat "was a
mathematician of rare power. He was an independent inventor of
analytic geometry, he contributed to the early development of
calculus, he did research on the weight of the earth, and he worked
on light refraction and optics. In the course of what turned out to
be an extended correspondence with Pascal, he made a significant
contribution to the theory of probability. But Fermat's crowning
achievement was in the theory of numbers." Regarding Fermat's work
in analysis, Isaac Newton wrote that his own early ideas about
calculus came directly from "Fermat's way of drawing
tangents."
Slide 6
The great 20th-century mathematician Andr Weil wrote that "...
what we possess of his methods for dealing with curves of genus 1
is remarkably coherent; it is still the foundation for the modern
theory of such curves. It naturally falls into two parts; the first
one... may conveniently be termed a method of ascent, in contrast
with the descent which is rightly regarded as Fermat's own."
Regarding Fermat's use of ascent, Weil continued "The novelty
consisted in the vastly extended use which Fermat made of it,
giving him at least a partial equivalent of what we would obtain by
the systematic use of the group theoretical properties of the
rational points on a standard cubic." With his gift for number
relations and his ability to find proofs for many of his theorems,
Fermat essentially created the modern theory of numbers.
Slide 7
Fermat was born in Beaumont- de-Lomagne, Tarn-et-Garonne,
France; the late 15th century mansion where Fermat was born is now
a museum. He was of Basque origin. Fermat's father was a wealthy
leather merchant and second consul of Beaumont-de-Lomagne. Pierre
had a brother and two sisters and was almost certainly brought up
in the town of his birth. There is little evidence concerning his
school education, but it may have been at the local Franciscan
monastery.
Slide 8
He attended the University of Toulouse before moving to
Bordeaux in the second half of the 1620s. In Bordeaux he began his
first serious mathematical researches and in 1629 he gave a copy of
his restoration of Apollonius's De Locis Planis to one of the
mathematicians there. Certainly in Bordeaux he was in contact with
Beaugrand and during this time he produced important work on maxima
and minima which he gave to tienne d'Espagnet who clearly shared
mathematical interests with Fermat. There he became much influenced
by the work of Franois Vite. From Bordeaux, Fermat went to Orlans
where he studied law at the University. He received a degree in
civil law before, in 1631, receiving the title of councillor at the
High Court of Judicature in Toulouse, which he held for the rest of
his life. Due to the office he now held he became entitled to
change his name from Pierre Fermat to Pierre de Fermat. Fluent in
Latin, Basque, classical Greek, Italian, and Spanish, Fermat was
praised for his written verse in several languages, and his advice
was eagerly sought regarding the emendation of Greek texts. He
communicated most of his work in letters to friends, often with
little or no proof of his theorems. This allowed him to preserve
his status as an "amateur" while gaining the recognition he
desired. This naturally led to priority disputes with
contemporaries such as Descartes and Wallis. He developed a close
relationship with Blaise Pascal. Anders Hald writes that, "The
basis of Fermat's mathematics was the classical Greek treatises
combined with Vieta's new algebraic methods."