Fermat

Pierre De Fermat

Born: - August 17, 1601                     Died: - January 12, 1665

Fermat was one of the leading mathematicians of early 17^th century. Pierre Fermat's father was a wealthy leather merchant and second consul of Beaumont- de- Lomagne. Although there is little evidence concerning his school education it must have been at the local Franciscan monastery. He was an amateur mathematician.

 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 Plane loci to one of the mathematicians there. From Bordeaux Fermat went to Orléans where he studied law at the University and spent his working life as a magistrate in the small provincial town of Castres.

After he moved to Toulouse , he gained a new mathematical friend Carcavi.  In 1636 Carcavi went to Paris as royal librarian and made contact with Mersenne and his group. Mersenne's interest was aroused by Carcavi's descriptions of Fermat's discoveries on falling bodies, and he wrote to Fermat. Fermat replied on 26 April 1636 and, in addition to telling Mersenne about errors which he believed that Galileo had made in his description of free fall. Fermat had little interest in physical applications of mathematics. Even with his results on free fall he was much more interested in proving geometrical theorems than in their relation to the real world. Fermat sent a letter to Mersenne containing two problems on maxima which Fermat asked Mersenne to pass on to the Paris mathematicians and this was to be the typical style of Fermat's letters, he would challenge others to find results which he had already obtained. Roberval and Mersenne found that Fermat's problems in this first, and subsequent, letters were extremely difficult and usually not soluble using current techniques. They asked him to divulge his methods and Fermat sent Method for determining Maxima and Minima and Tangents to Curved Lines.

His reputation as one of the leading mathematicians in the world came quickly but attempts to get his work published failed mainly because Fermat never really wanted to put his work into a polished form. However some of his methods were published in Cursus mathematicus a work by Herigone. With Pascal, Fermat stands as one of the founder of mathematical theory of probability. Pierre de Fermat independently founded the new branch of mathematics called Analytical Geometry. This work led to violent controversies over question of priority with Rene Descartes. Fermat's pioneering work in analytic geometry was circulated in manuscript form in 1636, predating the publication of Descartes' famous La géométrie. This manuscript was published posthumously in 1679 in "Varia opera mathematica", as Ad Locos Planos et Solidos Isagoge, ("Introduction to Plane and Solid Loci").^[

In Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum, Fermat developed a method for determining maxima, minima, and tangents to various curves that was equivalent to differentiation.

He is probably best known for his work on number theory. He also left one of the famous unsolved problems in maths called- Fermat’s last theorem. This theorem states that xⁿ + yⁿ = zⁿ has no non-zero integer solutions for x, y and z when n > 2. in the margin of Bachet's translation of Diophantus's Arithmetica , Fermat worte “ I have discovered a truly remarkable proof which this margin is too small to contain.” These marginal notes only became known after Fermat's son Samuel published an edition of Bachet's translation of Diophantus's Arithmetica with his father's notes in 1670. Unsuccessful attempts to prove the theorem over a 300 year period led to the discovery of commutative ring theory and a wealth of other mathematical discoveries. The truth of Fermat's assertion was proved in June 1993 by the British mathematician Andrew Wiles.

                                          

 

The second stamp was released after it was proved by Andrew Wiles.

In 1656 Fermat had started a correspondence with Huygens. This grew out of Huygens interest in probability and the correspondence was soon manipulated by Fermat onto topics of number theory. This topic did not interest Huygens but Fermat tried hard and in New Account of Discoveries in the Science of Numbers sent to Huygens via Carcavi in 1659, he revealed more of his methods than he had done to others. Fermat described his method of infinite descent and gave an example on how it could be used to prove that every prime of the form 4k + 1 could be written as the sum of two squares. 

He died at Castres, Tarn on January 12, 1655. The oldest and most prestigious high school in Toulouse is named after him: 

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