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Sunday, December 27, 2009

Pierre de Fermat (1601-1665)

Pierre de Fermat, was a lawyer who led a rather uninteresting and uneventful life by our standards. However, by the standards of physicsits and mathematicians his life was most interesting and eventful. It was his theorem, that deemed him fitting of the title, "The greatest French mathematician of the seventeenth century."

Pierre was born on August 20, 1601 near Toulouse, France. On the twentieth of that August he was baptized, and name after his uncle(and one of four siblings). Fermat led a comfortable French middle class life as a child. His father, Dominique Fermat, a successful leather merchant, and his mother, Claire de Long, whom belonged to the noblesse de robes, were able to provide a happy life for Fermat as a child. It is his hometown of Beaumont at the monastery of Grandselve where Fermat received his primary and secondary education. One would think once finishing his primary and secondary education he would pursue mathematics as a career but he decided against it, instead he decided to go toward a legal career at the University of Toulouse. And while some may think that he surely would have went into the field of math his career choice is not unheard of, or suprising, in fact the decision to go into law, taking into consideration his social status and background, it is hardly surprising at all. In May of 1631, from the University at Orleans, Fermat acquired his Bachelor of Civil Laws. In a short two weeks after he graduated, Fermat gained the position of councilor in the provincial High Court of Judicature in Toulouse. This job, which he remained in until his death, allowed Pierre Fermat to add the 'de' to his name. From then on being worldly known as Pierre de Fermat.

After beginning his career in the laws, Pierre had even more fortunate events. He was married in June, 1631 to a distant cousin of his, Louise de Long. The two had a strong and happy marriage that lasted untill Fermat passed away. Louise and Pierre had five children, three daughters and two sons.

Pierre de Fermat led a happy life by anyone's account.He had a loving family and a sucessful job. Aside from his outstanding mathematics recognition and his involvement with the law, Fermat was also excellent in the fields of languages. He had a good understanding of Latin, Greek, Italian, and Spanish. Pierre had a wonderful life, but soon it would all come to an end. In 1652 he was struck with the plague, and while he recovered from his illness in 1660, he suffered from bad health in which he never fully recovered. Finally, on January 12th, 1665 , Pierre de Fermat passed away.

It is still not known where Pierre de Fermat acquired his interest in the field of math. In fact to try and guess it would be merely speculation. Although it is possible that his interest was sparked by a friend of his, Etienne d'Espagnet. Etienne was 5 years older than Pierre and shared, or perhaps passed on a very deep interest in math. And while Fermat had a deep understanding and keen interest in mathematics, he did not however give proofs for equations he had written. Maybe if math were Fermat's main occupation then he would have presented proofs, but instead it was merely a pass time for him, and he enjoyed solving and writing equations rather than doing repetitive proofs. This resulted in later generations of mathematicians to work diligently on providing proofs for his equations.

Now I arrive to the equation that granted Pierre de Fermat the recognition he has today. Fermat's Last Theorem, or "FLT". It is not called his last theorem because it was his final piece of work to be discovered, but rather it is called Fermat's Last Theorem because it was the last of his equations to be proved correct or incorrect. Because of Fermat's lack of proofs in his work, it suggests that he himself had not solved his last theorem, which would explain for the hundreds of years of attempted solving. Although perhaps this is because FLT needed to be solved for prime numbers and 'n' had to equal 4. That is because any number that is greater then 2 is divisble by 4 or an odd prime number. His theorem states: 'x' raised to 'n', plus 'y' raised to 'n', equals 'z' raised to 'n'. But because of the latter information presented, his equation can be re-written as ('x' raised to 'm')to 'k', plus ('y' to the 'm')to 'k' equals ('z' raised to 'm')to 'k'. The latter will only work though if you factor, n=mk.

Now starts the history of tried proofs for his theorem. 1820 is when the first proof was tried. It was attempted by the french mathematician Sophie Germain. 1825, Dirichlet tried proving FLT for n=5. In 1832, Dirichlet found proof for 'n' to equal 14 while he was trying to prove FLT for 'n' to equal 7. Then in 1839, LamŒ succeeded in solving for n=7 where Dirichlet had not. After another hundred and fifty-four years in 1993 Adam Wiles announced he had solved FLT. Although after review of his manuscripts it was said that a mistake was made. However, Wiles did not give up hope, and in November of 1994 he released a new proof that cleared up the problem found in the original one. However to include his proof within this paper would not be practical, for it is 150 pages in length. His proof was reviewed and is now valid and accepted, so as a result Fermat's last Theorem is now proven offically.

To say Fermat led an uneventful life would be a mis-judgement on many people's part. In fact his life was everything but un-eventful. A predecessor of calculus, as founder of analytic geometry, and as the founder of the Number Theory. Even after his death his contributions to the mathematics community lives on. Fermat changed the face of mathematics. He did all of his math within his own free time, so a question is begged, what would mathematics be like today if the greatest mathematician had spent all of his life devoted to equations and proofs?


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