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Pierre de Fermat

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Pierre de Fermat, pronounced Fair-mah, was born on August 20, 1601. He shares a birthday with the 23rd President of the United States, Benjamin Harrison, American politician, Ron Paul, American television broadcaster, Al Rocker, and American singer, Fred Durst, also known as Limp Bizkit. He was born in the town of Beaumont-de-Lomagne, which is located in southwest France. His father was Dominique Fermat, a wealthy leather merchant, and his mother’s family was in the legal profession. Fermat’s uncle and godfather were also merchants. Because of his father’s money, Pierre de Fermat was privileged enough to receive an education at the Franciscan monastery of Grandselve. He then attended the University of Toulouse in Toulouse, France, which was founded 779 years ago, and received a Bachelor’s Degree in civil law. There is no trace of the youthful Fermat having any particular skill in mathematics.

Fermat was pressured by his family to have a career in the civil service. In 1631, he was appointed conseiller au Parlement de Toulouse, a councilor at the Chamber of Petitions. If locals wanted to petition the King of France, Louis XIII, on any matter, they first had to convince Fermat or one of his acquaintances that their request was important. Fermat and his associates provided a vital link between Toulouse and Paris and were a liaison between the locals and the monarch. They also made sure that royal decrees from Paris were executed throughout Toulouse. Fermat was ranked high enough to deal with very severe cases and once ordered a sentence to a priest to be burned at the stake for “abusing his functions”.

Fermat climbed quickly within the ranks of the civil service, thus becoming a member of the social elite. This entitled him to use de as part of his name. His rise in the social scene was not really because of how amazing people thought he was; the plague was raging through Europe and all of the higher socialites were dying, thus the people who survived the plague were elevated to fill the places of those who died. In 1652, Fermat was so ill from the plague that his friend, Bernard Medon, told several colleagues that he was dead. Soon after, he corrected himself, saying that he no longer feared for Fermat’s health, even though he had counted him among the dead a short time ago.

Fermat had no great political ambition and devoted all his spare energy and time to mathematics. He was an amateur mathematician and was called the “Prince of Amateurs” by E. T. Bell. Around Fermat’s time, Europe was still recovering from the Dark Ages and mathematicians were not very highly regarded. Oxford University was the only institution in Europe to encourage mathematics, thus it is safe to say that most mathematics at the time were amateurs. But Fermat was an amateur to the extreme.

Since Toulouse was so far away from Paris, where the small community of mathematicians existed, Fermat was very isolated. The only two people that Fermat discussed his mathematical studies with were Pascal and Father Mersenne. But this does not mean that he did not make contact with other mathematicians. In fact, Fermat was disliked by many mathematicians because of the contact he made with them. He was very brilliant and wrote letters to people stating his most recent theorem- without providing the accompanying proof. He would then challenge the people we was writing to to find the proof. He never reveals his own proofs, which led to René Descartes calling him a “braggart” and John Wallis referring to him as “that damned Frenchman”. Fermat did not like publishing his work, not only because he enjoyed taunting other mathematicians, but also because he knew that, if he did, he would have to “waste” his time explaining his methods and answering questions about his discoveries that would undoubtedly be asked. This way, after finishing one theorem, he could move on to a new mathematical idea right away.

The book The Last Problem by Eric Temple Bell contains one mathematical problem and no solution. It gives the history of a mathematical problem that has its roots in ancient Greece, but that reached full maturity only in the seventeenth century when Pierre de Fermat inadvertently set it as a challenge for the rest of the world. One great mathematician after another had been humbled by Fermat’s legacy, and for three hundred years nobody had been able to solve it. It is a simple problem that even the great mathematicians of history could not solve.

Usually half the difficulty in a solving a math problem is understanding the question, but that is not the case for Fermat’s Last Theorem. The problem is very straightforward: Prove that there are no whole number solutions for the equation aⁿ bⁿ = cⁿ for n greater than 2. It is based on Pythagoras’s Theorem:

a² b² = c².

Most people with a high school mathematics education know what Pythagorean Triples are. Pythagorean Triples are combinations of three whole numbers that perfectly fit Pythagoras’s equation: a² b² = c². One example would be if a=3 b=4 and c=5. By putting these numbers into the equation, you can see that 3²(9) 4²(16) = 5²(25).Another Pythagorean Triples is 5, 12, and 13. This equation is very simple to understand, however a similar equation is much more difficult: a³ b³ = c³. Finding whole number solutions (Pythagorean Triples) to the original equation seems easy, but changing the power from two to three and finding whole number solutions seems to be impossible. Generations of mathematicians have failed to find numbers that fit the cubed equation perfectly. Even more shocking is that if the power is changed from three to a higher number (4, 5, 6…), then finding a solution also seems to be impossible. Pierre de Fermat came to the conclusion that the reason why nobody could find any solutions was because no solutions existed. In other words, there are no whole number solutions to the equation aⁿ bⁿ = cⁿ for n greater than two.

Fermat even claimed to have a proof for this conclusion. In the margin of his copy of a book by Diophantus, he wrote that he had found a truly marvelous proof which the margin was too small to contain. Fermat died on January 12, 1665 without revealing the proof he had supposedly found. No other mathematician, although many have tried, has been able to come up with a proof for this theorem. That is, until June 23, 1993, when Andrew Wiles, a professor at Princeton University, presented his proof to a board of 200 mathematicians at Cambridge University. The theorem appeared to be solved, but the mathematics shown in Wiles’ proof were obviously not methods that had been around during Fermat’s time. Some people even doubt that Fermat was telling the truth about having a proof.
Pierre de Fermat made many contributions to the mathematical community, even though that, during his lifetime, he received very little recognition as a mathematician. Along with Rene’ Descartes, Pierre de Fermat was considered one of the fathers of analytic geometry and along with Blaise Pascal, he was considered to be one of the founders of probability theory. He wrote papers about calculus long before Isaac Newton and Gottfried Leibniz were even born. Fermat made contributions in the field of optics and provided a law on light travel. Fermat is best known for creating the most profound enigma in the history of mathematics. Fermat’s Last Theorem was central to the development of mathematics. He was the father of modern number theory and the account of Fermat’s Last Theorem is associated with the history of mathematics, touching on all of the main subjects of number theory.
Pierre de Fermat was an extraordinary individual whose contributions to mathematics go far beyond the Last Theorem. He is one of the most brilliant and intriguing mathematicians in history and will always be remembered for all of his success in many mathematic areas.

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