Fermat

Isaac Newton, Pythagoras, Carl Friedrich Gauss, and Euclid are among the most well-known mathematicians in history. Yet, no one recalls Pierre de Fermat. Fermat was just an amateur mathematician; however, his contributions to the world of mathematics have granted him the title, the "Prince of Amateurs" (Allenbaugh, 2001). Though most of his time was occupied by his duties as a lawyer, he played a role in forming the principles of analytic geometry, number theory, the theory of probability, and differential calculus. His most prevalent accomplishment was his infamous theorem, known as Fermat's Last Theorem, that left mathematicians puzzled for hundreds of years (Knight, 2001).

Born in Beaumont-de-Lomagne in France into a wealthy family, Fermat had great opportunities for education; he studied at a Francisan monastery and the University of Toulouse, Bourdeaux, and Orleans (Allenbaugh, 2001). He did not show any particular interest to mathematics while he went to school. Pierre went on to become a lawyer and entered civil service; his mom’s side of the family was composed of all lawyers, and this perhaps explains why Pierre chose law as his profession (Knight, 2001). Meanwhile, he wed his fourth cousin and had five children. His career was mainly focused on politics: he worked with the parliament and was the connection between the town and the king (Allenbaugh, 2001). Despite the focus of his professional life, Pierre de Fermat could not be kept away from his true love, numbers. He devoted much of his time away from work to mathematics. He was intrigued by the work of Diophantus, an ancient Greek mathematician and philosopher, who was the author of Arithmetica, which turned out to be the “inspiration” of his mysterious theorem. Arit...

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...subtracting y2 from both sides then factoring the right side of the equation. Each component, x, z+y, and z-y, is an even number and, thus, can be written in terms of the positive integers, u, v, and w: x=2u, z+y=2v and z-y=2w. If these values are substituted into the x2 + y2 = z2 equation and then simplified, the resulting equation is u2= vw. The greatest divisor for both v and w would be one. Any number that would divide both v and w would also divide v+w= ½ (x+y) + ½(z-y)=z and v-w= ½ (z+y) - ½(z-y)=y. It was proved earlier that y and z, or rather any pairing of x, y and z,could only have a common divisor of one, thus, v and w are divisible by one, implying that they are relatively prime. The significance of the prime nature of these number is that the only way two relatively prime numbers can be multiplied to equal a square (vw=u2) is if v and w are squares.