I sat down with French mathematician Pierre de Fermat recently to learn about his last theorem. Fermat lived from 1601 to 1665. In that time, he made several mathematical breakthroughs in various different fields, especially number theory and calculus. Unfortunately, he did not publish most of his manuscripts, and the methods he used to get to his conclusions are still unknown to us today.
WM Times: Tell me a little about yourself.
Pierre de Fermat: Well my father, Dominique Fermat, was a leather-merchant, and my mother, Claire de Long was the daughter of a family of parliamentary jurists. I was born in Beaumont de Lomagne in August 1601; I'm not sure of the exact date, but I was baptized on the twentieth. I received my degree of Bachelor of Civil Law at the University of Orleans sometime before 1631. In May 1631 I married my love and fourth cousin, Louise de Long. And in that year I also gained the status which entitled me to add the de to my name. Louise and I had five known children: Clement-Samuel, Jean, Claire, Catherine, and Louise. My eldest son, Clement-Samuel, shared my interest in mathematics. He edited my posthumous editions of Observations on Diophantus (1670) and Various Mathematical Works (1679). But I really don't like discussing myself.
WM Times: It is apparent from your dowry of 12,000 livres that money was not a problem for you. How did you win you win your bread?
Pierre de Fermat: I practiced law in Toulouse and my birth town of Beaumont.
WM Times: So where does math fit into this?
Pierre de Fermat: Well everyone needs a hobby. My job as a lawyer was full of unwanted controversy. Math is just numbers; no people. And since I was only an amateur, I never had to worry about pleasing anyone or ruining my reputation. I have always shied away from controversy and felt math was my only escape from people and arguments.
WM Times: But you were part of two of the most vehement and most famous mathematical disputes of your day!
Pierre de Fermat: Yes, but I never meant to hurt anyone's feelings. I tried as best I could not to upset anyone. Is it my fault I was always right and Wallis and Pascal were stubborn fools?
WM Times: Would you like to discuss what the controversies were about?
Pierre de Fermat: Not especially. It's too painful.
WM Times: Please.
Pierre de Fermat: Oh, alright I wanted to renew the classical traditions of arithmetic and the number theory, but I found the classics aimed at rational solutions instead of integral ones. I searched for a number theory that was more strict than the classical one of Diophantus, and ended up with something completely different.
WM Times: So what were your arguments about?
Pierre de Fermat: Well my disputes with Fernicle, Wallis and others rarely got passed an assertation and counterassertation of theorems or a basic disagreement over what number theory was or should be, or whether it was worth doing at all. That's really all I can say.
WM Times: You don't like to give a lot of details, do you?
Pierre de Fermat: The manuscripts I wrote were full of details about my mathematical breakthroughs; how I helped create the calculus, made great strides in analytical geometry, and founded probability and the modern number theory.
WM Times: What happened to the manuscripts?
Pierre de Fermat: I destroyed them.
WM Times: You seem to enjoy making my job as hard as possible.
Pierre de Fermat: Well, you know us mathematicians. We're sadistic in our own ways.
WM Times: I think it's time we get to your infamous last theorem.
Pierre de Fermat: Well, it's rather simple. You of course have had to solve problems in the form of a^2 + b^2 = c^2. But have you ever solved a problem such as a^3 + b^3 = c^3? As simple as Pythagorean's theory is; it is impossible to solve the problem when the numbers involved are raised to any power greater than two. In other words, there are no rational solutions for the problem a^n + b^n = c^n when n is greater than two.
WM Times: Are you sure? Just because it doesn't work for the third power does not mean that it is unsolvable for any other power.
Pierre de Fermat: Well I have discovered a truly marvelous demonstration to prove my theorem; however the word limit for this interview is much too small for me to explain it all to you now.
WM Times: Could you at least describe what methods you used to get to this conclusion of yours?
Pierre de Fermat: Well many mathematicians after me have done an excellent job of figuring out their own ways to get to my results, especially with regard to the calculus. I'll let you work on my last theorem since it is too late for me to publish my proof. You can ask your math teacher for help; she gets so lonely first period.
Ball, Rouse W.W. "Pierre de Fermat." A Short Account of the History of Mathematics. 3 March 2002. Online. http://www.maths.tcd.ie/pub/HistMath/People/Fermat/RouseBall/RB_Fermat.html
This website was easy to find. However, much of the information on it was in various other books. Of the five pages, there was one and a half of pure French.
Bell, E.T. Men of Mathematics. New York: Simon and Schuster, 1937
This book was short and to the point. The author was clear for the most part, but he assumed the readers all had a basic understanding of the calculus. He did not show Fermat's methods, but he did write his own methods that came to the same conclusion as Fermat had.
Mahoney, Michael Sean. The Mathematical Career of Pierre de Fermat. Princeton: Princeton University Press, 1973
This book contained the most information on Fermat's personal life. However, to understand the mathematical aspects of this book, the reader would also need a background in calculus.