France: Day 8 - Fermat

Today is the birthday of Frieda Nugel born 1884 in Cottbus, Brandenburg, Germany. Nugel was one of the first women to receive a doctorate in mathematics in Germany.

Today's quote is by Pierre de Fermat. He said "I am more exempt and more distant than any man in the world."

Pierre de Fermat

Pierre de Fermat was born August 17, 1601 in Tarn-et-Garnone, France. Fermat, a lawyer, was influential in the early developments of calculus and made significant contributions in the areas of analytic geometry, probability, and optics.

Thirty years after his death, a handed written note by Fermat was found in the margin of a book entitled "Arithmetica" written by Diophantus.  Fermat wrote, "It is impossible for any number which is a power greater than the second to be written as a sum of two like powers.  I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain." His quote means that there are no three positive integers, x, y, and z, where x^n + y^n = z^n and n is an integer greater than 2. This "marvelous demonstration" the Fermat refers to, was a mystery for 358 years, spawning a branch of mathematics called algebraic number theory and the modularity theorem.

Two examples I can give are: 3^1 + 4^1 = 7^1 and 3^2 + 4^2 = 5^2 and there are infinite number of examples for powers of 1 and 2 but none greater than 2. In 1994, Andrew Wiles successfully proved this mysterious conjecture that had baffled mathematicians for almost four centuries.

Fermat had made claims of original proofs on many of his theorems but only a few of those proofs are in existance. Many mathematicians doubt that those proofs existed due to the difficult nature of his theorems and the limitations of the mathematics at his time.

What type of man was Fermat? His contributions to mathematics are immense. He and Descartes are considered the emminent mathematicians of their lifetimes. Why did he choose to write that note in the margin of his father's book? Did he feel a need to overexagerrate his abilities? Was he concerned about his legacy and wanted a theorem that would live for centuries? Was he a prankster and some how knew that his brief commentary would drive future mathematicians to the edges of their own sanities? For myself, Fermat is the true mystery.