On this day back in 1578, the Italian Baroque painter Francesco Albani was born. He specialized in a kind of idyllic religious work that is not widely appreciated but which I rather like. Baroque composer Nicola Porpora was born in 1686. Here is a little bit from his opera Semiramide Riconosciuta that has a nice Bach feel to it:
FBI agent Mark Felt was born in 1913. He is best known as “Deep Throat,” the Watergate scandal leaker. It is interesting that Wikipedia refers to him as a “whistleblower.” And it should! But that is not the description that it gives to Edward Snowden. Today there is all kinds of discussion as to whether Snoden really qualifies as a whistleblower. There is lots of mud slung at him with the implicit and sometimes explicit claim that if Snowden’s purpose was not morally snow white, then he’s a villain. But Felt was nothing close to snow white. In 2010, Bob Woodward said this of Felt’s motivations:
The truth is that I have little doubt that Snowden will be seen as a hero in ten or twenty years. At the time, those in power always think such people are traitors. What’s different now is that the press itself has become so obsequious towards power that they are the ones calling for whistleblowers’ heads. I’ve been amazed that over the past few months, there has been fairly limited official attacks on Snowden. There hasn’t been the need. They can just depend on people like Bob Schieffer:
And poet and destroyer of unstable women, Ted Hughes was born in 1930.
The day, however, belongs to the French mathematician Pierre de Fermat who was born on this day in 1601 (or 1607). By profession, he was a lawyer. But his passion was mathematics and made a number of important contributions to the field, especially in number theory. And it is for one conjecture in that field that he is best known for: Fermat’s Last Theorem. He said that there are no three natural numbers a, b, and c that will make the following equation true for an integer n greater than 2:
If n is 2, then this equation can be true; for example: 32 + 42 = 52. But when n is 3 or higher, it did not appear to ever be true. This was widely believed. But Fermat wrote in the margin of a book (a habit of his), “It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” But for the 28 years of his life, he never mentioned the problem again. For centuries mathematicians searched for the solution, which was only found 358 years later.
Did Fermat really have a “marvelous” proof that everyone else missed? Alas, no. It is generally thought that he was either mistaken or had a more limited proof in mind. Remember, the proof was only in his mind, so he could have thought he had a proof, but there was actually a mistake in it. Or maybe he had a proof for n=3 that he thought would generalize. It is certainly possible that he later realized that he hadn’t solved the problem. After all, how likely would you be to go back to an old book and update something you had written in the margin of a page? “Update: oops! I was wrong.” What’s more, countless times over the years, other mathematicians thought they had solved the problem, only to be proven incorrect.
Here is a brief video with the man who finally solved Fermat’s Last Theorem in 1995, Andrew Wiles. He actually starts crying while talking about it. It’s an amazing thing. It doesn’t however talk about the math, which involves a number of developments and would just confuse all of us anyway. It took him 6 years of concentrated work, despite the fact that he was already a specialist in the subfield of mathematics. The proof itself is over 100 pages long.
Happy birthday Pierre de Fermat!