Nova Episode the Proof

¶ … Proof, a NOVA episode aired on PBS [...] review the video, with a focus on what the video tells us about how people learn to do mathematics. Compare and contrast this with your own experiences with mathematics, particularly your approach toward learning about new mathematical problems and trying to solve them. "The Proof" is more than just a video about solving a complex mathematical problem. It is a story of determination, setting goals, and finding out that solutions come from many different places and ideas. You have to be open to new ideas when you try to solve anything, whether it is a complex mathematical problem, or a personal problem. The proof is really about keeping an open mind, and looking at all the angles of a problem.

The Proof

The Proof" is an interesting look at one man's obsession with proving (or disproving) a theory (Fermat's Last Theorem), written over two hundred years ago and never proved. The NOVA Web Site notes, "Fermat's Last Theorem has since baffled mathematicians armed with the most advanced calculators and computers. NOVA chronicles the seven-year effort of one mathematician, Andrew Wiles, who methodically works in near isolation to determine the proof for this seemingly simple equation" (NOVA). Andrew Wiles, a noted Princeton mathematician, found evidence of Fermat's Last Theorem, and became determined to prove the Theorem. Fermat's Theorem is based on the Pythagoras theorem: "His equation is simple: a2 + b2 = c2. What it means is that in a right triangle (where one angle equals 90°), the sum of the squares of two sides equals the square of the hypotenuse (the longest side)" (NOVA).

The program then delves into how Wiles began obsessing about the "proof" when he was ten years old, and began a lifelong process of proving Fermat's Theorem. While the story is clearly mathematical, it becomes more than that during the course of the story. It becomes a tale about a man who cannot let go of his obsession, and how to creatively find the solutions to complex problems, whether they are mathematical or not. One mathematician in the show talks about making "good mistakes," and how difficult it is. This is the key to learning about mathematics, and solving mathematical problems. You will make mistakes. Learning how to make "good" mistakes is quite difficult. However, if you can learn from your mistakes, or your mistakes lead you in another direction, they are valuable, and can keep you always learning about mathematics, and other complex problems.

Wiles explained his rather unorthodox methods to solve complex mathematical problems. He never uses a computer. Sometimes he makes notes, scribbles, or doodles, and tries to come up with patterns. He might do calculations, and he may look up information in books. He also worked in total isolation, without sharing his thoughts or research with anyone else. These seem like odd ways to solve a complex problem, but as Wiles noted, "And sometimes, you realize that nothing that's ever been done before is any use at all, and you just have to find something completely new. And it's a mystery where it comes from" (NOVA).

NOVA attempted to take a complex problem solving exercise, and share it with a public who, for the most part, probably had absolutely no idea what Wiles and his colleagues were talking about. This is another way of looking at solving complex problems. The show made the problem seem all encompassing (which it was to Wiles), and used a variety of experts to explain just what Wiles was attempting to prove, and why it was so important to the mathematical community. They took a topic which could have been boring and nearly incomprehensible, and made it interesting enough to keep the viewer watching. In fact, NOVA managed to get the viewer behind Wiles, and by the end of the show, when it seemed like he might not prove his theory, it was almost as if I was rooting for him to continue and not give up. To end the program, NOVA said, "Andrew Wiles is probably one of the few people on earth who had the audacity to dream that you could actually go and prove this conjecture" (NOVA). Therefore, this story is as much about dreams and goals as it is about pursuing something complex throughout your life to fruition. Andrew Wiles dared to dream, and in the end, his most complex "proof" may have been that sometimes dreams come true - with hard work, determination, and thinking "outside the box," - or in this case, the theorem.