Proving Fermat's Last Theorem

The process of discovery isn't what most think it is.

For most, discovery is the result of steady, dedicated progress with a singular focus, punctuated by a “Eureka moment“, after which accolades come flooding in after a discovery is shared with the world.

In the real world, that experience is about as far from reality as you can get.

In reality, discovery is a process where irregular efforts made over a long period of time, involving lots of trial and error and ventures down multiple blind alleys that prove to be dead ends, but which ultimately leads to a sudden flash of insight that stands apart from all the failed paths that came before, and then a ton of work to verify the discovery, followed by the presentation of it to others who are qualified to evaluate it to determine its validity before a modest amount of praise is directed toward the discoverer. Assuming the evaluators don't shoot their discovery down and send the discoverer back to the drawing board to start the process all over again instead.

At least, that's the story of how Fermat's Last Theorem was proven after 350 years, except after the discoverer was sent back to the drawing board to start over after a false start, they succeeded! BBC Horizon's documentary tells the story of Andrew Wiles in a 41 minute documentary that is time well spent.

Last week, we featured an introduction to what might be found at the intersection of number theory and algebraic geometry, so we thought we'd follow up with what is perhaps the most remarkable thing to have been achieved with those tools this week!