Why I didn’t sign the Fields medallists’ letter

[This is a guest post by Timothy Gowers, crossposted from his blog. This blog post was initially written in a different file format and converted using AI. — T.] When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem statement, as well as by the accompanying story, and made a fairly serious attempt to prove it. And while, unsurprisingly, I failed, I learned a lot from the attempt. Blissfully ignorant of the fact that the case had been proved by Euler over 200 years earlier, I decided that that would be a good place to start: once I had sorted that out, I was optimistic that I would be ready to tackle the general case. Since I still couldn’t really see where to start, I decided to simplify the problem further and concentrate on successive differences of cubes, with a view to showing that such a difference could not itself be a cube. At the time I did not know how to express what I was doing in algebraic language, so I…