This paper explores the set theoretic assumptions used in the current published proof of Fermat's Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.

The creation of algebraic topology required “all the energy and the temperament of Emmy Noether” according to topologists Paul Alexandroff and Heinz Hopf. Alexandroff stressed Noether's radical pro-Russian politics, which her colleagues found in “poor taste”; yet he found “a bright trait of character.” She joined the Independent Social Democrats in 1919. They were tiny in Göttingen until that year when their vote soared as they called for a dictatorship of the proletariat. The Minister of the Army and many Göttingen (...) students called them Bolshevist terrorists. Noether's colleague Richard Courant criticized USPD radicalism. Her colleague Hermann Weyl downplayed her radicalism and that view remains influential but the evidence favors Alexandroff. Weyl was ambivalent in parallel ways about her mathematics and her politics. He deeply admired her yet he found her abstractness and her politics excessive and even dangerous. (shrink)