## ABSTRACT

In the late 19th and early 20th centuries, the study of Fermat’s Last Theorem built mainly on Kummer’s methods, with the notion of ideal numbers being supplanted by Dedekind’s theory of ideals in a commutative ring. The techniques required a high degree of mathematical and computational facility, and were applied to more and more special cases. For instance, in 1905 Mirimanoff extended Kummer’s results as far as n ≤ 257. In 1908 Dickson generalized the theories of Germain and Legendre by investigating xn + yn = zn in the case where (n is prime and) none of x, y, z is divisible by n. Fermat’s Last Theorem was proving to have a nasty sting in its tail. Despite the apparently simple statement of the problem, the proofs of special cases were becoming ever more complex, requiring the highly specialized activity of mathematical experts.