Stark–Heegner theorem

By replacing d with the discriminant D of Q(√d) this list is often written as:[2] This result was first conjectured by Gauss in Section 303 of his Disquisitiones Arithmeticae (1798).

[6] Stark's 1969 paper (Stark 1969a) also cited the 1895 text by Heinrich Martin Weber and noted that if Weber had "only made the observation that the reducibility of [a certain equation] would lead to a Diophantine equation, the class-number one problem would have been solved 60 years ago".

"[7] Deuring, Siegel, and Chowla all gave slightly variant proofs by modular functions in the immediate years after Stark.

For instance, in 1985, Monsur Kenku gave a proof using the Klein quartic (though again utilizing modular functions).

[9] And again, in 1999, Imin Chen gave another variant proof by modular functions (following Siegel's outline).