firstname.lastname@example.org wrote in message news:<email@example.com>...
> But the fault lies not with Wiles or other "establishment mathematicians," > since they haven't claimed that elliptic curves and modular forms are the > same thing.
> That's all correct, except that the part about "4 descriptors between > them" is not precise. The "4 descriptors" are properties of *Galois > representations*, not of elliptic curves or modular forms per se. To > an elliptic curve one can associate a Galois representation, and to a > modular form one can associate a Galois representation. Then we can > talk about comparing Galois representations to each other. One does > not directly identify an elliptic curve with a modular form anywhere.
> I don't follow you here. If I want to prove that every integer is > an algebraic integer, how do I do this without mentioning algebraic > integers?