To add to the Gowers examples: the fundamental theorem on finitely-generated abelian groups. It seems at least a mildly interesting linguistic point. German discriminates between Hauptsatz and Fundamentalsatz, i.e. main theorem and fundamental theorem (if satz is not quite "theorem"). That distinction seems less clear in the English usage. The German Wikipedia admits the Fundamental Theorems of Algebra, Analysis and Arithmetic, but others in pure mathematics aren't obvious. I would myself think of Galois theory (the perfect duality of subfields and subgroups) and projective geometry (collineations semi-coordinatised) as having "fundamental theorems".

To add to the Gowers examples: the fundamental theorem on finitely-generated abelian groups. It seems at least a mildly interesting linguistic point. German discriminates between Hauptsatz and Fundamentalsatz, i.e. main theorem and fundamental theorem (if satz is not quite "theorem"). That distinction seems less clear in the English usage. The German Wikipedia admits the Fundamental Theorems of Algebra, Analysis and Arithmetic, but others in pure mathematics aren't obvious. I would myself think of Galois theory (the perfect duality of subfields and subgroups) and projective geometry (collineations semi-coordinatised) as having "fundamental theorems".