- Mordell's conjecture was solved by Falting. It is now called Faltings' Theorem.
- Vazsonyi's conjecture was solved by Joseph Kruskal. It is now called The Kruskal Tree Theorem.
- Baudet's conjecture was solved by van der Waerden. It is now called van der Waerden's theorem . Even though van der Waerden's original paper has as its title (roughly translated) On a conjecture of Baudet, Baudet is not well known.
- Fermat's last theorem was solved by Wiles. If you type Wiles into Wikipedia you get as options Wiles Theorem which goes to a page whose web address is http://en.wikipedia.org/wiki/Wiles_theorem but whose title on the page is Fermat's Last Theorem. This one may still be in transition from being someones conjecture to someones theorem. It may be for a while. This one is so tied to Fermat that it might always have his name on it somehow.
Van der Waerden's TheoremSoifer calls
The Baudet-Schur-Van der Waerden Theorem.(Baudet is known to have conjectured it. Soifer argues convincingly that Schur also conjectured it.) Reading over van der Waerden's own account of how the theorem was discovered (included in Soifer's book) it seems to me that Artin contributed some to the solution of Baudet's conjecture. If standards for co-authorship were weaker then he may have been a co-author. In this alternative universe what I would call
The Artin-Van der Waerden TheoremSoifer would call
The Artin-Baudet-Schur-Van der Waerden Theorem.This is odd since you have prover-conjecturer-conjecturer-prover in the ordering. Perhaps another convention would arise. Perhaps it would be called the ABSV-theorem or ABSW-theorem. Perhaps we are better off, just for the sake of simplicity, using just the prover's name. There have been some fierce battles over who PROVED what. Do we really want to have fierce battles over who CONJECTURED what? I conjecture that we do not.