In proof theory, Harvey Friedman' grand conjecture implies that many mathematical theorems, such as Fermat's last theorem, can be proved in very weak systems.
His original statement of the conejcture was posted on the FOM mailing list in 1999 April 16.
References
Avigad, Jeremy (2003), "Number theory and elementary arithmetic", Philosophia Mathematica. Philosophy of Mathematics, its Learning, and its Application. Series III, 11 (3): 257–284, doi:10.1093/philmat/11.3.257, ISSN 0031-8019, MR 2006194