Proof
A proof of the level 1 and small weight cases of the conjecture was obtained during 2004 by Chandrashekhar Khare and Jean-Pierre Wintenberger, and by Luis Dieulefait, independently.
In 2005, Chandrashekhar Khare obtained a proof of the level 1 case of Serre conjecture, and in 2008 a proof of the full conjecture in collaboration with Jean-Pierre Wintenberger.
Read more about this topic: Serre's Modularity Conjecture
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