Langlands used the base change lifting to prove the tetrahedral case, and Jerrold Tunnell extended his work to cover the octahedral case; Andrew Wiles used these cases in his proof of the Taniyama–Shimura conjecture.
Langlands använde basbyteslyftet till att bevisa det tetrahedrala fallet, och Jerrold Tunnell utvidgade hans arbete till det oktahedrala fallet; Andrew Wiles använde dessa resultat i hans bevis av Taniyama–Shimuras sats.