Proofs that are partially or entirely checked by computer, including those formalised in interactive theorem provers.
Computer-assisted proofs are usually proofs by exhaustion where the number of cases is too large for humans to check by hand. The first major proof of this kind was of the four-colour theorem in 1976, and others have since followed (e.g. all Rubik's Cube positions can be solved in 20 moves).
Once such a proof is encoded in a proof assistant or interactive theorem prover, it becomes formal. Examples of such provers include Coq and HOL Light, the latter of which was used by Hales as part of the Flyspeck project to prove the Kepler conjecture.
