Experimental mathematics
Experimental mathematics can have two meanings:
Some people define it as a new field in mathematics which uses computers to carry out calculations which are too involved or lengthy for human calculation.
The proof of the four-color theorem was one of the first major results of experimental mathematics in this sense.
Some others define "experimental mathematics" to mean the application of the experimental part of the scientific method to mathematics, where mathematicians develop hypotheses before attempting proofs, and then see if their calculations are consistent or inconconsistent with their hypotheses. An inconsistency effectively disproves an hypothesis, by providing a counterexample; consistency suggests that it is worthwhile to attempt to prove the hypothesis rigorously.
