Experimental mathematics is sometimes said 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.
It should be pointed out, however, that mathematicians have always done this, and so this is nothing new. Thus experimental mathematics is used in common parlance among mathematians to refer to a special kind of experimentation, using computers to investigate a large number of cases, or perform computations that are difficult to do by hand. It's fair to say that the use of computers in this manner has become more accepted over time by the mathematical community as a worthy endeavour. Indeed, some well-respected journals have begun accepting papers that are largely consisting of experimental mathematics, and there is even a journal devoted entirely to it.
- Experimental Mathematics (journal)
- More links and resources on experimental mathematics