Experimental mathematics
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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 inconsistent 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.
Although chaos theory and fractals led to an increased emphasis on experimental mathematics beginning around the 1970s, following the work of Edward Lorenz and Benoît Mandelbrot, mathematicians have always done this, and so this is nothing new. Thus experimental mathematics is used in common parlance among mathematicians 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 is fair to say that the use of computers in this manner (not to be confused with automated theorem proving) 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.
[edit] See also
[edit] External links
- Experimental Mathematics (Journal)
- Experimental Mathematics: A Discussion
- Psychology of Experimental Mathematics
- Experimental Mathematics Website (Links and resources)
- An Algorithm for the Ages: PSLQ, A Better Way to Find Integer Relations
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