Chapter 3: The World of Simple Programs

Section 12: How the Discoveries in This Chapter Were Made

Attitudes of mathematicians

Mathematicians often seem to feel that computer experimentation is somehow less precise than their standard mathematical methods. It is true that in studying questions related to continuous mathematics, imprecise numerical approximations have often been made when computers are used (see above). But discrete or symbolic computations can be absolutely precise. And in a sense presenting a particular object found by experiment (such as a cellular automaton whose evolution shows some particular property) can be viewed as a constructive existence proof for such an object. In doing mathematics there is often the idea that proofs should explain the result they prove—and one might not think this could be achieved if one just presents an object with certain properties. But being able to look in detail at how such an object works will in many cases provide a much better understanding than a standard abstract mathematical proof. And inevitably it is much easier to find new results by the experimental approach than by the traditional approach based on proofs.

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From Stephen Wolfram: A New Kind of Science [citation]