Chapter 3: The World of Simple Programs

Section 12: How the Discoveries in This Chapter Were Made

The relevance of theorems

Following traditional mathematical thinking, one might imagine that the best way to be certain about what could possibly happen in some particular system would be to prove a theorem about it. But in my experience, proofs tend to be subject to many of the same kinds of problems as computer experiments: it is easy to end up making implicit assumptions that can be violated by circumstances one cannot foresee. And indeed, by now I have come to trust the correctness of conclusions based on simple systematic computer experiments much more than I trust all but the simplest proofs.

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