How Important are Computers in Mathematics?

Posted on March 21, 2008
Filed Under Math, Programming, Quote |

“The use of a program to prove the 4-color theorem will not change mathematics - it merely demonstrates that the theorem, a challenge for a century, is probably not important to mathematics.”~ From “Epigrams in Programming” by Alan J. Perlis

It’s hard to agree or disagree with this quote.

On one hand, results in mathematics often end up in strange places. For example, Fermat’s Little Theorem was little more than a curiosity for centuries. Its generalization is the basis of the RSA system, and it can be used in a pseudoprime generator. In fact, PGP uses it for just that very purpose.

The mere fact that a computer makes the result reachable not only means that other proofs can use the 4-color theorem, it means that computers can be used to prove other theorems. Many proofs are broken down into cases. This one just happens to have a lot of them that couldn’t be checked by hand. The computer helps advance mathematical results as well as humanity.

On the other hand, brute force isn’t a novel technique, so the process of getting the result is itself unimportant. The computer did what 1000 mathematicians with infinite cups of coffee could have done.

If you happen to know where I can witness 1000 mathematicians with infinite cups of coffee, please let me know.

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