Thu, 23 Aug 2012

Correctness in Computer Programs and Mathematical Proofs


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While reading On Proof and Progress in Mathematics by Fields Medal winner Bill Thurston (recently deceased I was sorry to hear), I came across this gem:

The standard of correctness and completeness necessary to get a computer program to work at all is a couple of orders of magnitude higher than the mathematical community’s standard of valid proofs. Nonetheless, large computer programs, even when they have been very carefully written and very carefully tested, always seem to have bugs.

I noticed that mathematicians are often sloppy about the scope of their symbols. Sometimes they use the same symbol for two different meanings, and you have to guess from context which on is meant.

This kind of sloppiness generally doesn't have an impact on the validity of the ideas that are communicated, as long as it's still understandable to the reader.

I guess on reason is that most mathematical publications still stick to one-letter symbol names, and there aren't that many letters in the alphabets that are generally accepted for usage (Latin, Greek, a few letters from Hebrew). And in the programming world we snort derisively at FORTRAN 77 that limited variable names to a length of 6 characters.

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