Tuesday, December 09, 2008

Mathematics is hard, even when it's fiction

I finished the novel about the murders in Oxford. The book was fine, but I got somehow disappointed about the mathematics story the author was telling. One of the main characters was a professor of mathematics and he was trying to somehow minimize the consequences of the incompleteness theorem of Godel. So his idea, as the author puts it, was to show that the statements that cannot be proved true or false in an axiomatic system will be somehow not-natural and at another level of detail, so they will be irrelevant for the work of a mathematician. But this is completely wrong and we have a famous and well known example of the Euclid's fifth axiom (parallel postulate). It took mankind almost 2000 years to prove it cannot be proved true or false based on the other axioms of geometry, but has to be considered as an axiom. And for sure the Euclid's axiom is not some obscure statement or at another level of detail, but a very intuitive and "obvious" statement. And in 1963 another not such obscure statement in mathematics, continuum hypothesis, was shown to be impossible to proof or disproof in the context of the standard axiomatic set theory. So Martinez's character was in an impossible quest, but luckily for him and the readers he got involved in a series of crimes just to entertain us :)
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