I know that Standard mathematical axioms yields lots of interesting results, but when it talks of the infinite and we are dealing with a practical subject like cryptography or even physics it should not be taken too seriously. (With respect to uncountable sets.)
Some of the applications of these theories are very relevant. For example, a theorem that proves that it is impossible to write a program that would determine if any other program would stop or loop forever, is very relevant and interesting.
Absolutely, something does not have to be practical to be interesting, Igor`s example of Cantors double slash argument (useful for example in AI research) is something that seems very abstract until we find a use for it, and most abstract mathematical concepts and theorems of this kind do eventually come into use by some other class of scientists. Datacomms Technologies web authoring and data security Paul Bradley, Paul@fatmans.demon.co.uk Paul@crypto.uk.eu.org, Paul@cryptography.uk.eu.org Http://www.cryptography.home.ml.org/ Email for PGP public key, ID: 5BBFAEB1 "Don`t forget to mount a scratch monkey"