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I don't know the answer to your question but want to state the a differing point of view in the same vein which is how I understood it as the contrast might be
by harry8 8y ago
I don't know the answer to your question but want to state the a differing point of view in the same vein which is how I understood it as the contrast might be something I learn from.
There can never be practically useless mathematics. Someone will always find a practical use in the physical world for any new mathematics that is developed. The story I heard illustrating this was that in the shadow of WW1 various mathematicians who lived through that horror became (understandably) pacifists (Hardy?) and decided they wanted to make sure their work would never be useful in weaponry and so devoted themselves to the utterly useless number theory. Sadly for them in a world of crypto number theory has a major use and that is military.
- perl4ever 8y agoThis is a layman's view, but I thought Gödel's incompleteness theorem means there must be in principle mathematics that can never be connected to other parts of mathematics. And if something is part of the universe, it must be connected to something we can perceive, so I conclude that not all math can be connected to that which concerns something real. In other words, even though math that was thought to be useless has repeatedly been applied to physics, I think the claim that it is "always" applicable is too strong and in fact proven false in principle.
- entrypoint0 8y agoThis may or may not be helpful: Geometry is decidable per tarski's axioms of elementary geometry. As far as I know physical theories are dominantly geometric. Unfortunately I know little in the topic, so I cannot add anything beyond noting his work.
- joker3 8y agoThat's not what GIT says. See https://plato.stanford.edu/entries/goedel-incompleteness/ https://plato.stanford.edu/entries/goedel-incompleteness/ for a description of what it does say.