I have always been fascinated by how well conclusions drawn from mathematical models could fit reality, so I wondered if there are any counter examples.
In "Gödel, Escher, Bach" I could already find some pathological examples where axiomatic models seem to fit something like addition, but its implications do not fit anymore–however, I would like to know if there are any (historical) real world examples of something like this.
Wall of text for clarification: I would be very grateful if answers could be split up into the two categories "assumptions were not correct" (e.g. pre-relativistic physical models when gravity was thought to be exerted instantly over any arbitrary distance or economic models that did not take Newcomblike-problems into account) and "the mathematical models fit observed reality, however their implications do not anymore" (or the ones that cannot be made correct by adjusting assumptions). Latter might seem impossible as we are talking about implications, but equivalence or implications are only defined within our "arbitrary" axiomatic system. So while you may argue that our models are defined in order to reflect reality (e.g. our concept of natural numbers), they can only do so marginally as even the existence of their majority (e.g. irrational (Pythagoreans), negative and imaginary (pretty much every mathematician at the time) numbers) has been disputed to a great extent. So I came to the conclusion that it is a nice "coincidence" that these models, relying on so many little helpers, really seem to be equivalent to observed reality.