I have a question that seems natural in Physics and Mathematics mainly in Statistical Mechanics of Equilibrium.
Results that are proven by formal mathematical methods that were already seem intuitive results and experimentally verified when proofs by mathematically rigorous methods were obtained.
In many fields of science, most notably physics, there are many historical examples that refute this view.
An example of this type that I know is the General Theory of Relativity and GPS (the original English acronym for Global Positioning System). It is possible that one may disagree. Without explaining in detail the formulas of contraction / dilation of spacetime which is obtained formally Theory of Relativity are used to "sync" properly watch each of the GPS satellites with the clocks of a point on Earth. For more see here and here.
However, I can not get an explicit example in Statistical Mechanics. That is, would an example of resutado first obtained by formal mathematical methods and was discovered by experimental means later.
Question: There is a exemple of same result in Statistical Mechanics that was first discovered by "theoretical mathematical methods" and only later confirmed experimentally ?
Question: Some example explicit or reference for the Ising model?