> It might have been thought, by some scientists in the 1890's, that refined mathematical analysis of this kind would play a role in resolving the fundamental problems of classical physics associated with the apparent failures of the equipartition theorem. But that is not what happened.
> Although the quantum hypothesis did dispose of the paradox of specific heats of polyatomic gases, and eliminated the possibility that ether-vibrations (having an infinite number of degrees of freedom) would drain an indefinite amount of energy out of material systems at any finite temperature, these were not the anomalies that provoked the introduction of the quantum hypothesis in the first place. Max Planck was not one of the physicists who worried about the validity of the equipartition theorem before 1900, and the myth that his distribution law for blackbody radiation was concocted merely to escape from an "ultraviolet catastrophe" predicted by the Rayleigh-Jeans law has now been thoroughly demolished. It was Paul Ehrenfest who invented the ultraviolet catastrophe (eleven years after the publication of Rayleigh's and Planck's papers in 1900) in order to dramatize what would have been the consequences of the equipartition theorem if it had been valid for all classical dynamical systems (though neither Rayleigh nor Planck believed that it was).
I have this saved as a note, but can't find the exact source atm. Here's another source though, from the 60s: