The ULTRAVIOLET CATASTROPHE

There's absolutely nothing wrong with the mathematical theory of classical physics. The mistake Rayleigh and Jeans made was to assume a blackbody exists in classical physics. Nothing would emit infinite energy; instead, the energy would just dissipate to higher and higher frequencies, never reaching a steady state. But we do see things in reality that look a lot like blackbodies. The conclusion is that the world is not classic. But the mathematical theory is still perfectly consistent. There is no "ultraviolet catastrophe" because in classical physics blackbodies don't exist.

This is crucial, because Planck seems to have been the only one that started with a finite amount of energy and then thought of how to distribute it through different vibrational modes to get the observed spectrum. Everyone else was starting with the wrong assumption that a blackbody had infinite energy. If you start with a finite amount of energy, it's easy to see that a blackbody can only exist if the energy is somehow quantized.