Catastrophe!

Let me present for your consideration a rather frightening mass of algebra:\[B_{\lambda}(T) = \frac{2hc^2/\lambda^5}{e^{hc/\lambda kT}-1}\] That's the Planck function, which describes the radiation curve of a perfect blackbody as a function of its temperature--the constants in it are wavelength ($\lambda$), the speed of light ($c$, as always), the Boltzmann constant $k$, and Planck's constant $h$. This equation was the result of centuries of head-scratching on the part of physicists, who had noticed fairly early on that a blackbody would emit light at different temperatures depending on how hot it was. The first real attempts to model this phenomenon led to the Wien Approximation, which accurately described short-wavelength emission, and Rayleigh-Jeans Law, which accurately described long-wavelength emission. However, under a contemporary understanding of physics, Rayleigh-Jeans also implied that a blackbody contained an infinite amount of energy due to the presence of an infinite number of infinitesimally short wavelengths. Scientists don't always name things particularly creatively...

Credit: The inimitable Bill Watterson

... but they managed to come up with a pretty dramatic-sounding one for the implications of the Rayleigh-Jeans law at shorter wavelengths: the ultraviolet catastrophe. This inconsistency between mathematics and observations remained until 1900, when Max Planck came along with a critical realization: there weren't actually infinite possible standing waves that could exist within a blackbody; rather, the only possibilities were integral multiples of a minimum possible wave energy, or quantum--this shows up as the $hc/\lambda$ in the Planck Function. As a result, the model no longer predicted energy going to infinity at short wavelengths, and the Wien Approximation and Rayleigh-Jeans Law had been tied together rather prettily in an extremely accurate model.

Planck's Function predicts the colored radiation curves, while Rayleigh-Jeans predicts the black curve. (Source)