Planck's quantization
In December 1900 Max Planck found the formula that finally fit the blackbody curve at every wavelength, and to derive it he had to make an assumption he himself found uncomfortable. He supposed that the little oscillators in the cavity walls could not emit or absorb light energy in any amount whatsoever, but only in whole-number multiples of a basic packet whose size is set by the frequency: E = hf.
This single restriction quietly tames the ultraviolet catastrophe. To excite a high-frequency oscillator you must hand over a large packet of energy all at once, and at ordinary temperatures the thermal jostling rarely musters that much. So the short-wavelength, high-frequency modes are starved of energy and stay quiet, bending the predicted curve back down to zero exactly as nature does. The fit to experiment was perfect.
Planck regarded this at first as a mathematical trick — an 'act of desperation', as he later called it — rather than a claim about how light really behaves. He hoped a more classical explanation would eventually replace it. None did. The idea that energy is exchanged in discrete steps turned out to be deeply true, and Planck's reluctant hypothesis is now counted as the birth of quantum physics.
Energy comes only in whole multiples of hf — and that one rule fits the blackbody curve exactly.
Planck quantized the oscillators in the walls, not light itself. It was Einstein, five years later, who took the bolder step of saying that light energy is genuinely quantized as photons.