Only by introducing a new assumption, that the energy of the radiation does not act continuously, into his mathematics in essence Planck had discovered the quantum structure of electromagnetic radiation.
In 1905 Einstein attempted to resolve the conflict between wave and particle theories by demonstrating that part of Planck's formula can arise only if electromagnetic radiation behaves as if it actually consists of individual "quanta" of energy.
With his light quantum hypothesis Einstein could derive both Planck's formula and also account directly for certain previously perplexing phenomena. Foremost among them was the photoelectric effect: the ejection of electrons from a metal when irradiated by light. The wave theory of light could not yield a suitable account of this, since the energy of a wave is spread over its entire surface. Light quanta, on the other hand, acting like little particles, could easily eject electrons, since the electron absorbs the entire quantum of energy on impact.
Einstein used his statistical mechanics to demonstrate that when light interacts with matter, Planck's entire formula can arise only from the existence of light quanta—not from waves.
Einstein considered that light quanta, together with the equivalence of mass and energy, might result in a reduction of electrodynamics to an atom-based mechanics. But in 1907 he discovered that atoms in matter are also subject to a quantum