Who first proposed the idea of quanta?

Answer 1

Steve is right.

More details if you're interested: Max Planck came up with

E = h nu

to explain how the colour of hot bodies varies with temperature, and in particular why they give out so little energy in the far UV. Einstein realised that if light was emitted in quanta, it must be absorbed in quanta, and used this to explain the photoelectric effect.

Answer 2

Max Planck, although he hated the idea. Einstein had to convince him that he was correct!