Feynman asked the simple question – if you cannot add probabilities – like in the classical case, what CAN you add to get a complete picture?

It was obviously going to be the wave function amplitude. Amplitudes take the place of probabilities, in Quantum Mechanics. This single mathematical fact is responsible for ALL the weirdness that comes about (interference, entanglement…).

Feynman proceeded – if amplitudes are to be added, how about adding ALL the amplitudes for a particle to get from A (emitter) to B (screen)? This seemed like a ridiculously infinite sum, but Feynman proceeded undaunted. And sure enough, several amplitudes canceled themselves out  – leading to the now famous Feynman Integral approach to Quantum Mechanics.