To add, perhaps in a very general hand wavy way "quantisation" is something like replacing a commutative algebra A, with a non commutative algebra A_h. I do not

To add, perhaps in a very general hand wavy way "quantisation" is something like replacing a commutative algebra A, with a non commutative algebra A_h. I do not necessarily think there is something discrete in this process. In physics functions get sent to operators. States get sent to rays. It turns out that a lot of interesting physics these operators have physically interesting discrete spectrum.