I would like to know what is to quantize some thing, I mean I would like to have some elementary examples, some soft non technical definition, some explanation abuot what do the mathematicians quantize?, does it has sense to quantize a function?, a set?, a theorem?, a definition?, a theory? I supose it has sense to quantize a theory because there is something called Quantum Field Theory, But I have no real idea.

I would like to know what quantization is, I mean I would like to have some elementary examples, some soft nontechnical definition, some explanation about what do mathematicians quantize?, can we quantize a function?, a set?, a theorem?, a definition?, a theory?