What does it mean for a wave to quantize? That is not something I (as a mathematician) are familiar with. It feels like something that bears a lot of explanatio

What does it mean for a wave to quantize? That is not something I (as a mathematician) are familiar with. It feels like something that bears a lot of explanation. I would hazard a guess that the explanation makes it decently reasonable to call this process 'a particle'. Certainly, to me it feels like saying 'it is just a wave' doesn't describe it because this quantization is a special thing.