What is a particle, what is a wave? QM entities are neither. They are a 3rd thing. A quantised wave is the term my university professor used as a short hand. The nature of that wave is described by the Schroeder equation + its constraints. Certain interactions will bound it heavily, and so make it look particle like, others emphasise the wavelike properties.

You require the maths to actually do anything useful with it, but not to get the basic concepts. It’s no different to the rest of physics, in that. E.g. you can understand the concepts of orbital mechanics, without being able to calculate them.