In some experiments the weird mathematical thing can be approximated as an almost classical particle. That approximation simplifies the calculation a lot, and sometime you can get some result intuitively. But it is never true, it is only a very good approximation.
In some experiments the weird mathematical thing can be approximated as an almost classical wave. That approximation simplifies the calculation a lot, and sometime you can get some result intuitively. But it is never true, it is only a very good approximation.
Try to read again everything you have read about the subject, but every time the text says "here light is a wave/particle" use a red marker to rewrite that sentence as "here light can be approximated as a wave/particle".
Basically: particle are the quanta of waves. So it's not really a duality in the end.