There’s a huge difference between math and physics. Many things are possible in mathematics that are impossible physically. Some examples:
Infinity, math functions can pass from negative infinity to negative infinity in zero time; physically, you cannot even reach either end, much less move from one end to the other instantly.
Singularity, a singularity can have mass at zero volume.
A circle whose diameter asymptotically approaches zero has finite volume and infinite surface area; you can fill it with paint but you can’t paint it even though the wall thickness is zero.
That said, scientists have produced an experiment that can be analyzed using quantum mathematics and also wave mathematics. That doesn’t prove that it is either or both physical embodiments or neither.
Had a course in which the (take home) final posed a problem with no solution. The correct answer was to prove it.