Points of energy

My friend and me have reached an impasse. We can’t agree on the nature of whether a photon is a point (he says that). I tend to disagree with this assertion because this means that some energy would need to be stored in a point, which by simplistic math seems impossible to me. But there seems no way that something with size or mass to move at the speed of light while following those laws presented in relativity, the special and general theory. If someone has an answer to this question please tell me because it's been bugging me of late.

 

First of all saying something is contained with no size seems to indicate that it would have infinite density, in addition the simple math I referred to was the property of 0 which states any number times 0 is 0. It also seems that a photon that hits another object needs surface area to interact this that other object and from surface area I derive size.

So I was thinking that this might make the idea of a photon in a point impossible, but that there seems to be some proof for it. In addition I don't see how I can be right either, as a photon, with size, that could moves along a path curved by gravity indicate one side gos faster than the other and therefore at least on the sub-photon level something to exceed the speed of light. We had worked out the math for a spinning photon but realized that this spinning action would cause the photon to gain mass. Making it impossible for it to move at the speed of light.

He means, if I'm not mistaken, that a photon has no size or mass.

oh I am so confused by this.