The math treats the "particles" usually as being nowhere and everywhere. The logic behind the implications of the math is as follows: if we set up an experiment to detect an electron and we do detect it in some location, then we must assume that had we not tried to detect it where we did, it wouldn't have been there. QM works by assuming that "particles" have locations because we tried to observe them, and that if we hadn't tried to observe them there then they would not have been there.
As Einstein pointed out, this is akin to saying that the moon is only there when you look at it. The difference is that while this isn't true of the moon, without it being true in quantum physics we don't have quantum physics.
Thats a huge assumption. I assume, like with the moon, that it would be there without detecting and that if we managed to detect it it is because it was there. With the photon acts as if it is everywhere probably because it is.