[unlaxedneurotic]

The photon paths bend due to the curvature of space-time caused by gravity. This does not mean that they have non-zero mass. iirc, it has been proved that photons have non-zero _momentum_ but I am not sure about mass.

[cwillu]

As I understand it, the relevant thing for gravity is energy. Mass is a particular form of energy, which photons do not have. It's energy that causes space to bend, but in most cases energy-in-the-form-of-mass completely dominates.