Why is light not a form of matter?

It doesn't have mass or take up space.

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Light is energy, and energy is matter, according to Einstein. Besides, it has been proved that light is affected by Gravity and, in order to do that, it has to have mass. Look again at Einstein and others, such as Lorentz... The photon has no mass, or does it? True, it seems to have no mass, but that is at rest state. Multiply that by infinity to account for mass increase and time dilation due to traveling at the speed of light, and what do you get? Something that looks like a particle, having mass, traveling at the speed of light.