I read somewhere that Einstein found out in 1905 that as an object approached the speed of light (c), the object's mass would increase. He also found out that as the object goes faster and approaches "c", it also gets heavier. In fact, at "c" itself, an object's mass and energy should both be infinite. Now my questions are: a) How come photons (quantized energy particles of light) can travel the speed of light and yet have no mass? Doesn't that somehow violate what Einstein said in 1905? b) If photons carry energy, which I am sure they do, shouldn't they have mass considering E= MC2? c) I read somewhere that in math equations relating to physics, when you get an answer that comes up "undefined" or that approaches an "infinity" vale, you are usually wrong somewhere and have to go back and either add some more missing variables or re-calculate the equation. Shouldn't the fact that Einstein got a value approaching "infinity" when trying to calculate and object's mass and energy at the speed of light be a red flag of some sort?