Newton’s book Opticks is probably the first piece of literature to propose that light is not continuous. And this (closely) is his argument in the very second page of the book:
In the same place you may stop light which comes one moment, and let pass that which comes presently after; and in the same time you may stop it in any one place, and let it pass in any other. For that part of Light which is stopped cannot be the same with that which is let pass. The least Light or part of Light, which may be stopped alone without the rest of the Light, or propagated alone, or do or suffer any thing alone, which the rest of the Light doth not or suffers not, I call a Ray of Light.
It is amazing how he incorporated discreteness in both space and time right there. This not just convinced me, but blew my mind!
Stay tuned to find more interesting things from the book.