It is often said that in general relativity time does not exist. This is because the Einstein equations generate motion in time that is a symmetry of the theory, not true time evolution. In quantum gravity, the timelessness of general relativity clashes with time in quantum theory and leads to the ``problem of time'' which, in its various forms, is the main obstacle to a successful quantum theory of gravity. I argue that the problem of time is a paradox, stemming from an unstated faulty premise. Our faulty assumption is that space is real. I propose that what does not fundamentally exist is not time but space, geometry and gravity. The quantum theory of gravity will be spaceless, not timeless. If we are willing to throw out space, we can keep time and the trade is worth it.