From an article by Edward Frenkel in today’s New York Times:
Many mathematicians, when pressed, admit to being Platonists. The great logician Kurt Gödel argued that mathematical concepts and ideas “form an objective reality of their own, which we cannot create or change, but only perceive and describe”. But if this is true, how do humans manage to access this hidden reality?
We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.
This hypothesis is by no means new; in Are you living in a computer simulation, Nick Bostrum argues that one of the following propositions is true:
- the human species is very likely to go extinct before reaching a “posthuman” stage;
- any posthuman civilisation is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
- we are almost certainly living in a computer simulation.
Also see: Constraints on the Universe as a Numerical Simulation.
Digital, Data & Policy 
Hmmmmm: Physicists find we’re not living in a computer simulation.