Are there limits to what we can discover about our physical universe? Are some regions of the future beyond the predictive powers of science and mathematics? Is time before the big bang a no-go arena? Are there ideas so complex that they are beyond the conception of our finite human brains? Can brains even investigate themselves or does the analysis enter an infinite loop from which it is impossible to rescue itself? The Simonyi Professor for the Public Understanding of Science asks: Are there true statements that can never be proved true?