The pace of scientific discovery in the last few decades has been extraordinary. We’ve discovered new particles; seen habitable planets orbiting distant stars; detected gravitational waves; mapped the complete neuronal network of a C Elegans worm; and built new forms of carbon called graphene. In 2014 the science journal Nature reported that the number of scientific papers published has been doubling every 9 years since the end of World War Two.  So is there anything science cannot answer? Or could we possibly know it all?

Identifying the known unknowns was the task I set myself on the journey I’ve been on for the last three years writing my new book What We Cannot Know. Not just things we don’t know now. I wanted to identify whether there are any problems that are intrinsically unanswerable. One of the motivations for my journey comes from a proof that my own subject of mathematics has provable limits.

Called Gödel’s Incompleteness Theorem, the discovery made by Austrian logician Kurt Gödel in the 1930s rocked the mathematical community to its core. Ever since the ancient Greeks introduced the powerful tool of mathematical proof, mathematicians believed that, given any true statement about numbers, mathematicians should be able to produce a proof from the axioms of mathematics of the truth of that statement.