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.