Whether or not there is a fundamental difference between those two great streams of mathematics is a source of deep fascination for Prof. Minhyong Kim, the director of the International Centre for Mathematical Sciences in Edinburgh. He is a leader in the field of arithmetic geometry, which seeks to build the familiar world of geometry from deep structures in numbers. He also has a long interest in fundamental physics, and particularly the still unanswered challenge of reconciling quantum theory with Einstein’s general relativity. Could that problem, he asks, be rooted in the question: is the universe algebraic or geometric?