A mathematician is a machine for turning coffee into theorems. This was a line often invoked by the Hungarian mathematician Paul Erdős, who was fuelled by coffee and amphetamines, slept little, travelled near-constantly, never married or had children, and published almost fifteen hundred papers in his lifetime, in collaboration with hundreds of other mathematicians. But Erdős was, in most ways, not machinelike. He called lecturing in mathematics “preaching,” woke friends at odd hours by asking, ...