In 2006 the Fields Medal — one of the highest honours in mathematics — was awarded to Grigory Perelman for solving the Poincaré conjecture, a famously difficult problem that had stumped mathematicians for a century. To the surprise of many, and the excitement of the media, Perelman declined the award and withdrew not only from mathematics but from the world generally. In *Perfect rigour* Masha Gessen sheds some light on this brilliant and perplexing character and the reasons why he would renounce both the worldly rewards of his mathematical achievement and also his beloved vocation, mathematics itself.