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Paolo Zellini’s A Brief History of Infinity (Penguin, £8.99) is more than a grouping of who thought what about infinity. It also lures you into thinking, an infinitely pleasant pursuit. Keith Devlin positively encourages new thoughts with The Millennium Problems (Granta, £9.99). These seven unsolved maths problems could win you a million apiece, he points out – apart, of course, from the intellectual triumph.