Imagine. Close your eyes and imagine a space without limits, or the infinitesimal events that can stir up a country’s revolution. Imagine how the perfect game of chess might start and end: a win for white, or black or a draw? Imagine numbers so vast that they exceed every atom in the universe, counting with eleven or twelve fingers instead of ten, reading a single book in an infinite number of ways. Such imagination belongs to everyone. It even possesses its own science: mathematics. Ricardo Nemirovsky and Francesca Ferrara, who specialise in the study of mathematical cognition, write that, ‘Like literary fiction, mathematical imagination entertains pure possibilities.’ This is the distillation of what I take to be interesting and important about the way in which mathematics informs our imaginative life. Often we are barely aware of it, but the play between numerical concepts saturates the way we experience the world.

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