You might think that mathematics is the most trustworthy thing humans have ever come up with. It is the basis of scientific rigour and the bedrock of much of our other knowledge too. And you might be right. But be careful: maths isn’t all it seems. “The trustworthiness of mathematics is limited,” says Penelope Maddy, [Distinguished Professor emerita], a philosopher of mathematics at the University of California, Irvine. Maddy is no conspiracy theorist. All mathematicians know her statement to be true because their subject is built on “axioms” – and try as they might, they can never prove these axioms to be true.

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