I’ve yet to encounter a maths book with the winning charm of Alex Bellos’s Alex’s Adventures in Numberland (UK) (Here’s Looking At Euclid in the US). Strongly recommended journey through mathematical ideas, both whimsical and essential.
A more unusual pick: Apostolos Doxiadis offers us the rather brilliant mathematical novel Uncle Petros and Goldbach’s Conjecture (UK) (US) which works very well as a novel of obsession and secrecy, but will teach you a bit of maths as a side effect. Doxiadis also wrote the ambitious and excellent Logicomix (UK) (US) – a history of logic in comic form.
Vicky Neale’s Closing the Gap (UK) (US) is an excellent account of recent progress in prime numbers, but also one of the best accounts you’ll read by a mathematician about how mathematics research is done and how it feels to do it.
And recently arrived on my pile, David Acheson’s The Calculus Story (UK) (US) which is a very clear explanation of calculus (wish I’d had it as a maths student!) along with some history of the subject.
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