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Ian Stewart
Letters to a Young Mathematician
It would be a mistake, though, to see this as a book just aimed at giving advice to prospective mathematicians. Indeed, the letters go from Meg encountering mathematical ideas at school to her becoming a tenured professor, so most chapters wouldn't match the situation of any reader. Rather the book is an opportunity for Stewart to talk about his ideas about mathematics. How do mathematicians find the solution to challenging problems  can your subconscious work for you? How should mathematics be taught, and how should teachers respond to the question 'why is a minus time a minus equal to a plus'? Why is so little recognition given to all the uses of mathematics in our society? There are plenty of mathematical ideas in the text, but wery little in the way of equations or mathematical notation (there are notes at the end for those wishing to take a topic further). All of this is mixed in with stories of the life of a mathematician. I'd certainly recommend the book to anyone who wants to find out what it is that mathematicians actually do.