My good friend David Cushing popped on Facebook messenger to ask me a question:
I did tweet it, and I got a lot of good responses. Before I tell you about those, I’ll quickly list the books we mentioned above, that of course a keen 13-year-old already has.
I also recommended 50 Mathematical Ideas You Really Need to Know by Tony Crilly. It looks like a bog-standard pop maths compilation, but it’s packed full of really interesting stuff. Blame the publishers for the generic title.
Now, here’s what everyone else recommended.
Math Girls is a novel “combining mathematical rigour with light romance”, and a few people chimed in to agree that it would be a good present. The Number Devil is an illustrated children’s book. The Man Who Counted recounts the adventures of the character Beremiz Samir, who uses his mathematical know-how to settle disputes and win fame and fortune. There’s a nice article about Malba Tahan in the BBC Magazine).
Evelyn Lamb said that she read Douglas R. Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid at around the same age as David’s cousin. While it’s certainly got lots of inspiring maths in it, to do with logic and the mathematical way of thinking, I have to say it’s a hard slog.
Blake Stacey reminded me about Donald Knuth’s book Surreal Numbers, which it turns out we both read in our teens. It’s a book about an area of maths you’re extremely unlikely to need or even encounter in grown-up life, but presented through a most charming, whimsical story. Lots of the books in this post have been recommended by people who credit them with inspiring them to do maths in later life. Surreal Numbers is the book that did that for me.
Blake also recommended The Cartoon Guide to Algebra and The Cartoon Guide to Calculus, both by Larry Gonick, and had another excellent shout: a great way to get into mathematical thinking is to start programming computers.
Tom Edgar said he’s always liked The Book of Numbers by John Conway and Richard Guy. I don’t think I’ve ever read it to cover, but it’s my go-to reference for the names of really big numbers of the nonillion, decillion, … sort.
Marc Chamberland told me about his book, Single Digits: In Praise of Small Numbers, which I hadn’t heard of. It’s a collection of very small, independent sections on all sorts of topics, gathered together in chapters linked to single digits.
Colin Wright recommended Michael Spivak’s Calculus textbook. I haven’t read it, but I’ve heard it mentioned before and in a world full of awful doorstop calculus textbooks, one that’s aimed at giving a good first encounter with “real” maths is to be applauded. And if Colin says it’s good, it must be.
Dave Radcliffe suggests “any book by Martin Gardner”. I’ll pick Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi, Martin Gardner’s first book of mathematical puzzles and games. It’s got more than enough stuff in it to captivate a young mathematician for a good while, and it’s the first in a long series of similarly fascinating books. Dave said he also likes Ingenuity in Mathematics by Ross Honsberger. It’s a collection of 19 essays about different aspects of mathematical thinking.
Hanneli Tavante offered The Manga Guide to Calculus by Hiroyuki Kojima and Shin Togami. “Comics inside!” declares the cover – that would’ve appealed to a 14-year-old me.
Sue van Hattum popped in again to add a recommendation for The Cat in Numberland by Ivan Ekeland, a picture book about a cat. It looks a bit young for our target teenager. Sue also sent me a link to her list of mathematical books on her blog.
Steve wrote in very late on to suggest The Emperor’s New Mind by Roger Penrose, and Cakes, Custard and Category Theory by Eugenia Cheng. That reminds me that I was given Jim Henle’s The Proof and the Pudding recently. It’s a very good book!
So we got loads of book recommendations. David’s original question was about books that actually teach real maths, which not all of the books above do. Of the ones I know well enough to recommend, I think Hofstadter’s Gödel, Escher, Bach, Knuth’s Surreal Numbers, Conway and Guy’s The Book of Numbers and Gardner’s Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi are our best bets. I’m going to add quite a few of the others to my wish list, though!