This page contains a few of the books on my bookshelf. Common for them all is that they relate to mathematics and/or computer science and that I recommend them. I plan to gradually expand this page as I get around to writing a few words on some of the great books that are placed on the shelf. And of course, whenever I have finished reading a book that I can recommend, I will make a note of it here—perhaps together with a more thorough review.
I am currently reading God Created the Integers
You can find links to other people’s book recommendations among my bookmarks.
Derbyshire: Prime Obsession
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics is a book about the Riemann Hypothesis, posed by Bernhard Riemann in 1859. As the book title says, it is one of the greatest unsettled mathematical conjectures remaining today. It is among David Hilbert‘s list of twenty-three mathematical problems and one of the seven millennium problems presented by the Clay Mathematics Institute. It could be called a popular math book, meaning that it is a narrative and the math is not too advanced. While describing the history and mathematics of the Riemann Hypothesis, the author manages to make to story interesting from beginning to end. The break-throughs, the set-backs, the key persons, the seemingly random events that suddenly made this unsolved problem interesting again. You can read a more detailed review.
Körner: The Pleasures of Counting
The Pleasures of Counting is a book about people working with mathematics and challenges they have faced. It addresses history, short biographies, mathematical theories, physics, biology, to name some. Apart from many applications of mathematics, most chapters contain a lot of background information including politics, historical events, relations between the individual characters, and so on. At least half of the book, I would say, is this kind of background information. It was included, I think, to not only focus on applications of mathematics, but also to present the persons behind the mathematics in a historical, cultural and political context. You can read a more detailed review.
Conway & Guy: The Book of Numbers
The Book of Numbers is a wonderful book about, well, numbers. And lots of them. From ancient ways of writing numbers to Gaussian integers to surreal numbers. With a vast amount of topics and only 300 pages, no topic is treated in depth, some taking up only half a page. But many of the facts stated or questions raised in this book are nontrivial. I found myself repeatedly staring blankly into the air, wondering about some result or comment from the book—or simply thinking that I had to find some more information on this subject. And that is, in my opinion, a great quality for a math book. You can read a more detailed review.
Nelson: Proofs Without Words
Proofs Without Words and Proofs Without Words II are filled with visualizations of theorems from geometry, algebra, trigonometry, inequalities, sequences, series, and others. One page is typically dedicated to each visualization and each book contains around 130 pages. You don’t read these books from start to end, but flick through them and find interesting, odd, elegant, strange, and wonderful visualizations. People may be sceptical about so-called visual proofs, but I think they have a place in (recreational) mathematics, if only for inspiration. This site has several articles related to visualizations, most of whose figures can also be found in these books.
