What gives a math book (textbook or otherwise) longevity? Is there more to a book than just a record of current knowledge, or an aid and reference for a class? Some books continue to be read and reread, and used over and over from one generation to another defying loss of novelty and fashion. What makes a math book great? Is it the subject matter, the presentation, the author’s personal touch or something else that keeps a book relevant over generations?
The answers to these questions may be personal. They could be tied up with memories of a favorite spot in the library; the music that was playing as you worked; or the people who were around you. Or perhaps there are universal qualities that make a book great. Style, elegance, care, quirkiness, beauty, originality…what resonates most with you?
One book that continues to be relevant despite the passage of time is Knots and Links by Dale Rolfsen (AMS Chelsea Series), an introduction to knot theory and low-dimensional topology that was first published in 1976 (Publish or Perish press). One reason for its lasting significance is that `Rolfsen’s knot and link table’ is still commonly used to quickly identify knots and links with low crossing numbers. But what really distinguishes the book, especially for its time, is that it facilitates (in a very effective way) active learning by emphasizing well-chosen hand-drawn illustrations and exercises over long explanations and proofs.