You are here

Mathematical Writing

Buy Now:

Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts
Mathematical Association of America
Publication Date: 
Number of Pages: 
MAA Notes
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Allen Stenger
, on

This book, based on a course given by Knuth at Stanford in the Autumn 1987 quarter, does spend a lot of time on traditional writing subjects such as word choice and punctuation, but the most interesting and probably most useful parts are about publishing. Knuth brought in guest lecturers about once a week; most of these were noted scientists, but he also recruited two professional editors to talk about the work that goes on at a publisher. Knuth’s coauthors Larrabee and Roberts were the teaching assistants for the course; they produced a series of notes handed out during the course that were then collected into this book.

Jeff Ullman gave a guest lecture, nominally on the subject “How to get rich by writing books,” but really about the process and especially the economics of publishing textbooks. He says that people stop buying a book after it’s been out about five years, so it’s important to keep issuing revised editions of your books. This is nearly as much work as writing a new book, but you can save a lot of effort if you can re-use your examples (he also says that he never saw a book with too many examples). He revealed that the best way to get rich quick in the textbook business is to specialize in some up-and-coming field where there is a lot of interest in textbooks but few experts to write them. The financial arrangement with publishers are very flexible, and if you can convince the publisher that your book will sell lots of copies, you can negotiate a much higher royalty rate on each copy.

The book has several pages about refereeing: why it is important, how to do it, and the difficulties of getting your paper adequately refereed, especially if you are a famous scientist. Knuth once resorted to submitting a paper under a pseudonym to ensure that it would be checked critically. He recommends sending your papers, not to the most prestigious journals, but to the ones with the best referees.

Knuth took several lectures to recount the “Scientific American Saga,” in which he revealed that many of the difficulties in writing about a technical subject for a general audience lie with the publishers rather than the readers. Many non-mathematical publishers have peculiar house styles that are intended to make their publications easier to read but often work against the accuracy and understandability of mathematical articles. Knuth and the editors of Scientific American fought to a draw over his article on algorithms. Each side got part of what they wanted, but Knuth admitted that he was “pretty happy” with the final article, and said it continued to sell thousands of reprints and was the only article of his to be translated into Farsi.

Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.

1. Minicourse on technical writing

2. An exercise on technical writing

3. An answer to the exercise

4. Comments on student answers (1)

5. Comments on student answers (2)

6. Preparing books for publication (1)

7. Preparing books for publication (2)

S. Preparing books for publication (3)

9. Handy reference books

10. Presenting algorithms

11. Literate Programming (1)

12. Literate Programming (2)

13. User manuals

14. Galley proofs

15. Refereeing (1)

16. Refereeing (2)

17. Hints for Referees

18. Illustrations (1)

19. Illustrations (2)

20. Homework: Subscripts and superscripts

21. Homework: Solutions

22. Quotations

23. Scientific American Saga (1)

24. Scientific American Saga (2)

25. Examples of good style

26. Mary-Claire van Leunen on 'hopefully'

27. Herb Wilf on Mathematical Writing

28. Wilf's first extreme

29. Wilf's other extreme

30. Jeff Ullman on Getting Rich

31. Leslie Lamport on Writing Papers

32. Lamport's handout on unnecessary prose

33. Lamport's handout on styles of proof

34. Nils Nilsson on Art and Writing

35. Mary-Claire van Leunen on Calisthenics (1)

36. Mary-Claire's handout on Composition Exercises

37. Comments on student work

38. Mary-Claire van Leunen on Which vs. That

39. Mary-Claire van Leunen on Calisthenics (2)

40. Computer aids to writing

41. Rosalie Stemer on Copy Editing

42. Paul Halmos on Mathematical Writing

43. Final truths