Mathematical Writing

Mathematical Writing presents the content and wisdom from Donald Knuth's 1987 course at Stanford University on writing about mathematics. The book compiles lectures, assignments, and discussions from this course, capturing both theoretical principles and practical advice. The text covers core topics like mathematical notation, proof writing, exposition structure, and the relationship between formal and informal language. Students' writing samples and class exercises demonstrate the concepts in action. Knuth draws from his experience as both an author and computer scientist to address the specific challenges of conveying mathematical ideas with clarity and precision. The book includes contributions from other mathematicians and technical writers who participated as guest speakers. This work serves as a manual for mathematical communication while raising broader questions about the intersection of logic, language, and human understanding. The principles extend beyond mathematics to technical and scientific writing in general.

Readers appreciate the practical advice and exercises for improving mathematical writing. Many note that the book helps bridge the gap between informal mathematical thinking and formal written presentation. Likes: - Clear examples of good vs poor mathematical writing - Tips for structuring proofs and explanations - Guidance on notation and formatting - Collection of writing exercises with solutions Dislikes: - Some find the dialogic format distracting - Content can feel dated (pre-LaTeX era) - Coverage of some topics is brief - Focus mainly on academic paper writing vs other math writing forms Ratings: Goodreads: 4.2/5 (42 ratings) Amazon: 4.5/5 (12 ratings) "The examples of revising mathematical text were illuminating" - Goodreads reviewer "Helped me understand how to present complex ideas clearly" - Amazon review "Format is hard to follow at times, but advice is solid" - Mathematics Stack Exchange user

Style: Lessons in Clarity and Grace by Joseph M. Williams This guide presents principles for writing complex ideas with precision and clarity through detailed examples and practical techniques.

A Manual for Writers of Research Papers, Theses, and Dissertations by Kate L. Turabian This reference work provides frameworks for organizing mathematical and scientific research writing, with specific attention to structure and citation methods.

How to Write Mathematics by Norman E. Steenrod, Paul R. Halmos, Menahem M. Schiffer, and Jean A. Dieudonné The text outlines methods for conveying mathematical concepts through written expression, focusing on proof structure and notation.

Science Research Writing for Non-Native Speakers of English by Hilary Glasman-Deal This guide breaks down the components of technical writing into systematic patterns and structures that support mathematical and scientific communication.

Writing Science by Joshua Schimel The book presents a structured approach to writing scientific papers and proposals, with emphasis on story structure and clear presentation of technical content.

📚 The book originated from a course taught jointly by Donald Knuth, Tracy Larrabee, and Paul Roberts at Stanford University in 1987. 🖋️ Knuth offers to pay a reward ($2.56) to the first person who finds each technical, typographical, or historical error in his books - this policy applies to Mathematical Writing as well. 📖 The book includes actual homework assignments and solutions from the original Stanford course, giving readers practical exercises in improving their mathematical writing. 🎓 Donald Knuth is also famous for creating TeX, a computer typesetting system widely used for mathematical and technical writing, which he developed to improve the quality of mathematical publications. 💡 The book emphasizes that good mathematical writing should be "alive" - suggesting authors should write as if speaking to someone, rather than just documenting formal proofs.