How To Write Mathematics
by Norman Earl Steenrod, Paul R. Halmos, Max M. Schiffer, Jean Alexandre Dieudonné · first published 1973
75% recommend25% neutral
Why HN recommends it
A short, practical essay by a famously clear mathematical expositor on writing papers and talks. It suits graduate students, thesis writers, and anyone who wants clearer mathematical prose, as a first read.
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This is a sensible guide, by Kevin P. Lee, aimed at undergraduates taking math classes. A similar guide, aimed at people writing research papers, is “How to Write Mathematics” by Paul Halmos (1970) [1]. They both start from a similar assumption: Lee: “When you write a paper in a math class, your goal will be to communicate mathematical reasoning and ideas clearly to another…
on “A Guide to Writing Mathematics [pdf]” ↗The article "How to Write Mathematics" http://www.math.uga.edu/~azoff/courses/halmos.pdf by the late Paul Halmos, a mathematician famous for his clarity of writing, suggests procedures for making mathematical papers less painful to read.
on “Why math is painful to read” ↗…authors like Paul Halmos are rightly celebrated as great expositors, e.g. see his books like Naive Set Theory, Finite Dimensional Vector Spaces, Measure Theory etc. and his expository writing such as "How to Write Mathematics" and "How to Talk Mathematics": [PDF] http://www.math.uh.edu/~tomforde/Books/Halmos-How-To-Write.p... http://www.math.northwestern.edu/graduate/Forum/HALMOS.html collected in his Selecta of expository…
on “The pitfalls of jargon and the damage it does to mathematics” ↗For anyone looking for more of Halmos, his book "I want to be a mathematician: an automathography" is worth a look. Also well worth a look is Serre's "How to write mathematics badly": https://www.youtube.com/watch?v=ECQyFzzBHlo
on “How to write Mathematics (1970) [pdf]” ↗…the latter can be slowed down/sped up, you don’t know what you miss by skipping even just a few seconds ahead. You loose this spatial orientation that is a given for texts. EDIT: Mentioning Halmos’s How To Write Mathematics book is probably a good fit here.
on “Why Books Don't Work: Constructivism over Transmissionism” ↗Two resources which helped me improving my writing, when I was writing my thesis were "How to Write Mathematics" by Paul R. Halmos and "Mathematical Writing" by Donald E. Knuth et al. I would always start with Halmos to get into the spirit of perusing clear and precise communication. The "Bad/Better/OK" suggestions…
on “My PhD advisor rewrote himself in bash (2010)” ↗There are lots of good books on writing mathematics: 1. How to Write Mathematics — Paul Halmos 2. Mathematical Writing — Donald Knuth, Tracy Larrabee, and Paul Roberts 3. Handbook of Writing for the Mathematical Sciences — Nicholas J. Higham 4. Writing Mathematics Well — Steven…
on “Weighting an average to minimize variance” ↗Finally, re high-school or undergrad “calculus”, I’m tempted to just quote Halmos (one of the foremost expositors of “higher mathematics”—that is, mathematics—of the 20th century) from his classic “How to write mathematics”[1] ... > [T]here are many books that violate the principle of having something to say by trying to say too many things. Teachers of elementary mathematics in the U.S.A. frequently complain that all…
on “In Praise of Open Source Textbooks” ↗…was pretty relevant to my studies, though left quite a few gaps for the reader to fill in. Meier's Groups, Graphs and Trees is much more accessible and visual. Strongly recommended! Knuth's notes on how to write mathematics well [1] were very influential. Munkres' Topology is a classic, but I think I leaned more on Hatcher's Algebraic Topology towards the end. Drobot's Formal Languages and Automata Theory was a lot of…
on “Ask HN: Which mathematics books taught you the most in your career?” ↗…Better question: why use it, when you can use the real thing? Mathematicians concerned by typography universally use real boldface. For example: Terrence Tao's blog, Donald Knuth, Paul Halmos (author of "how to write mathematics"), and the famous journal "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography. They use real boldface for the number sets N, Z, Q, T, R, C. I've never…
on “The Art of LaTeX: Advice for Typesetting Beautiful, Delightful Proofs” ↗Paul Halmos in How to Write Mathematics says: “A good attitude to the preparation of written mathematical exposition is to pretend that it is spoken. Pretend that you are explaining the subject to a friend on a long walk in the woods, with…
on “Write like you talk” ↗…never heard anyone advocate your position until you did, just now Many mathematicians concerned by typography use real boldface. For example: Terence Tao's blog, Donald Knuth, Paul Halmos (author of "how to write mathematics"), and the famous journal "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography. They use real boldface for the number sets N, Z, Q, T, R, C. I've never…
on “Unicode Character “𝕏” (U+1D54F)” ↗…descriptively rather than honorifically. I recall his argument was that it aids in recall and understanding to name descriptively, and that there are better ways to honor discoverers. I found this statement in "How to Write Mathematics" (https://bookstore.ams.org/hwm): "... surely I cannot stop without a discourse on the proper naming of concepts (why 'commutator' is good and 'set of the first category' is bad) and the proper way to…
on “Mathematicians should stop naming things after each other” ↗