> Why not use it? 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 seen a boldface R to mean a set different than the real numbers. Maybe this is some fringe custom in model theory, but in mainstream…
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 especially reminded me of the discussions in the lecture notes from Knuth et al. And at a third step a linter such as the proposed one is probably helpful, if something slips through. I think these resources are essential for anyone who writes on any subject which at least…
I recall Paul Halmos (https://en.wikipedia.org/wiki/Paul_Halmos) once advocated for naming things in mathematics 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 baptize theorems (why 'the closed graph…
I understand the problem. I used to manage an English academic writing program at a university in Japan, and what guidance to give to students about pronoun usage was a frequent topic of discussion among the teachers. One problem was that the students had learned a moderately informal version of English in which first-person pronouns are common. Also, they were young and used to writing and speaking about themselves. That led to what some teachers perceived as excessive use of “I” for the research papers the students were being taught to write. Another issue was that the teachers themselves…
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 person. The writing done in a math class is very similar to the writing done for other classes. You are probably already used to writing papers in other subjects like psychology, history, and literature. You can follow…
Thanks for linking this! I like Halmos‘ clarifications on the editorial “we“. I don’t know if this is because I‘m living in a non English speaking country but at our university students often get told to use ”we” instead of ”I” in their papers. I always found this weird. If you‘re the only author you can‘t just refer to yourself as ”we” — just to avoid the use of ”I”. It sounds wrong — especially if the reader knows that you’re the only author — and eventually leads to absurd constructs such as the example in the essay: ”We thank our wife for her help”.
The article by William P. Thurston (a Fields medalist) called "On Progress and Proof in Mathematics http://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-... (which I learned about from a comment here on HN, thanks) does a good job of demonstrating how a mathematician who makes new discoveries has to invent a new language for describing those discoveries. Then the mathematician has to relentlessly practice communicating those results first to other professional mathematicians, helping them to see the connections between their research and the new research results. Mathematicians who…
Classic: Simon says how to write a paper and give a talk: Overview page: http://research.microsoft.com/en-us/um/people/simonpj/papers... PDF slideshow: http://research.microsoft.com/en-us/um/people/simonpj/papers...
I agree with Constructivism over Transmissionism (though learning being an active process seems trivial, though I am just a laymen in this field), but I have to disagree on the book part. It is not an easy feat, but some author can write a book that target their audience’s previous knowledge so well, that it is a joy to read. I believe many have such a science book as an example. What make books such a timeless tool of learning is that it is “self-pacing”. If a given idea is hard to grasp, I can take my time on it, while easier parts can be quickly skimmed. This is not possible on a lecture…
> I’ve literally 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 seen a boldface R to mean a set different than the real numbers.