I am thinking about writing a paper: "How (not) to write a mathematical paper." I want to share my thoughts and experience about good and bad habits, and common mistakes. While it will be a subjective point of view and some of the readers may not agree with my ideas, I think it still could be a useful source. My question is where can I publish such a paper? Is there any journal that would publish such work?
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asked Dec 15, 2023 at 16:25
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6$\begingroup$ I know that the Notices of the AMS has advice columns of various sorts. But this is just a guess. $\endgroup$– Donu ArapuraCommented Dec 15, 2023 at 16:44
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4$\begingroup$ There's, by the way, a talk by J-P. Serre in Harvard around 2010 "How to write mathematics badly" youtube.com/watch?v=ECQyFzzBHlo&ab_channel=ChristophPegel $\endgroup$– YCorCommented Dec 15, 2023 at 16:57
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2$\begingroup$ How to Write Mathematics by P. Halmos appeared in [L’Enseignement mathématique 16 (1970), 123-152]. What about submitting your work to the journal? $\endgroup$– Salvo TringaliCommented Dec 15, 2023 at 17:11
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5$\begingroup$ Possibly even more appropriate than Notices of the AMS is The Mathematical Intelligencer. $\endgroup$– Dave L RenfroCommented Dec 16, 2023 at 8:59
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6$\begingroup$ @DaveLRenfro I think that The Mathematical Intelligencer would be a more appropriate venue for an unconventional essay on this topic; e.g., one that is humorous or tongue-in-cheek, or that offers unorthodox or controversial advice. But a conventional essay seems more suitable for the Notices, which in recent years has increased its emphasis on career advice. $\endgroup$– Timothy ChowCommented Dec 16, 2023 at 13:40
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1 Answer
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Whenever you write anything, including a paper on "How (not) to write a mathematical paper," it is wise to ask yourself who is my intended audience? That influences the choice of where to publish and of course how to frame your argument.
If your audience is professional mathematicians seeking actual advice, then Notices of the AMS has already been suggested. On their Information for Authors page, they write:
Topics. Notices seeks exceptional articles that report on major new developments in mathematics or that describe great mathematicians or episodes from mathematics history that have connections to current research in the field. We also welcome articles discussing aspects of the mathematics profession, such as grant programs, the job market, professional opportunities for mathematicians, publishing, electronic communications, and mathematics education, at all levels. In addition, we publish reviews of books. The Notices does not publish articles which are offensive or inflammatory.
For something unconventional, controversial, or humorous, Math Intelligencer has been suggested. Their aims and scope says:
The Mathematical Intelligencer publishes articles about mathematics, about mathematicians, and about the history and culture of mathematics. Written in an engaging, informal style, our pages inform and entertain a broad audience of mathematicians and the wider intellectual community. We welcome expository articles on all kinds of mathematics, and articles that portray the diversity of mathematical communities and mathematical thought, emergent mathematical communities around the world, new interdisciplinary trends, and relations between mathematics and other areas of culture. Humor is welcome, as are puzzles, poetry, fiction, and art.
If your audience is graduate students, then the Graduate Journal of Mathematics could be a good option.
If your goal is to influence how we teach mathematical writing, or supervising undergraduates in their first exposure to research (e.g., at an REU), then PRIMUS might be a good choice. I published a paper there about how to teach statistics. Another option would be Involve. A colleague published a paper there about how to teach students how to give good talks, and how to write.
If your goal is to comment on issues with mathematical writing on an even larger scale, you might consider the Journal of Humanistic Mathematics. Their aims and scope page says:
The Journal of Humanistic Mathematics provides an open forum for both academic and informal discussions on the various threads of mathematical inquiry. The focus of submitted papers should be on the aesthetic, cultural, historical, literary, pedagogical, philosophical, psychological, and sociological aspects of doing, learning, and teaching mathematics. Authors should keep in mind that the Journal publishes work that appeals to a general mathematical audience. This includes people who are seriously interested in mathematics, but may come from a variety of backgrounds both within and beyond academia.
I published two papers there (The User's Guide Project: Giving Experiential Context to Research Papers, and The User's Guide Project: Looking Back and Looking Forward) that were related to the topic of how math papers are written and consequences of our ways of doing things, from the point of view of welcoming and encouraging junior researchers.
As others have pointed out, one could also just host the note on your webpage or on arXiv, but in general I think it's a service to actually get such things published. Doing so provides a canonical reference, staying power (webpages don't last forever), and authority to your argument. Also, I've found that the process of getting such essays through peer review really does improve my writing and the framing of the argument I'm trying to make. More focus on quality writing is always welcome, and is definitely needed (as I'm sure you know). I encourage you to write the paper you have in mind, and go through the steps of getting it published!
answered Feb 25 at 23:48
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$\begingroup$ Thank you for your answer. I think I will stick to arXiv at least for a while. Regarding Notices, I know it would be by far the best choice, but publishing there might be perceived as immodest since it will be my own thoughts and others might disagree with me. $\endgroup$ Commented Feb 26 at 0:46
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1$\begingroup$ I would not let concerns of modesty hold you back, if you think your article has value for the readership. Certainly plenty of others have published in notices and ignored the potential criticism of immodesty. Wasn't there a big issue a few years ago about diversity statements and loyalty oaths, with strong opinions published in the Notices? I might be misremembering. Anyway, for sure any opinion piece has opinions, and this is what they are looking for (well-argued, of course)! $\endgroup$ Commented Feb 26 at 0:51
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2$\begingroup$ Regarding modesty, if you send it to the Notices, the worst they'll do is say no. Let the editors there decide if you are being overly immodest. $\endgroup$– JoshuaZCommented Feb 26 at 2:51