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I want to write a mathematical paper that is tailored for applied mathematics. To be more specific, it is using extensively differential equations and integrals. I observed that there are two writing style. First one is more concise and abstract. It uses a lot of theorems, proofs, lemmas, definitions etc. This is the direction I am not very familiar (I am physicist). A second style is more like a flow of thoughts like in this following article written by Belendez I personally like this style. It is simple and with the flow. However, this second style writing is very uncommon in mathematical journals. I assume two possible reasons. First, its not popular. Second, it is related to applied mathematics only and possible too elementary for publishing. Or first style is not applicable to applied mathematics meaning that its applicable for number theory and abstract analysis. Am I right in this reasoning? If not, how do you write the Belendez paper in the first style if applicable? On my part, I would write like this:

  1. Definition - use equation 1) , 2) and 3) (in Belendez paper)
  2. Theorem - use equation 31)
  3. Axioms - use equation 24) , 25) and 29)
  4. Proof - all the remaining equations and the plot.
joriki
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Aschoolar
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  • Does this answer your question? Advice for writing good mathematics? – jasmine Feb 26 '24 at 18:30
  • There are mathematical writing style guides. I enjoyed Knuth, et al. "Mathematical Writing" (PDF via mit.edu); also Gillman "Writing Mathematics Well" (via amazon.com). A web search turns up lots of advice. ... If you're targeting a specific journal, check their website for "Advice to the Author" notes, which typically cover preferred style and formatting issues. (They may even provided a dedicated LaTeX template.) – Blue Feb 26 '24 at 18:35
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    I think the Belendez paper is much better as presently written than trying to fit it to a definition-theorem-proof-remark style because it seems to me it is intended as an expository paper rather than a research paper. More specifically, it does not introduce a lot of terminology where it would be very helpful to the reader to have definitions of those terms in easy to find ways (i.e. as labeled definitions), and it does not have long chains of results used to obtain other results and so on where it would be helpful to have the earlier results in easy to find ways (i.e. as labeled theorems). – Dave L. Renfro Feb 26 '24 at 19:20
  • Have a look at nearly any SIAM journal. They provide examples of quality applied mathematics writing. Otherwise, target a physics journal. In the end know, and write for, your target audience. – A rural reader Feb 27 '24 at 01:20
  • @DaveL.Renfro, from your answer, it seems that if I do math like Belendez then I should write in Belendez (first style). However, you mentioned that second style is better. Then is my example of Belendez adaptation good ? @A rural reader, I have looked at both departments, the physics j. insists that the paper is for applied math, then the applied math j. insists that it is not mathematical enough or not in first style. – Aschoolar Feb 27 '24 at 02:59
  • It sounds like you already got two rejections from Journals who each wants something different? If that's the case I would recommend to find other ways of reaching an audience. Who reads journals anyway? Feedback from readers will tell you how good your paper is. – Kurt G. Feb 27 '24 at 08:26

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