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JR Learnstomath (Apr 05 2026 at 07:57):@Patrick Nicodemus , you wrote about a theorem you wrote up in a
Patrick Nicodemus said in #practice: communication > Publishing technical lemmas:
10-12 page research note.
From this, I'm guessing a research note of this sort is the kind of "shape" you'd put your ideas down as.
I'm working on learning how to write my ideas down, without necessarily publishing it, but would like some tips on how to even go about producing a "10-12 page resesarch note".
Might anyone have a recommended resource I can use to do such a thing -- like a YouTube video, or a paper/article? (Ideally a pdf that's available, not a book that needs buying)
Does anyone have a favorite template or model favorite research note for someone writing something simple/a beginner?
I work on Overleaf and can do all the typesetting - this question is more about how to go from a blank page and a brain full of thoughts to something coherent and readable and interesting.
Thank you!
fosco (Apr 05 2026 at 13:22):The first iteration of a manuscript has to satisfy only one requirement: it has to exist. Do not trust anyone trying to teach you how to write well, it's usually debatable matter of taste; the only exception is Serre's "how to write mathematics badly", teaching you how not to write. Finish the first version of the manuscript, and then give it to someone trusted, who can help with advice. Then follow the advice you get.
Ryan Wisnesky (Apr 05 2026 at 15:42):caveat: it has to exist, and you have to understand everything that it says (or say explicitly when you don't) and be willing to be accountable for whatever text is in it, because once papers go on the internet they never leave. Nowadays with LLMs, these are stronger properties than existence. FWIW, in college the faculty made us read books on rhetoric, on argumentative writing, like how to make claims about justice and morality, in addition to technical writing, to make sure our technical writing was sufficiently focused on making claims rather than just listing observations. I learned more in those rhetoric classes than I would have thought possible and they became one of my favorite parts of undergrad.
JR Learnstomath (Apr 06 2026 at 08:44):Thank you both! @fosco This is very much like when I used to write novels for National Novel Writing Month. Who knew I could use this as a transferable skill! For the rhetoric @Ryan Wisnesky , I will now read papers with that lens on... It feels very unintuitive to me to not just list observations, but I guess this is where math is done -- you find something very interesting, make a claim about it, and then prove it? What is a "claim", exactly?
Ryan Wisnesky (Apr 06 2026 at 09:06):One thing I still do now as a result of the rhetoric class is write every paper specific to an audience or venue, because rhetoric says that even the same content should be presented differently depending on the audience, whereas others might submit the same list of observations to multiple venues on the grounds that people can draw their own conclusions. Neither approach is right or wrong, I just agreed with the rhetoric course’s argument that all communication is innately persuasive. The course notes are no longer online, but here’s something similar: https://pressbooks.umn.edu/techwriting/chapter/chapter-1/
Just be sure to only use rhetoric for good, lest you veer into sophistry and be ostracized from 5th century BC Athens or its modern equivalent of being mistaken for an llm.
John Baez (Apr 06 2026 at 15:31):JR Learnstomath said:
but I guess this is where math is done -- you find something very interesting, make a claim about it, and then prove it?
Right!
What is a "claim", exactly?
A claim is a mathematical statement that might or might not be true, like 25 15 = 325, or 25 15 = 425, or "every symmetric monoidal category is cartesian closed", or "not every symmetric monoidal category is cartesian closed". But typically a claim is a mathematical statement that you're claiming is true.
I suggest reading math papers, textbooks, and also math blog articles, to become accustomed to the way mathematicians think and talk.