Jean-Pierre Serre: How to write mathematics badly
Why MathOverflow recommends it
MathOverflow users link it as a funny but pointed guide to sloppy mathematical writing, such as vague references and clashing sign conventions.
Recommended by 2 people across 2 different months, 2013 to 2017.
What it is
A recorded lecture by Jean-Pierre Serre, in English, on the ways to write bad mathematical papers, delivered with a lot of humor. The uploader notes the audio is very quiet and the recording quality is poor.
What people said
Recommends LSpice · 2017-07 · MathOverflow · on “Parodies of abstruse mathematical writing”
It's not quite in the spirit for which you ask, but it's always a good time to mention Serre's How to write mathematics badly [this video] . (I'm sorry for the abysmal video quality, but you can still get much of the sense of it. Did anyone ever make a transcript?)
Recommends R. van Dobben de Bruyn · 2017-11 · MathOverflow · on “Using a known result without a specific reference”
@JohnPardon: totally agree. Perhaps Serre's *How to write mathematics badly* [this video] should be mandatory viewing (imprecise references is one of the examples given).
Cites Theo Johnson-Freyd · 2013-12 · MathOverflow · on “A good reference for learning about super-differentiation & super-integration?”
I have never tried to keep straight the different sign conventions in the literature. There is a good reason for this: it is a theorem of category theory that any reasonable sign convention is as good as any other (viz: the monoidal category of $\mathbb Z/2$-graded vector spaces admits precisely two symmetric monoidal structures up to symmetric monoidal equivalence, determined by whether the non-unit invertible object is bosonic or fermionic); but it is therefore a corollary that whatever paper you're reading will use different sign conventions than you do, and therefore you should not trust their formulas (see J.P.Serre, How to write mathematics (badly) [this video] ). I bring this up to say tha
Cites R. van Dobben de Bruyn · 2017-11 · MathOverflow · on “Using a known result without a specific reference”
As a person who is very precise, I have thought about this question quite a bit (and discussed it with many other mathematicians, junior and senior). Some observations: You can never give references for everything you use. If you give a reference that an arbitrary base change of a flat map is flat, do you also give a reference that arbitrary base change exists? Etc. Thus, you have to draw the line somewhere. Where you draw this line is to some extent up to you; I have certainly seen different authors with quite different approaches to this. General conventions may also vary from field to field; e.g. I have often had the impression that post-Grothendieck algebraic geometry is more precise wit