Cormac McCarthy on how to write a science paper
This looks pretty good mostly, but I'd emphasize more that the most important thing is to be understood. When it comes to a difficult mathematical concept, this is actually really really hard. If you can nail that, then worry about stylistic stuff, but you probably didn't nail it.With that in mind, this advice is really problematic:> Try to avoid jargon, buzzwords or overly technical language. And don’t use the same word repeatedly — it’s boring.Boring is better than incorrect! I love when authors clearly define a term and use it over and over, because I know exactly what they mean every time. Jargon may be necessary to communicate precisely (but define your jargon, avoid assuming it's familiar). E.g. mathematically, there is a difference between a ball and a sphere. And if your L2 ball becomes an L2 balloon in the middle of a proof, readers will be very confused.Also, this is just dead wrong:> Avoid placing equations in the middle of sentences. Mathematics is not the same as English, and we shouldn’t pretend it is.I can see this being useful advice when a proof is full of dense lines of inequalities, but the reasoning is still incorrect. Mathematical notation is nothing more nor less than shorthand for English (or any other language). The following is fine for example: If f(x) >= 1, then either x = 0 or x \in [1,2]. So is this: Noting that x = 3] <= 0.1. Perfectly grammatical.