While "easy programming tricks" are not all it takes to understand difficult mathematics, writing a math paper like good code makes it drastically easier to und

While "easy programming tricks" are not all it takes to understand difficult mathematics, writing a math paper like good code makes it drastically easier to understand what's going on. E.g., encapsulation - given a theorem with a highly technical proof, but ideas from the proof are not super important, hide the proof in an appendix. This is directly analogous to private functions which are only used to power a public one. Naming lemmas is also helpful, although not sufficient. Mathematicians aren't dumb. But they do have a set of traditions and a rhetorical style which is often blindly copied. Also, most mathematicians haven't been exposed to good software engineering practices - consider how few use git and instead just email around "paper_v3_chris_edits.tex". Having worked in both the math world and the CS world, math folks can learn quite a bit from software. (And vice versa - e.g., I just wrote a blog post about how some abstract math solved a real software engineering problem for me: http://engineering.wingify.com/posts/Free-objects/ http://engineering.wingify.com/posts/Free-objects/ )