How math is written

Link: How math is written

Abstruse Goose, the mathy-est comic there is (even beating out has this great look at how math proofs are written.

I, meanwhile am in the middle of writing my thesis, and I just discovered a much quicker proof for a result that was pretty long before. So, should I replace the long version with the short, or put them both in? Is it more useful to know that I had a long, twisted version of things before I happened on this slicker path? Or just I just present the pared down version like everyone else tends to?