I was doing a little late-night reading tonight, and it is amazing how poorly some proofs are written by very intelligent people in our field. I’ve even seen poorly written proofs in the midst of a well-written paper. I understand that the primary concern with proofs is correctness, but shouldn’t proofs also be readable? My question is, how essential are nice, clean, understandable proofs in a journal draft? If the goal of our paper is understanding, then clearly they should be just as readable as the text. Maybe that’s why most authors place them in the appendix…so their hideous features don’t destroy the rest of the paper. Of course, some will tell you that if the math in your publication is too understandable, then your peers won’t respect it as much. The point being that, if your proof is straightforward, the result must have come to you easily and is therefore not worthy of publication. You might think I’m joking, but I’ve heard this from many academics over the years.
This really makes me appreciate my first undergraduate class in algebra and number theory. The professor in this class was a bit “picky'’ about the structure of proofs and the logic used to draw conclusions. At the time it made assignments dreadfully tedius, but in the end it made me appreciate a well-written proof. For those of you who didn’t have the opportunity to take undergraduate classes focused on proof-writing, how did you pick up your skills? If you’d like to learn more about proofing skills, check out this link (courtesy of Professor Cusick at Cal State Fresno).