Proving stuff yourself is hard, and my initial attempts were catastrophic. I wrote one proof that began with a stronger statement than the conclusion I was attempting to draw, rendering the proof useless even in the unlikely case it was otherwise successful. It was not otherwise successful. Jumping through several dodgy implications and logical errors, it eventually arrived at a conclusion that was substantially weaker than what I was attempting to prove. The worst part? I couldn’t even spot my own mistakes, and I thought the proof was probably quite good.
This post is about my approach to real analysis. In many areas of theoretical research, proving things is of paramount importance. Sadly, I didn’t have the foresight to take a heavy math curriculum as an undergrad, and like many, my skills were lackluster at best. My solution? Prove every theorem in an intermediate analysis course.Continue reading Trial by fire: My mission to prove every real analysis theorem from scratch