Why is analysis so hard? At most universities, I imagine Real Analysis is the one class that makes people quit. It makes them writhe in pain and hatred, cursing themselves for ever choosing to major in mathematics. All of the intuitions that come out of nowhere, the frighteningly low grades on practically every midterm, and the appearance of \(\epsilon\) in dreams that become nightmares. Real Analysis isn’t kind, and I’ve certainly learned that early on (luckily I’m not interested in becoming an analyst). I’m taking comfort in the fact that even though Real Analysis is humbling my knowledge of proofs and gaining intuition from nothing, I’m better now. I’m better at writing proofs. I’m better at coming up with intuition that seems buried. In the long term, this is the one course that will define how I approach future courses in mathematics. After final exams this semester, I might look back fondly on the trivialities of Real Analysis and dream of the wonders it beheld. And perhaps I should in the future, but for posterity, I would like this post to remember the malevolent ghost of Real Analysis that wanders my mind at the most troubling times.

(20 November, 2025)