Tbh this is exactly how I felt in my algebraic geometry class. I still remember the fear I had when reading this from the blackboard Defn. f: X → Y is flat

Tbh this is exactly how I felt in my algebraic geometry class. I still remember the fear I had when reading this from the blackboard Defn. f: X → Y is flat ⇔ O_{Y,f(x)} → O_{X,x} flat ∀ x. Then immediately I dropped that class. Turns out I like real analysis much more