The Beauty of Complex Analysis

Real calculus is messy, but complex analysis is where math actually gets perfect.

In the real world, a function can be smooth and then suddenly break. But with complex

numbers, if a function is differentiable just once, it is automatically

differentiable forever. It is called being holomorphic, and it is a total superpower.

There is even a rule called the Identity Theorem where if you know what a function

does on a tiny little line, you instantly know what it does everywhere else in the universe.

It feels like cheating, but it is actually the most beautiful theory in mathematics.