How many symmetries can a curve possess? It turns out that once the (smooth projective) curve is "complicated enough"—specifically, if it has genus at least 2—then its automorphisms group is always finite. In this talk, I will show a new simple, but conceptual proof of this fact based on a one-pager by Daniel Litt. I will also explain how the same method extends to higher-dimensional cases under mild assumptions. It’s a fun example of how geometry puts hard limits on symmetries. No special background in algebraic geometry is needed!