The Uniformization Theorem

The Uniformization Theorem states that every simply connected Riemann surface (a kind of smoothly structured shape that can be described with complex numbers) can be classified into one of three types: it’s either equivalent to the complex plane, the unit disk, or the Riemann sphere. This means any such surface can be "mapped" in a way that simplifies its structure, revealing a standard geometric form. Essentially, it shows that all these complex shapes are fundamentally built from just three basic geometries, allowing mathematicians to understand and analyze their properties through these standard models.