Riemann-Roch Theorem

The Riemann-Roch theorem is a fundamental result in mathematics that relates the number of independent functions (or sections) you can define on a curved shape (called a Riemann surface) to its geometric features. Essentially, it provides a formula to calculate the dimension of certain function spaces based on the shape's topology and its special points (like holes or punctures). This theorem helps mathematicians understand how complex functions behave on these surfaces, linking geometry and analysis in a precise way. It's a key tool in fields like algebraic geometry and complex analysis.