The Atiyah-Singer Index Theorem is a fundamental result in mathematics that connects analysis, geometry, and topology. It provides a formula for calculating the index of an elliptic differential operator on a manifold, which essentially counts the number of solutions to a certain type of equation. This index is influenced by the geometric properties of the manifold and the nature of the operator. The theorem was developed by mathematicians Michael Atiyah and Isadore Singer in the 1960s. It has profound implications in various fields, including theoretical physics, particularly in quantum field theory, where it helps in understanding anomalies and topological features of space.