 The degree of a map was first defined by Brouwer, who showed that the degree is homotopy invariant (invariant among homotopies), and used it to prove the Brouwer fixed point theorem.In modern mathematics, the degree of a map plays an important role in topology and geometry.In physics, the degree of a continuous map (for instance a map from space to some order parameter set) is one example of a topological quantum number.