Hermann Hankel was a German mathematician who lived in the 1800s. He is best known for his work on the theory of complex functions and his contributions to number theory. He also made important discoveries about the properties of analytic functions, which are functions that can be expressed as the sum of an infinite number of polynomials (polynomials are things made up of numbers and letters like x + 2x^2 + 6x^3). His work helped to advance mathematics in the 19th Century.