David Mumford is an American mathematician known for his work in algebraic geometry, a branch of mathematics that studies geometric properties of solutions to polynomial equations. He was born on July 31, 1937, and has made significant contributions to the field, including the development of Mumford schemes and geometric invariant theory. Mumford received the Fields Medal in 1974, one of the highest honors in mathematics, for his innovative research. He has also been involved in education and has authored several influential books, helping to shape the understanding of complex mathematical concepts for students and researchers alike.