In 1937, Underwood Dudley was born in New York City. He graduated from Carnegie Institute of Technology with bachelor's and master's degrees, as well as a Ph.D. In 1965, he earned a bachelor's degree in mathematics from the University of Michigan. He was a professor at Ohio State University and DePauw University before retiring in 2004. He is the author of The Trisectors, Mathematical Cranks, and Numerology, an elementary number theory course, as well as the editor of two collections of mathematical essays.

He was the editor of the Collegiate Mathematics Journal, the Pi Mu Epsilon Journal, and two book series published by the Mathematical Association of America. He is a member of the American Mathematical Society, the Society for Industrial and Applied Mathematics, and the Mathematical Association of America.