Underwood Dudley (born January 6, 1937) is a mathematician, formerly of DePauw University, who has written a number of research works and textbooks but is best known for his popular writing. Most notable are several books describing crank mathematics by people who think they have squared the circle or done other impossible things. These books, which alternate between appreciation and exasperation, include The Trisectors (MAA 1996, ISBN 0-88385-514-3), Mathematical Cranks (MAA 1992, ISBN 0-88385-507-0), and Numerology: Or, What Pythagoras Wrought (MAA 1997, ISBN 0-88385-524-0). They helped him win the Trevor Evans Award for expository writing from the Mathematical Association of America (MAA) in 1996.
Dudley has also written and edited straightforward mathematical works such as Readings for Calculus (MAA 1993, ISBN 0-88385-087-7) and Elementary Number Theory (W.H. Freeman 1978, ISBN 0-7167-0076-X). He is the discoverer of the Dudley triangle.
Dudley is a native of New York City. He received bachelor's and master's degrees from the Carnegie Institute of Technology and a Ph.D. from the University of Michigan. His academic career consisted of two years at Ohio State University followed by thirty-seven at DePauw University, from which he retired in 2004. He has edited the College Mathematics Journal and the Pi Mu Epsilon Journal, and was a Pólya Lecturer for the MAA for two years.
In 1995, Dudley was one of several people sued by William Dilworth for defamation because Mathematical Cranks included an analysis of Dilworth's "A correction in set theory",  an attempted refutation of Cantor's diagonal method. The suit was dismissed in 1996 due to failure to state a claim.
The dismissal was upheld on appeal in a decision written by Richard Posner. From the decision: "A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise ... To call a person a crank is basically just a colorful and insulting way of expressing disagreement with his master idea, and it therefore belongs to the language of controversy rather than to the language of defamation." 
- Dilworth, William (1974), "A correction in Set Theory" (PDF), Transactions of the Wisconsin Academy of Sciences, Arts and Letters, 62: 205–216, retrieved June 16, 2016
- Caselaw: United States Court of Appeals, Seventh Circuit, ruling on Dillworth vs. Dudley, 1996
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