# The Curious History of Faa du Bruno's Formula

by Warren P. Johnson

Year of Award: 2003

Publication Information: The American Mathematical Monthly, vol. 109, 2002, pp. 217-234

Summary: The history of di Bruno's formula for the $$m$$th derivative of a composite function $$g(f(t))$$ is recounted, including the fact that di Bruno was neither the first to state the formula nor the first to prove it.

Warren P. Johnson was an undergraduate at the University of Minnesota. He received his Ph.D. from the University of Wisconsin under the direction of Richard Askey. He has taught at Penn State University, Beloit College, and the University of Wisconsin, and is now at Bates College. He always enjoyed the historical notes in Askey's special functions courses, and this paper satisfies the vague ambition he had of discovering such a thing himself some day. His other research interests are in combinatorics and $$q$$-series.