# Exponentials Reiterated

by R. Arthur Knoebel

Year of Award: 1982

Award: Lester R. Ford, also the Chauvent Prize in 1984

Publication Information: The American Mathematical Monthly, vol. 88, 1981, pp. 235-252

Summary: Starting from the question, "When is $$x^y$$ less than $$y^x$$?" this article touches on Bernoulli's work in integral solutions, algebraic numbers, some noteworthy facts about the non-commutativity of $$x^y$$, iterated exponentiation, and even an application to biochemistry.