The May 2013 issue of the American Mathematical Monthly includes a timely reprint of the influential 1962 article “College Admissions and the Stability of Marriage” by David Gale and Lloyd S. Shapley. This paper serves as an exemplary model of mathematical exposition, one that every author should strive to emulate.
With admirable brevity and dry wit, the six-page article presents a set of novel ideas in a way that is both engaging and informative. It uses examples effectively, and it offers arguments carried out not in mathematical symbols but in ordinary English. It has no references, but it does conclude with a provocative paragraph about the nature of mathematical thinking:
“What , then, to raise the old questions once more, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inferences.
“This observation will hardly be news to those engaged in the teaching of mathematics, but it may not be so readily accepted by people outside of the profession. For them, the foregoing may serve as a useful illustration.”
Ehud Kalai introduces the Monthly reprint of the Gale-Shapley article with a brief foreword titled “The High Priest of Game Theory.” It describes the paper in the context of the development of game theory and the 2012 Nobel Prize in economics that was awarded to Shapley and Alvin Roth in 2012.
Interestingly, the original 1962 article did not win an MAA writing award. The Lester R. Ford awards for outstanding expository writing in the American Mathematical Monthly didn’t start until 1965. The Chauvenet Prize to the author of an outstanding expository article on a mathematical topic, first awarded in 1925, went to Leon Henkin for “Are Logic and Mathematics Identical?“, published in 1962 in Science.
And the original article was not reviewed by Mathematical Reviews—a striking omission in light of its subsequent history. Even today, the 1962 Gale-Shapley effort ranks among the top five of most-accessed or cited Monthly articles on JSTOR.—Ivars Peterson