How Economics Became a Mathematical Science

How Economics Became a Mathematical Science By E. Roy Weintraub. Durham, NC: Duke University Press. 2002. Pp. xiii, 313. $18.95 (paperback). It is a contemporary truism that if you hope to make a contribution to the field of economics, or even to study it, you had better first get a solid background in mathematics. It should also be evident that this has not always been the case, as anyone who has read Adam Smith or Karl Marx, or for that matter Frank Knight, J. M. Keynes, or F. A. Hayek, well knows. Sometime in the twentieth century economics changed, and changed profoundly. In How Economics Became a Mathematical Science, Roy Weintraub attempts to make some sense of the transformation. I was not prepared to enjoy this book. I knew Weintraub to be a lively writer, but his topic was daunting. I was half expecting a forthrightly pedantic and in the end (at least, given my own tastes) ploddingly dull monograph that followed the usual formulaic listing of "seminal contributions" on the road to full mathematization. In glum anticipation I imagined the questions to be covered: Shall we start with Cournot? With Bentham and the felicific calculus? Was Walras, as Schumpeter wrote, the greatest economist who ever lived, at least that is until his twentieth century successors, Arrow and Debreu and McKenzie, surpassed him? There would of course be the obligatory chapter on Samuelson's Foundations, another on the introduction in economics of fixed point theorems, still another on the fine points of proof strategies. At least for me, reading such a book would be a real challenge. It would be a duty, and a grim one. To my great good fortune, Roy Weintraub's How Economics Became a Mathematical Science is neither pedantic nor dull. It is, in fact, an altogether extraordinary book. Organized not in terms of a grand narrative, it is instead a series of snapshots. The snapshots are not necessarily of seminal moments, but of representative ones, and they are well chosen. Like all good history, the stories Weintraub recounts are multilayered, complex, even messy, a word he uses (p. 207). It would be unfair to expect that such a collection of vignettes should hang together. Incredibly, though, they do. As a final bonus, there are real surprises to be found in nearly every chapter. This, then, is an enjoyable book to read. But it is also an important one. I do not think it is an exaggeration to say that How Economics Became a Mathematical Science itself promises to change the way that people view the relationship between mathematics and economics. Weintraub says as much at the start of one of his chapters: "Modern controversies over formalism in economics rest on misunderstandings about the history of mathematics, the history of economics, and the history of the relationship between mathematics and economics" (p. 72). I usually hate such bald statements. It turns out, though, that he's right. Weintraub starts from a startlingly simple premise-both economics and mathematics have changed over the course of the past 100 plus years, so it makes sense to look at them both. Looking at how they have changed, and their interaction, might reveal some things that would be lost if one followed the all-too-usual Whig history route, the latter a form of backward induction in which one uses the present state of economics as a guide for picking out which episodes in the past are worthy of attention. The surprises begin in the first chapter. When most economists think of mathematics, they think of a stable discipline consisting of a set of related subject areas (algebra, geometry, calculus, topology) that yield tools for economists to use in constructing models of varying levels of generality. The tools are out there, as it were, sitting in books on the shelf, only to be learned and applied.' This "bookshelf view of mathematical knowledge" is challenged in the very first chapter, one that carries the intriguing title, "Bum the Mathematics (Tripos). …