The transformation of economics through its mathematization has been of interest to historians of economics and economic thought. While considering aspects of this history, Philip Mirowski (1986a, 1992) and Lionel Punzo (1989, 1991) have introduced David Hilbert's work, the Hilbert program, formalism, and Kurt GddePs results into their discussions in a way that is inconsistent with the mathematical community's understanding of mathematical history.

In the past three decades economics has entered a new phase in its development. The new stage did not involve a revolutionary change of basic tools as occurred with the triumph of neoclassical economics at the turn of the twentieth century and Keynesian economics in the post World War II era. Rather the recent mutation involves the introduction of economic tools of analysis into areas which have traditionally been part of contiguous disciplines. The invasion of economics came to be referred to, even by its enthusiasts (e.g., Stigler 1984; Radnitzky and Bernholz 1986), as “economics imperialism.”

My work as a historian of economic thought and methodologist has had several dimensions. One comprises a heavy research program. Another involves some major editing projects, several long term. Still another involves a synergistic relationship between my work on the history of economic thought and methodology and on the economic role of government. Another involves my participation in the founding and operation of both History of Political Economy and the History of Economics Society. If all this sounds like a lot of activity, it must be understood that my research and professional activities have been both my vocation and principal avocation. I use the word “work” in the title reluctantly and where others might say “career.” I have never thought of my professional activities as either toil or a career; indeed, I have both engaged in and seen them as a joyful adventure—so much for the theory of the marginal disutility of labor! Especially important has been the continued support of my wife, Sylvia. She has not only understood and supported, albeit sometimes with difficulty, my time-consuming involvement with intellectual work, she has nurtured a wonderful family life.

In his contribution to the 1987 conference that celebrated the fiftieth anniversary of Ronald Coase's “The Nature of the Firm” (1937), Harold Demsetz noted that from the birth of modern economics to 1970, “only two works seem to have been written about the theory of the firm that have altered the perspectives of the profession: Knight's Risk, Uncertainty, and Profit (1921) and Coase's ‘The Nature of the Firm’” (Demsetz 1993, in Williamson and Winter 1993, p. 159). It is easy to feel uncomfortable with this observation. First, Coase's article was ignored for decades. Second, Knight's book did not receive much attention because of its theory of economic organization, but because of its statement of the theory of perfect competition (Stigler 1957; Machovec 1995), its distinction between risk and uncertainty, and its theory of profits (see, e.g., Boulding 1942 and Papandreou 1952).'

The laissez-faire welfare theory of classical economics was very much concerned with demonstrating the optimality of the competitive market system, or, more generally, the harmony between individual and social interests. Under the influence of J. S. Mill and Henry Sidgwick, however, this view gradually began to erode. Sidgwick (1901), for example, pointed to a number of factors, including what we now call externalities, that can cause individually-optimal behavior to diverge from the social optimum, and suggested that these potentially call for governmental corrective measures. Alfred Marshall carried this discussion a bit further, but it was through A. C. Pigou's analysis—particularly in The Economics of Welfare (1932)—that the theory of market failure, and the need for government correction of these failures, reached full flower. His work formed the foundation for “modern” welfare economics. The contrast between the “old” and the “modern” welfare economics was pointed out by James Buchanan:

In an episode that reflects tellingly on the state of the economics profession in England circa 1870, John Morley presented himself as a candidate for the London University Chair of Political Economy that John Elliot Cairnes was obliged to vacate because of advancing paralysis. Morley, perhaps the most unswervingly loyal disciple of John Stuart Mill and the editor of the Fortnightly Review, was undeterred by the fact that he had published nothing on the subject, apart from an article on Turgot. Nor, in his letter seeking Mill's endorsement, did Morley feel the need to hint at any prospective scholarly contributions to the discipline. He suggested only that he was “a competent person and likely to discharge the duties of the post industriously” (Morley 1872).

Are Pierre Leroux, Pierre-Joseph Proudhon and Leon Walras economists? Certainly, but to a different extent. This alphabetical order, which is also that of chronology, seems to be in inverse order of merit—at least in the opinion of Joseph A. Schumpeter, who praised Walras as “the greatest of all economists…as far as pure theory is concerned” (1954, p. 827), but who briefly described Proudhon as someone who defended “results that are no doubt absurd” (ibid., p. 457). Leroux's name does not even appear in Schumpeter's 1954 book, nor in any other history of economic thought. Although the judgment pronounced by a historian on one or another of our three authors may be contested, there seems no reason to call into question the hierarchy implicitly established by Schumpeter. In a certain way the succession: Leroux, Proudhon, Walras, represents and summarizes the development of political economy, beginning with the embryonic stage (which would be represented by Leroux), passing through the disorders of adolescence (Proudhon), and finally arriving at the stage of scientific maturity (Walras).