Born in Calais in 1921, Gérard Debreu died on the last day of 2004 in the Paris area where he spent the last years of his life. He graduated from Ecole Normale Supérieure, one of the elite schools in France with a strong program in mathematics. While studying there he came to economics through the influence of Maurice Allais, who was teaching economics in a neighboring school, Ecole des Mines. In 1949 a Rockefeller fellowship allowed him to visit American universities and, in particular, the University of Chicago. He was then offered a position of research associate by the Cowles Commission for Research in Economics. In 1962, Gérard Debreu accepted a position of professor of economics (transformed later into a joint professorship of economics and mathematics) at the University of California, Berkeley. He was President of the Econometric Society in 1971 and received the Nobel prize in 1983.

Gérard Debreu belongs to that small and exclusive set of economists who shaped the evolution of our profession. His name is associated with a research program aimed at consolidating the foundations of the most influential strand of economic thinking, the origin of which is attributed to Léon Walras. Debreu's work reassesses the foundations of analytical economics of Walrasian inspiration by appealing to the new mathematical tools that had become available at the time, briefly speaking, convex analysis and fixed point theorems.

A few remarks on a selection from his oeuvre may serve to characterize Debreu's scientific contribution, though this selection cannot do justice to, nor record satisfactorily, the significance and impact of his work on economics.

The first “coup de maître” occurs with his 1951 article, “The coefficient of resource utilization.” Pareto (1909) had given a geometric intuition linking the equilibria and optimal states of an economy. Inaugurating a method that was going to prove so fruitful, Debreu uses convex set theory and demonstrates in a very elegant manner the two laws of welfare linking market equilibria and optima.

Kenneth Arrow had a similar contribution in 1951, and the two joined forces to produce a truly pathbreaking article, their 1954 “Existence of an equilibrium for a competitive economy.” The problem of the existence of a general equilibrium had been pending since Walras's contribution in the 1870's. Some progress was made by Wald in the 1930's, and the problem was again set aside by economists. Arrow and Debreu show that demonstrating the existence of an equilibrium amounts to finding a fixed point in a generalized game, an issue that Debreu had investigated in a 1952 article, “A social equilibrium existence theorem.” Arrow and Debreu's article, together with the related companion article by McKenzie (1954), marks the birth of modern general equilibrium theory.

Then comes his treatise, Theory of Value (1959). It is difficult to think of a book in the last 50 years that had more impact on economic theory. Providing a fully consistent axiomatic approach to Walrasian general equilibrium theory in just over $100$ pages, this book has become the standard reference on the subject. In a rigorous and logical succession of chapters, “Mathematics, Commodities and Prices, Producers, Consumers, Equilibrium, Optimum, Uncertainty,” it presents the major primitives of the theory and introduces new mathematical techniques and concepts into economics, standard today but unheard of before. The flawless and elegant progression reconciles rigor and relevance in a truly exceptional book.

Another most well known piece is his article with Herbert Scarf (1963), “A limit theorem on the core of an economy.” It was known since Edgeworth (1881) that allocations that possibly emerge from the decentralized interaction between agents could form a large set, the “contract curve.” He noted that this contract curve was shrinking as the number of agents was growing, leading eventually to the competitive equilibrium. Debreu and Scarf made the argument fully rigorous, using the game concept of the core as a representation of agents' decentralized interaction. Considering n-fold replicas of the original economy, they showed that the core of these replicas converges toward a market equilibrium as n goes to infinity, validating Edgeworth's intuition 80 years later.

Other contributions raised new conceptual issues and introduced new techniques, for example, measure theoretic concepts in “Neighboring economic agents” or concepts from differential topology in “Economies with a finite set of equilibria” (1970), “Smooth preferences” (1972), and “Excess demand functions” (1974).

Although Gérard Debreu always constrained himself to microeconomics, he turns out to have had influence in macroeconomics as well. Indeed, Arrow (1953) and Debreu (1959) pictured the economy under uncertainty as subject to stochastic events, and organized under a set of so called complete markets. Nowadays students in the macroeconomic field of “Dynamic stochastic general equilibrium” picture similarly macroeconomic fluctuations as an intertemporal equilibrium whose fluctuations are driven by stochastic shocks (the “states of nature” in Arrow–Debreu terminology), but under the more realistic assumption of incomplete markets. Hence, if microeconomics and macroeconomics are more united nowadays, it is under the flag of general equilibrium.

Gérard Debreu will always be remembered by colleagues and students as a grand seigneur among the economists, driving for utmost perfection, uncompromising in his demand for clarity and rigor, while choosing tools and form of presentation with parsimony. The profession has lost not only one key promoter of modern mathematical economics but also one of its great minds who contributed significantly to shaping modern economic theory.