Oskar Morgenstern, “Von Neumann, John” (1968)

Oskar Morgenstern’s biographical encyclopedia entry presents John von Neumann’s career as a decisive encounter between creative mathematics and the social sciences. Its governing claim is historical: von Neumann changed not only the techniques available to economists but also the conception of what an economic problem requires mathematically. The entry moves from biography and a survey of mathematical and scientific achievements to concentrated accounts of game theory and economic equilibrium, concluding with von Neumann’s understanding of mathematics’ relationship to empirical inquiry. A bibliography of his works and supplementary studies supports this compact intellectual portrait.

Born in Budapest in 1903, von Neumann studied in Budapest and Zurich, taught in Berlin, and moved to Princeton University in 1931 before joining the Institute for Advanced Study in 1933. Morgenstern also records his appointment to the U.S. Atomic Energy Commission in 1955, locating his career within scientific institutions and public service. But the organizing distinction appears at the outset:

He was the first of the great creative mathematicians to devote major effort to the social sciences.

The survey of pure mathematics establishes the breadth behind this claim: set theory, mathematical logic, Hilbert spaces, operators, groups, measure theory, ergodic theory, and continuous geometry. Numerical computation belongs within the same intellectual range. Von Neumann’s interest extended beyond computing techniques to the mathematical validity of large-scale operations performed by electronic machines. Morgenstern thus presents abstraction and practical calculation as connected activities.

The discussion of physics develops this connection through von Neumann’s foundations of quantum mechanics and his investigation of its logical structure. His suggestion that individual sciences possess specific logics anticipates the entry’s concluding argument about the distinctive mathematics of social phenomena. Work in hydrodynamics, astrophysics, meteorology, statistics, computer design, and self-reproducing automata further demonstrates the movement between foundational questions and particular scientific problems.

Game theory is the central example of that movement into social science. Morgenstern explains the 1928 minimax theorem through the finite, two-person, zero-sum game: each participant chooses independently without knowing the opponent’s choice, yet optimal strategies exist. Crucially, optimality may require probabilities assigned to the available pure strategies. Strategic rationality therefore need not mean selecting one action with certainty; it can require a calculated mixture.

The account then turns to Theory of Games and Economic Behavior (1944), which Morgenstern coauthored with von Neumann. It extends the analysis to more than two participants and to constant or variable total winnings, while also developing individual choice under risk and stimulating subsequent utility theory. The conceptual importance of games lies in the kind of uncertainty they represent:

Game theory, besides analyzing games proper, is taken as a model for economic and social phenomena; it applies to all situations where the participants do not control or know the probability distributions of all variables on which the outcome of their acts depends, situations that therefore cannot be described as ordinary maximum or minimum problems (even allowing for side conditions).

This passage distinguishes strategic interaction from an ordinary optimization problem with a fully specified environment. The significance of game theory is consequently broader than its application to recognizable games: it supplies a mathematical approach to outcomes shaped by other participants whose choices cannot simply be treated as known conditions.

Morgenstern’s second major example is von Neumann’s 1937 model of a uniformly expanding closed economy. Under constant returns to scale and an unlimited supply of natural resources, minimax reasoning establishes equality between the expansion factor and the interest factor. Alternative production processes, indirect relations among industries, and linear inequalities make the model a precursor of linear programming and activity analysis. Morgenstern connects these developments through the minimax theorem and identifies this work, together with Abraham Wald’s, as opening a new period in mathematical economics.

The methodological lesson concerns existence, not merely calculation. Economic quantities and prices must satisfy nonnegativity restrictions, so counting equations and unknowns cannot establish that an admissible solution exists:

A solution of the system must satisfy the inequality constraints, and the existence of a solution is not ensured merely by the equality of the number of unknowns and the number of equations.

Here mathematical rigor changes the formulation of economic theory itself. Inequalities express substantive restrictions on possible economic states rather than incidental complications added to an equation system.

The conclusion makes explicit the principle connecting these achievements:

He was firmly convinced that the greatest stimulus for mathematics has always come from the mathematician's involvement with empirically given problems; the simultaneous development of calculus and mechanics is the most striking example.

Yet empirical engagement does not imply transferring physics’ mathematics unchanged into economics. Morgenstern emphasizes von Neumann’s conviction that social and physical sciences possess different mathematical structures, and his expectation that social inquiry would generate new techniques. Game theory’s largely combinatorial approach suggested that this development might still be distant. The closing comparison of social science with physics before Newton conveys both its immaturity and its promise. The entry’s lasting relevance lies in this double commitment: rigorous mathematics can transform social inquiry, but doing so requires discovering structures appropriate to its problems.