Samuelson and Wilson
However, for all that Schumpeter mattered to Samuelson, it is Wilson whose attitudes pervade Samuelson's work. His debt to Wilson cannot be overestimated. It was at Chicago that he had realized the importance of mathematics to economics; Schumpeter encouraged him to enter the Promised Land of mathematical economics, offering him continued guidance and advice, and Leontief had provided Samuelson with his first training in mathematical economics.
But it was Wilson who, more than anyone else, set him on the path toward his PhD thesis and Foundations of Economic Analysis (1947a). Wilson taught him how to be rigorous in his mathematical analysis in a way that Schumpeter, or even Leontief, could never do and, equally important, shaped his conception of economic theory. Though there will have been an element of politeness involved, there is no reason to doubt what he wrote to Wilson on the occasion of his move to MIT:I have benefitted from your suggestions, perhaps more than from anyone else in recent years, and even chance remarks which you have let fall concerning Gibbs's thermodynamical systems have profoundly altered my views in corresponding fields of economics.[47]
Wilson's remarks concerning thermodynamics encouraged Samuelson to study the subject more deeply. Wilson also made it clear that the value of turning to physics was in learning to understand mathematical structures common to both disciplines, a view that would have been reinforced by reading works such as Bridgman's The Nature of Physical Theory (1936), published while Samuelson was attending Wilson's classes. Samuelson also learned from Wilson the importance of basing economic theory on a clear set of postulates and of analyzing the general case where functions were not necessarily smooth and differentiable. Wilson pushed Samuelson to analyze finite changes and, as Gibbs had done, to base conclusions on inequalities linked to generalized notions of convexity.48 He thus pushed Samuelson away from relying too extensively on methods based on calculus. It also appears to have been Wilson who directed Samuelson to the types of mathematics he was to use extensively, recommending a textbook on numerical methods, The Calculus of Observations by Whittaker and Robinson (1926).
This book covered many of the techniques on which Samuelson was later to work: interpolation, difference equations, determinants, linear equations, and statistical theory (linear regression and correlation analysis), with an emphasis on methods for obtaining numerical solutions.49However, though Wilson pushed Samuelson to go beyond the calculusbased methods that had generally been associated with mathematical economics since the late nineteenth century, he remained an applied mathematician whose conception of mathematics had been formed by the turn of the century.50 He sought precise arguments. He did not expose Samuelson to twentieth-century mathematics—to the methods that John von Neumann and other mathematicians were to apply to economic problems. He rejected the topology and existence proofs to which economists with a different mathematical training were to turn. Samuelson, too, was to find little use for topological methods, relying primarily on techniques for analyzing difference and differential equations and matrix methods for the analysis of systems of equations. Samuelson appears also to have picked up something of Wilson's skepticism of elaborate empirical methods. Like his mentor, he appreciated the data-intensive methods of economists such as Mitchell, in which as much importance was attached to the sources of the data as to the use of rigorous theory—this over the formal statistical modeling that was, from the 1940s, to become increasingly common in economics. However, this side of Samuelson's work was not to develop until after he had left Harvard.g
g. This will be discussed in part III of this volume.