Mathematics doesn’t substitute for genuine insight or knowledge of the real world, but it is necessary if economists are going to craft logically coherent models of complex phenomena. While many mathematical models failed to predict the current downturn, plenty of non-mathematical seers also failed. If we ever do come to understand the vicissitudes of asset markets, that understanding will come in the form of formal mathematical analysis, ultimately inspired by Samuelson.
Glaeser's eulogy also hints at how the time may be ripe for a revision to Samuelson's Foundations:
If people can rank outcomes in terms of their desirability, and if they choose one outcome over another, then people have preferences. (Who can disagree with that?) And if, as Samuelson taught us, those preferences follow a few simple rules, then human behavior can be described with a utility function. That conclusion allows economists to turn to Newton and optimization theory.
The principle of revealed preferences results in a mean-field approximation of individual preferences. The incremental step beyond mean-field theory is gauge theory, and this is why the Coase Theorem and New Institutional Economics are more relevant now than neoclassical theory. What NIE has lacked thus far is a theoretical foundation equal in rigor to the foundations Samuelson laid for neoclassical theory.
Samuelson was like Newton also in that he brought his gifts to bear on solving practical problems for his country. Newton completely redesigned the Royal Mint, caught some of the worst counterfeiters, and advised on how to end a 17th century version of the carry trade, which was draining England's royal coffers. Samuelson led the Federal Reserve through several financial crises and advised countless students in high places on economic issues that affected billions of lives.
Not everybody makes this big a dent in history.
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