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Paul Samuelson made mathematics the language of economics

Paul Samuelson's Foundations of Economic Analysis, published in 1947 from his Harvard thesis, showed how mathematics could make economics a rigorous science.

Paul Samuelson
Paul Samuelson · 1915–2009
Person
Paul Samuelson
Lived
1915–2009
Field
Economics
From
American

The story

As a graduate student at Harvard in the late 1930s, Paul Samuelson was troubled by the contradictions, overlaps and fallacies in the classical language of economics. Different branches of the subject used different arguments for what seemed to be the same problems. He sought to unify and clarify them through mathematics.

His doctoral thesis, Foundations of Analytical Economics, won Harvard's David A. Wells Prize in 1941 and became his first major book, Foundations of Economic Analysis, published by Harvard University Press in 1947. Its title page quoted the physicist J. Willard Gibbs: mathematics is a language. Samuelson told economists that they had been practising mental gymnastics of a particularly depraved type, and that they were like highly trained athletes who never ran a race. He did not claim that mathematics would cure every problem, but he insisted that it was essential.

The book showed that a common mathematical structure underlay many branches of economics, resting on two basic principles: that consumers and firms try to maximise something, such as satisfaction or profit, and that economic systems tend toward stable equilibrium. It set out the method of comparative statics for working out how a change, such as a new tax, would affect an economy, and its correspondence principle linked the stability of an equilibrium to testable predictions. It also advanced the theory of index numbers and generalised welfare economics.

The Nobel committee later said that in this book and many articles Samuelson had rewritten considerable parts of central economic theory. The economist James Heckman said he made economics into a formal science using mathematics, and predicted that a century on he would be mentioned in the same breath as Adam Smith. Robert Lucas recalled studying the book to prepare for graduate school and loving it, and said that, like many in his generation, he absorbed its view that a problem not formulated mathematically was not properly understood.

An enlarged edition appeared in 1983, more than 35 years after the first, a sign of how long the book remained in use.

Why it matters

Foundations set the standard for rigorous economic analysis and shaped how economics has been done ever since.

About Paul Samuelson

MIT economist who gave modern economics its mathematical foundations, wrote the best-selling economics textbook of all time and became the first American to win the Nobel Prize in economics.

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Paul Samuelson
1915–2009 · Economics
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