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The term mathematical economics is employed in two main senses:

(1) As a specialized area of study, mathematical economics is a distinct sub-field within the discipline of economics concerned with the application and development of mathematical techniques to shed light on economic problems. Paul Samuelson's Foundations of Economic Analysis (1947) is considered a classic statement of contemporary mathematical economics.

(2) As a general set of analytical methods, mathematical economics—or, to distinguish it from the first sense employed above, the mathematical method of economics—represents a widely though by no means universally adopted approach to the presentation and interpretation of economic problems.

While the field of mathematical economics is widely acclaimed (due in large part to the success of its progeny, mathematical finance), the widespread use of mathematical methods in economics is controversial. Opponents of the mathematical method, notably the Austrian School, argue that the use of formal techniques lends to the field an impression of scientific exactness that, by nature of the eccentricities of its human subject matter, is unfeasible, even in principle. By contrast, proponents argue that the validity of the mathematical method derives from economists' distinctive assumptions about the internal mechanics of economic decision-making: economic agents are generally (and, to many social scientists, strangely) assumed to be (i) rational and (ii) self-interested, from which it follows that an economic agent's deductions and behaviour may be compared against the calculations reached using formal logical and analytical techniques, including optimization and other advanced mathematical procedures. The rational-actor framework has been disputed as a valid characterization of human decision-making, but it remains the primary framework in mainstream economics.

Although the mathematical method of economics has evolved through geometric, algebraic and higher forms, a solid grasp of modern algebraic methods is a prerequisite for formal study, not only in mathematical economics, but in economics generally. For instance, the Journal of Economic Theory, one of the most prominent academic references in the field, is the apotheosis of the mathematical approach—though surprisingly, according to the Editors, it is a non-specialist journal.

Contents 1 Issues within mathematical economics 2 Mathematical economists 2.1 19th century 2.2 20th century 3 See also 4 References 5 External links

• Arbitrage
• Black-Scholes equation
• Game theory
• Growth theory
• Information theory
• Wealth condensation

Famous mathematical economists include, but are not limited to, the following list (by century of birth).

• Antoine Augustin Cournot
• Enrico Barone
• Francis Ysidro Edgeworth
• Irving Fisher
• Vilfredo Pareto
• Léon Walras

• Kenneth Arrow
• Gerard Debreu
• Leonid Kantorovich
• Sir James Mirrlees
• John Nash
• Frank Ramsey
• Paul Samuelson
• Amartya Sen
• Herbert A. Simon
• John von Neumann
• Alpha Chiang

• Econometrics
• Mathematical finance
• Mathematics of random variables
• Pareto distribution
• Probability theory
• Zipf's law
• Extreme value theory
• Fractal
• Systems theory
• Self-organization
• Self-similarity
• Randomness

• Alpha C. Chiang and Kevin Wainwright, Fundamental Methods of Mathematical Economics (McGraw-Hill Irwin, 4th edition, 2005) ISBN 0-07-010910-9
• Gerard Debreu (1987). "mathematical economics," The New Palgrave: A Dictionary of Economics, v. 3, pp. 399-404.
• F.Y. Edgeworth ([1925] 1987). "mathematical method in political economy," The New Palgrave: A Dictionary of Economics, v. 3, pp. 404-05.

• Keyword list from Journal of Mathematical Economics
• Mathematical Economics and Financial Mathematics at the Open Directory Project (suggest site)
• Wealth Condensation in Pareto Macro-Economies