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Columbia. Friedman’s lecture notes to first Hotelling lecture in Mathematical Economics, 1933



On October 3, 2017, Antoine Missemer tweeted an image of an undated examination question by Harold Hotelling “Describe two mathematical contributions to economics published before 1910”. One should note that asking students to talk about work published at least a quarter century before the current academic year is not necessarily a deep dive into the history of economics, though of course Cournot, Bertrand and Edgeworth had achieved “historical” fame by 1933.

From Harold Hotelling’s course in Mathematical Economics taught in the first semester of 1933/34 at Columbia, Milton Friedman kept about forty-five 3 by 5 inch index cards worth of notes (both sides). From his first lecture, we can put together a convenient “short list” of Hotelling’s chosen greatest hits in mathematical economics. I have taken the liberty of expanding Friedman’s abbreviations, figuring the main purpose of transcribing archival material is to ease digital search down the road.

Earlier postings include a list of Hotelling’s courses and his class rolls at Columbia as well as an outline and exam for his course in mathematical economics offered at North Carolina (1946, 1950).


Milton Friedman’s student notes to Harold Hotelling’s first lecture in Mathematical Economics (1933)

9/2/33 (1)

Hotelling, Harold on Mathematical Economics

Has been stated that methodological difference between economics + natural sciences is that in former cannot + in latter do experiments

Not entirely true: in econonomics may experiment, + in some physical sciences (e.g. astronomy, meteorology etc.) do not experiment.

Better dividing line to be found in number of relevant factors


Use of Mathematics in Economics:

A. Cournot 1838

J. Bertrand 1883 Journal des Savants (reviewed Cournot)

F. Y. Edgeworth 1881 Math. Psychics. Papers relating to Pol. Economy.


Alfred Marshall Principles of Economics

(Edgeworth laid foundation of many theories more modern than Marshall

Using higher Mathematics in Economics

G. C. Evans

C. F. Roos


Pareto in Encyclopedie des Science Math, Vol I, Tome IV part 4 (Tome I, Vol. IV)

[Yes, that is all that Friedman wrote down for that lecture]

Source: Hoover Institution Archives. Milton Friedman Papers, Box 120, Class note cards.


Links to Works Referred to by Hotelling

Cournot, Augustin. Recherches sur les Principes Mathématiques de la Théorie des Richesses. Paris: Hachett, 1838.

Nathaniel T. Bacon translation: Researches into the Mathematical Principles of the Theory of Wealth with a bibliography of Mathematical economics by Irving Fisher. New York: Macmillan, 1897.

Bertrand, J. (Review of) Théorie Mathématique de la Richesse Sociale par Léon Walras: Recherches sur les Principes Mathématiques de la Théorie des Richesses par Augustin Cournot. Journal des Savants 67 (1883), 499-508.

Edgeworth, F. Y. Mathematical Psychics. An Essay on the Application of Mathematics to the Moral SciencesC. Kegan Paul & Co., 1881.

Edgeworth, F. Y. Papers Relating to Political Economy.  Volume I;  Volume II; Volume III. London: Macmillan, 1925.

Pareto, Vilfredo. Économie mathématique, —in Encyclopédie des sciences mathématique, Tome I, vol. 4 (Fascicule 4, pp. 590-640), 1906 [?].

Marshall, Alfred. Principles of Economics (8th edition). London: Macmillan, 1920.

Griffith C. Evans. Mathematical Introduction to Economics. New York: McGraw-Hill Book Co., 1930.

Reviewed by Hotelling in Journal of Political Economy, 39, no. 1 (Feb 1931) pp. 107-09.

F. Zeuthen Problems of Monopoly and Economic Warfare. London: Routledge, 1930.

Reviewed by Corwin D. Edwards (New York University) in AER, 21, no. 4 (December, 1931), pp. 701-704.

Charles Frederick Roos. Dynamic Economics—Theoretical and Statistical Studies of Demand, Production and Prices. Monographs of the Cowles Commission for Research in Economics, No. 1. Bloomington, Indiana: Principia Press, 1934.


Image source: From a photo of the Institute of Statistics leadership around 1946: Gertrude Cox, Director, William Cochran, Associate Director-Raleigh and Harold Hotelling, Associate Director-Chapel Hill. North Carolina State University.

Irwin Collier

Posted by: Irwin Collier