In the Spring of 1933 Joseph Schumpeter got the ball rolling for a project to introduce an introductory course in mathematical economics at Harvard. I include here first a memo from statistics professor W. L. Crum to the economics department chair, Professor H. H. Burbank. This is followed by the subsequent proposal signed by six professors (Burbank, Chamberlin, Crum, Mason, Schumpeter and Taussig), presumably sent to some university level curriculum approval committee. From the enrollment records included below we see that 23 people attended that class in the first term of 1933-34. Starting the following academic year the course was taught by Leontief and a new course “primarily for Graduates”, “Mathematical Economics”, was introduced by Professor E. B. Wilson. Course descriptions and enrollments through 1936-37 are included in this posting. Here is an interesting 1936 letter from E. B. Wilson to Columbia’s W. C. Mitchell about what Schumpeter has wrought with economics in the curriculum.
An update with additional material for this course has been included in a later post.
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Memorandum for Professor Burbank
4 April 1933
- I discussed, at his request, the mathematical economics project with Professor Schumpeter last Friday. I will give further consideration to his suggestions, and to the conversations I have had with you on the same subject; and then I will write out, for discussion with you, an outline of my thoughts on the matter.
- In the meantime, I am making a specific suggestion with reference to one of the points you raised earlier. You indicated that it might be desirable for those officers interested in mathematical economics to get together as a group and discuss prospects. As things are developing rapidly it seems to me that such a committee (perhaps informal) could well be set up promptly. I hope you will feel that you can meet with the group and act as its chairman. If you cannot, I suggest Professor Schumpeter be asked to head the group. I suggest that its members include also: Professor Black (I think it very desirable that he be brought in early), Professor Wilson, and me. I think it well that this original group be empowered to add shortly the following: Professor Frickey, Dr. Leontief, and Professor Chamberlin (or one of the other interested younger men).
[Signed]
WLC
Source: Harvard University Archives. Department of Economics, Correspondence & Papers, 1902-1950. (UAV.349.10) Box 23, Folder “Course Administration: 1932-37-40”.
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Tentative Proposals for a Course on the Elements of Mathematical Economics to be Given during the Winter Term
The advanced student who is interested in the mathematical aspects of our subject has had in most cases some mathematical training and can be taken care of individually. But something should be done to acquaint a wider circle of less advanced students, or even of beginners, with those fundamental concepts of mathematics which are necessary to understand, say, Marshall’s Appendix and the more important and more accessible parts of the literature of mathematical economics, such as the works of Cournot, Walras, Edgeworth, and a few others. Since the necessary minimum of mathematics can be procured with little expenditure of time and energy, the experiment is proposed of importing this modicum of information to such graduate and undergraduate students as may wish to have it–subject to the approval of tutors in the case of undergraduates.
A half-course two hours a week would meet the case. Since any teaching of mathematics must work with examples if it is to convey any meaning, these examples will be drawn from economic problems. The course, therefore, should not be simply one on “mathematics for economists” but rather on “mathematical theory of economics.” Discussion will cover a number of simple and fundamental problems of economic theory, the mathematical concepts being explained as they present themselves. In the first term the whole venture will be frankly experimental. Coöperation and critique from all members of the economic staff is cordially invited. The final shape of this addition to our offering should, through common effort, be evolved during the next term. The following list is suggested of mathematics subjects with which it is proposed to deal in which seem to be both necessary and sufficient. The economic problems from which, and in connection with which, these mathematical topics are to be developed are merely the time-honored problems of marginal analysis.
(1) The fundamental concepts of analytic geometry, coordinates, transformations, equations of straight-line and curves, tangents, and so forth.
(2) Some fundamental notions of algebra, the theory of equations, forms, matrices, determinants, vectors, and vectorial operations.
(3) The concept of the integral and some of its applications, definite integrals, multiple integrals, and multiple integrals in polar coordinates.
(4) Functions and limits, differential coefficients, the elementary differential operations, maxima and minima, partial differentiations, developments, Taylor series.
(5) Simplest elements of the theory of differential equations. Functional equations and here and there some simple and useful tools from other mathematical fields as occasions may arise.
The course should be open to all who are interested, and participation of those wishing to follow it as auditors will be welcomed. It is highly desirable that as many tutors as possible should be present at the sessions of the first experimental term in order to contribute their advice, so that in the future the course may embody those topics and methods of present presentation which are found to be useful.
April 1933
H. H. Burbank
E. H. Chamberlin
W. L. Crum
E. S. Mason
J. A. Schumpeter
F. W. Taussig
Source: Harvard University Archives. Department of Economics, Correspondence & Papers, 1902-1950. (UAV.349.10) Box 23, Folder “Course offerings 1926-1937”.
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1933-1934
[Courses offered]
Economics 8a 1hf. Introduction to the Mathematical Treatment of Economic Theory
Half-course (first half-year). Mon. 4 to 6, and a third hour at the pleasure of the instructor. Professor Schumpeter, and other members of the Department.
Economics 8a is open to those who have passed Economics A and Mathematics A, or its equivalent. The aim of this course is to acquaint such students as may wish it with the elements of the mathematical technique necessary to understand the simpler contributions to the mathematical theory of Economics.
Source: Harvard University. Announcement of the Courses of Instruction Offered by the Faculty of Arts and Sciences during 1933-34, 2n ed., p. 126.
[Course Enrollment]
[Economics] 8a 1hf. Professor Schumpeter and other members of the Department. — Introduction to the Mathematical Treatment of Economic Theory.
15 Graduates, 3 Seniors, 5 Instructors. Total 23.
Source: Harvard University. Report of the President of Harvard College and Reports of Departments for 1933-1934, p. 85.
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1934-35
[Courses offered]
Economics 8a 1hf. Introduction to the Mathematical Treatment of Economic Theory
Half-course (first half-year). Mon. 4 to 6, and a third hour at the pleasure of the instructor. Professor Schumpeter.
Economics A and Mathematics A, or their equivalents, are prerequisites for this course.
Economics 13b 2hf. Mathematical Economics
Half-course (second half-year). Tu., Th., 3 to 4.30. Professor E. B. Wilson.
Arrangements for admission should be made with the Chairman of the Department
Omitted in 1935-36.
Source: Harvard University. Announcement of the Courses of Instruction Offered by the Faculty of Arts and Sciences during 1934-35, 2n ed., p. 126-7.
[Course Enrollments]
[Economics] 8a 1hf. Professor Schumpeter. — Introduction to the Mathematical Treatment of Economic Theory.
2 Seniors, 1 Junior, 1 Sophomore. Total 4.
[Economics] 13b 2hf. Professor E. B. Wilson. — Mathematical Economics.
2 Graduates, 1 Junior, Total 3.
Source: Harvard University. Report of the President of Harvard College and Reports of Departments for 1934-1935, p. 81.
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1935-1936
[Course offered]
Economics 8a 2hf. Introduction to the Mathematical Treatment of Economic Theory
Half-course (second half-year). Mon. 4 to 6. Assistant Professor Leontief.
Economics A and Mathematics A, or their equivalents, are prerequisites for this course.
[Economics 13b 2hf. Mathematical Economics]
Half-course (second half-year). Tu., Th., at 2. Professor E. B. Wilson.
Arrangements for admission should be made with the Chairman of the Department
Omitted in 1935-36.
Source: Harvard University. Announcement of the Courses of Instruction Offered by the Faculty of Arts and Sciences during 1935-36, 2nd ed., p. 138-9.
[Course Enrollment]
[Economics] 8a 2hf. Professor Leontief. — Introduction to the Mathematical Treatment of Economic Theory.
4 Juniors, 2 Sophomores. Total 6.
Source: Harvard University. Report of the President of Harvard College and Reports of Departments for 1935-1936, p. 82.
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1936-1937
[Courses offered]
Economics 4a 2hf. (formerly 8a) Introduction to the Mathematical Treatment of Economic Theory
Half-course (second half-year). Mon. 4 to 6. Assistant Professor Leontief.
Economics A and Mathematics A, or their equivalents, are prerequisites for this course.
Economics 104b 2hf. (formerly 13b). Mathematical Economics
Half-course (second half-year). Tu., Th., at 2. Professor E. B. Wilson.
Arrangements for admission should be made with the Chairman of the Department
Source: Harvard University. Announcement of the Courses of Instruction Offered by the Faculty of Arts and Sciences during 1936-7, 2nd ed., p. 140, 142.
[Course Enrollments]
[Economics] 4a 2hf. Professor Leontief. — Introduction to the Mathematical Treatment of Economic Theory.
1 Graduate, 2 Seniors, 3 Juniors, 2 Sophomores, 1 Other. Total 9.
[Economics] 104b 2hf. (formerly 13b) Professor E. B. Wilson. — Mathematical Economics.
2 Graduates. Total 2.
Source: Harvard University. Report of the President of Harvard College and Reports of Departments for 1936-1937, pp. 92,93.
Image Source: Schumpeter, Leontief, Wilson from Harvard Album, 1934, 1939.
One reply on “Harvard. Mathematical Economics, 1933-37”
Thanks for all these treasures from the archives posted during this year! I liked this one in particular as it sets out how mathematics was introduced into the teaching of economics at Harvard. Schumpeter’s proposal/project can be directly linked to the founding of Econometric Society two years earlier. It seems that Schumpeter’s proposal could not be effectuated by the department of economics without approval from above(?). And if Leontief had not just been hired as instructor the proposal would perhaps not have come to anything. Bob Solow who arrived in 1941 has stated somewhere that Leontief then still was the only mathematical economist at Harvard.