“Generals” and Summer School in Madison

Samuelson's first year at Harvard was completed with his “generals.”^a If Wilson is to be believed, Samuelson, contrary to his claims about his bound­less self-confidence, was anxious about this.^b Part of the reason for his anxiety was probably that the content of the examination was a lottery, for it was an oral examination and the questions the candidate was asked depended on the examiners present.

a. Harvard also had language requirements. He passed a reading examination in French on November 5, 1935, and on February 25, 1936, the university ruled that a reading test passed in Chicago satisfied the German requirements. M. L. Ballard, March 4, 1936, Letter to Miss Campbell, HUESR (PAS student folder).

b. See chapter 8 this volume.

c. This remark has been widely quoted, though it is often claimed that it was made at Samuelson’s defense of his thesis in 1941. However, Leontief was not involved in that event. Moreover, it makes more sense in the context of his generals, when Samuelson was still only twenty-one and a year into his graduate study. The remark is consistent

Samuelson’s ability to pass his generals a year earlier than usual was in part the result of his having a strong undergraduate education in econom­ics. This meant that he could read widely in the Widener Library, where he acquired a desk in the stacks, and take his mathematics further. He wrote that “instead of spending hours trying to understand the Harvard lectures, I was free to attend optional mathematics courses on differential equations, numerical analyses, applied rational mechanics and classical thermodynam- ics.”1 On another occasion he wrote that he attended courses in “real vari­ables, differential equations, Fourier analysis, and calculus of variations,” again without specifying who taught him.^2,d He referred to the usefulness of the calculus of variations, “taught by Bliss and Graves at Chicago and George Birkhoff and Hestenes at Harvard.”³ It is natural to deduce that he attended the course on the calculus of variations (Math 15) that Magnus Rudolph Hestenes, a young instructor who had recently obtained a PhD at Chicago, and who jointly authored an article on the subject with Birkhoff, taught in the second half of his first year.^e Wilson will have known about the work of Birkhoff and Hastenes on this subject, because they had had an article published in the Proceedings of the National Academy of Science, which he edited, and which Samuelson later cited.

Working out which other mathematics courses he took is more specula­tive because, when asked about his mathematical training, Samuelson liked to emphasize the extent to which he was self-taught. He could easily have attended Birkhoff’s course on differential equations in the fall of 1936, and the course he took on thermodynamics was probably the one offered by Percy Bridgman (Physics 41a), also in the fall of 1936.^f No one at Harvard taught a course on Fourier analysis while Samuelson was there, but there was a course

with what is known about Schumpeter’s sense of humor. Robert Solow, who knew all the people involved, is among those who is convinced that the remark was genuinely made.

d. The non-mathematician should note simply that these are advanced mathematical techniques, familiar to many engineers but with which very few economists of the time would have been familiar.

e. Attending this would have provided justification for substituting Wilson’s statistics course for the second half of Crum and Frickey’s, for it was taught at precisely the same hours as the latter.

f. This course was offered only in alternate years, so it would not have been available in 1937. The only other course on thermodynamics was Heat and Elementary Thermodynamics, intended for undergraduates; but given Samuelson’s self-confidence, his rapidly growing mathematical skills, and that Wilson had introduced him to the subject the previous spring, he would have opted for Bridgman’s more advanced course. in the subject offered at MIT, again in the fall of 1936. If he did attend this, it may have been one of his earliest contacts both with the institution he later made his own and with the mathematician behind much work in cybernetics, Norbert Wiener, who taught the course.^g

There is, however, one part of Samuelson’s mathematical education after Chicago that has been recorded. In 1936, after taking his generals, he spent part of the summer attending courses at the University of Wisconsin-Madison.

[Marion’s] plan was to go once again to the Wisconsin summer school in Madison. I then realized that my math needs required that I master Fourier analysis in Madison. I roomed in a fraternity house. She roomed in a nearby sorority house. Times were different then. (Example: It never entered my head that a male could go above the first floor in Whitman House, Marion’s Radcliffe dorm on Walker Street. Autos, park benches, and dark movie houses had to suffice.)⁵

He neglected the additional factor—namely, that there would have been a matron or house mistress experienced in stopping men from reaching parts of the building they were not allowed to enter. Samuelson took courses in German, the theory of equations, and the theory of analytic functions (not Fourier analysis). The German course, also attended by Marion, was a “rapid reading course” in nineteenth- and twentieth-century literature, taught intensively, at 7:30 every morning from Monday to Friday. Taking this course after he had been exempted from the requirement to take an examination in German implies that it was a language he intended to use. Marion attended the German class with Paul, though each day, when they had finished doing German, Marion moved to a course in money and bank­ing, while Paul turned to the Theory of Equations, taught by Margarete Wolf, one of the few American women to obtain a PhD in mathematics at this time.^h The course description explained that it covered “systems of lin­ear equations and determinants with applications.” Margarete and her sis­ter, Louise, had both obtained their doctorates at Wisconsin in 1935, with theses involving matrix algebra.ⁱ A paper written jointly with her sister and ^{[16] [17] presented to the American Mathematical Society two years later dealt with the problem of deriving necessary and sufficient conditions for the existence of solutions to linear matrix equations and determining the number of solu­tions.[18] Though the course she taught may not have covered these topics, she was certainly working on problems that Samuelson would, had they got into them, have considered relevant to economics, given his exposure to Leontief the previous term.}

After an hour with Wolf, Samuelson turned to the Theory of Functions of Complex Variables with Herman W. March. March, like Wilson, was an applied mathematician. He had worked as an assistant in astronomy, and for a year as an instructor in physics at Princeton, before taking a PhD in Munich in 1911. His research covered the flow of liquids and the deflection of plates under stress—both problems important in aeronautical engineer­ing, one of the subjects on which Wilson had published. Significantly, this involved using experimental data to obtain numerical solutions for differen­tial equations, illustrating—so the university’s memorial notice argued—the unifying power of mathematics. When he entered his second year at Harvard, Samuelson had significantly increased his knowledge of mathematics.