A Century from Now John Ewing

Mathematics: A Century Ago—A Century from Now John Ewing I am not a historian, but I believe in history. His- to sketch mathematical life in America as it was tory lends perspective to the way we view our- near the start of the twentieth century and to use selves and our future. Oliver Wendell Holmes that as a background for a peek at what it might said: be like a century from now. I warn you in advance “When I want to understand what is happen- that I want to draw a moral from this sketch. I ing today or try to decide what will happen to- am therefore heeding the advice of a real histo- morrow, I look back.” rian, Herodotus (450 B.C.): Of course, Holmes also said: “A page of history “Very few things happen at the right time, is worth a volume of logic”…even wise men make and the rest do not happen at all. The conscien- mistakes. If we want to understand our profes- tious historian will correct these defects.” sion today, if we want to guess what will happen In preparing this article, I made all the nec- tomorrow, we ought to study yesterday. It’s almost essary corrections. a new century, and so, in a reflective mood, I de- cided to look back at the turn of the last century America a Century Ago? for our yesterday. The aim of this article then is What was happening one hundred years ago? In 1895 America was still in the throes of severe depression, which began two years before. The This article is an adaptation of an address given at the Supreme Court ruled 5–4 that the income tax was AMS-MAA Mathfest, Burlington, VT. unconstitutional. A new enterprise, Sears-Roe- buck, was struggling: A. C. Roebuck sold his in- John Ewing is executive director of the American Math- terest for $2,000, getting out while the getting ematical Society. His e-mail address is [email protected]. was good, or so he thought. The Underwood JUNE 1996 NOTICES OF THE AMS 663 Typewriter Company was founded to market a the democratic community.… [8, p. new machine: a typewriter that actually allowed 118] the typist to see what was being typed. A young A few held out—Princeton was among them. man named Marconi transmitted a message to The elective system had many consequences. his brother on the other side of a hill. People Eliot boasted that it made scholarship possible thought it a hoax because there was nothing not only among undergraduates but among grad- connecting them. An enterprising young farmer uates and faculty as well. It promoted special- ran boiled wheat through his wife’s dough ma- ization; teaching special courses required ex- chine and baked the thin film to produce edible perts in the field, and “fields” might be narrowly flakes. A strange idea, but people bought 10 oz. defined. The old prescribed course of study was bags for 15 cents. The farmer was John Harvey elementary, shallow, superficial. Election per- Kellogg. mitted faculty to become deep, to indulge their All those things took place in 1895. own interests. The American University This in turn promoted departmentalization [7, p. 400]. In 1893 the biology department at the The American university in 1895 was emerging from a quarter century of change that had new University of Chicago split into five: zool- shaped it into a new form. That new form would ogy, botany, anatomy, neurology, and physiol- continue throughout the twentieth century. It ogy. Everywhere, departments of modern lan- was a frantic period of growth, and universities guages became departments of German or madly sought both students and money. French or Spanish. Departments of history be- During that growth, there was an earnest pub- came departments of European history and lic debate about the purpose of a university. In American history and political science. Depart- 1906 the editor of Outlook magazine summa- ments of mathematics sometimes became de- rized the popular view: The English university, partments of pure mathematics and depart- he said, revolved around culture, the production ments of applied. of gentleman aristocrats. The German university In part it was the elective system that led to found its life not so much in culture but in schol- the notion that a university was a place for re- arship, in erudition, in the production of schol- search. The idea was reinforced by the German ars. But in the American university the empha- model, but it was characteristically American, sis often was neither on culture nor scholarship, based on utility. but on service, on the preparation of young Professional requirements changed: by 1893 Americans for active lives of service [7, p. 356]. some amount of graduate work was required to New university presidents made it their mis- hold a permanent position at nearly every promi- sion to sell their universities to the public, and nent institution. By 1900 the Ph.D. degree became to a large extent the sales pitch was utility. In almost universally mandatory. From there, it 1888 David Starr Jordan, then president of In- was a short step to an insistence upon the con- diana University and soon to be president at tinued publication of scholarly studies. In 1901 Stanford, gave speeches enticing prospective the president of Yale made a statement that students. Among the reasons to go to college: the ought to sound familiar: Promotion at New benefit to society, the virtue of hard work, the Haven, he decreed, depends upon “productive financial worth of a degree [8, p. 342]. work” which gives the professor “a national rep- Utility was bundled with another idea, the utation”. Stanford began publishing an annual elective system. A prescribed curriculum, espe- list of its faculty’s output for each year. Presi- cially a traditional one in the classics and phi- dents kept index cards for every faculty mem- losophy, did not lend itself to the arguments of ber with precise lists of publications and talks. utility and service. So during this period the It was during this period that the term “publish elective system was born—students and faculty or perish” was first used. Research had become were encouraged to choose courses and topics. an essential part of university life [7, p. 404]. By 1900 Harvard had virtually no required There was a continuing debate about the bal- courses; Cornell had switched to an almost en- ance of teaching and research. Abraham Flexner, tirely elective system, as did Wisconsin, Michi- who came down squarely on all sides of the gan, and Yale. The greatest proponent of the issue, wrote an article in the Atlantic Monthly [7, elective system, Charles W. Eliot of Harvard, p. 403]. He told the story of asking a college dean waxed grandly in 1908: who was the best teacher in his institution. The dean named a certain instructor. “What is his rank?” he asked. [Because of the elective system,] teachers and students alike are pro- “Assistant professor.” foundly moved by the desire to serve “When will his appointment expire?” 664 NOTICES OF THE AMS VOLUME 43, NUMBER 6 “Shortly.” Mathematicians were feeling good. And math- “Will he be promoted?” ematicians in America were taking part in the transformation of universities, accommodating “No.” many new roles—utility, service, specialization, “Why not?” research. The elective system had an especially “He hasn’t done anything!” profound effect on mathematics. Before this Service to the community, utility, electives, time, almost all mathematics instruction was specialization, research. It was a logical pro- broad and shallow, often done by faculty as their gression and a major theme in the growth of obligatory extra course (a bit like coaches in American universities. high school who often seem to teach algebra Of course, this is only a partial picture. While and geometry courses). In 1888 Florian Cajori universities were marching forward towards re- conducted a survey. Of 118 college mathemat- search, they were also spending large sums of ics teachers, 73 reported teaching outside mathematics, and 32 of those taught outside the sci- money on boat houses and gymnasiums. They ences altogether—art, music, languages, and needed to attract more students. Was there am- Bible. By the turn of the century, mathemati- bivalence about the role of the university? At the cians taught mathematics. turn of the century, President Eliot at Harvard William Duren wrote a survey of American threw away many of Harvard’s books rather than mathematics for the centennial of the AMS [3, spend money on their storage. Columbia Uni- part II, p. 399]. Looking back, he laments the loss versity built an ornate new library, mainly de- of the traditional importance of mathematics, signed for holding receptions to honor bene- which had been, along with Greek and Latin, factors. At the singularly research-minded part of the required curriculum for many years. University of Chicago, in 1897 in existence only The evidence doesn’t bear this out: mathemat- five years, President Harper complained loudly ics grew, the profession prospered, and there was that his professors were offering entirely too greater concern about teaching—all because of many graduate courses and they had better stop the elective system. [8, p. 178]. The Society American Mathematics Specialization and research had two conse- At the turn of the century, mathematics world- quences: professional societies and professional wide was healthy and vigorous and savoring its journals. They arose naturally and sponta- triumphs—a bit like the present. In the previous neously. There was a new Athletic Research So- quarter century, some major problems had been ciety, for example, holding annual meetings of solved—the transcendence of e and π, the prime coaches and athletic directors to present (and to number theorem, the finiteness theorems in in- publish) research papers on athletics [7, p.

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