Dissertation Review: Mathematical Professionalization in Mid-Century America

Review June 15, 2014 7:27 pm
Observation of fluids (1950). From right to left: Louis Nirenberg, Anneli Lax, Harold Grad, Eugene Isaacson, Joe Keller, an unknown and Richard Courant. Image from this article.

Observation of fluids (1950). From right to left: Louis Nirenberg, Anneli Lax, Harold Grad, Eugene Isaacson, Joe Keller, an unknown and Richard Courant. Image from this article.

Historical studies on scientists in the Cold War university have surged in recent years. Perhaps more significantly, research on this topic has diversified. Recently described by Steven Shapin in one instance, “it was immediately understood that it was the natural scientists and engineers who had departed the Ivory Tower en masse, leaving the humanities and most of the human sciences behind” during the Cold War. The options of federal contracts and grants implied an alternative to university support to which scientists could turn. But whereas many twentieth-century treatments were content to leave conclusions at that, more recent scholars—such as David Engerman, Ron Theodore Robin, and Louis Menand—have invested the subject with more nuanced analyses into the alliances formed between military agencies, industries, and academia.

HASTS alum Alma Steingart’s dissertation, Conditional Inequalities: American Pure and Applied Mathematics, 1940-1975, seeks to add to this literature. And it is with great pleasure that as my first contribution to this blog, I provide a review of her dissertation. Taking on a generation of scholarship on board, Alma offers a full-length examination into the consequences of these series of turns on the mathematics discipline during the American postwar period. She tracks the development of the American mathematical community in two areas of mathematics that became institutionalized in this time: the pure and the applied. Alma’s ambitious and well-argued excavation of the professionalization of pure and applied mathematicians in changing institutional settings is a study that historians of mathematics, science, politics, and education have been waiting.

One of Alma’s key arguments can be summed up in a deceptively simple claim: namely, that mathematicians enjoyed the fiscal benefit of the Cold War while maintaining the autonomy of their research by continuously redefining the nature of their field. What this implies is that far from being a stable discipline, mathematics—in its pure and applied dimensions—is incredibly malleable. In short, Alma is disinterested in discerning which mathematical subfield developed more superiorly than the other. Her focus remains on analyzing the debates over the demarcation between these two fields and how they revealed, “mathematicians were in fact asking how relevance should be established and by whom” (314). At stake were the dynamic relations between institutions, practices and ideas.

The first chapter sets the mobilization of American mathematicians’ during World War II in the context of both mathematicians and governments’ perceptions of the potential contributions the mathematical discipline could provide. The result, a tension created early on in the war between the physicists and leading mathematicians, was by most measures a philosophical disagreement over the nature of mathematical work: mathematicians’ “self-conception as detached intellectuals devoted to formal abstractness and generalizations” deemed them “as simply unsuitable for defense work. Practical individuals who could step out of their private university offices and take part in military-controlled research groups were needed, not individualistic free thinkers consumed by airy abstractions” (44). Yet if pure mathematics were lofty, its growing counterpart of applied mathematics offered an alternative contribution to defense work seen on both sides. It was topologist-turned-statistician John Tukey’s proposal to create a separate division for applied mathematics within the American Mathematical Society that encapsulated a new mathematical “type” born out of war research, a new professional identity fashioned as a mathematician by training and scientist by discipline.

The second chapter takes on the consequences of the division between pure and applied mathematics in the immediate postwar period. Here the main challenge was the development of applied mathematics, which experienced a catch-22. While the field increasingly received monetary support from the federal government, such funding at the same time served to detract the field from certain mathematical activities. Conscious of these effects, mathematicians became aware that the “reliance on defense money” served to set applied mathematics “apart institutionally and organizationally from pure mathematics” (128). Historical actors outside of the established mathematical community thus came to help underwrite epistemological differences. Yet, the upshot was—from the efforts of mathematicians like Stone and MacLane—that pure mathematics “continued to receive federal support” (144). This was done primarily by appropriating the ideology of basic research into the rhetoric of applied promise and returns.

Chapter 3 deals with a more specific and equally significant aspect of reinforcing the construction of two opposing professionalizing mathematicians, the establishment of training programmes at Brown University and NYU. Here the two key movers were Dean R.G.D. Richardson at Brown and Richard Courant at NYU. Tracing each figure’s conceptualization of how applied mathematics should be taught and for what ends, Alma shows poignantly what was at stake in seemingly administrative tasks: a “social distinction” in which “the question of how to train applied mathematicians became how to produce mathematicians whose interests and attitudes were those desired” (197). Producing a body of applied mathematicians centered not around shared practices, skills, or subject matter, but rather on a shared set of norms and values.

Chapters 4 and 5 turn to the decades of the 1960s and 1970s, in which the former decade reflected unprecedented growth for the mathematics discipline, and the latter, a job market crisis. In these chapters Alma reveals how pure mathematics followed a different path to its applied mathematics counterpart. The development of mathematics as an abstract field with no direct relation to the external world actually increased in this period, maintaining some form of autonomy. And in this instance applied mathematics served as a “mediator” between “core mathematics and science” (252). Picking up from there, Chapter 5 turns to the response of the mathematical community to a job market crisis that ensued from decreased funding for the sciences. Reactions ranged, from summer institutes providing mathematicians with continuing education in fields such as statistics and computing, to a more radical resolution for graduate students to attain a second “saleable skill” in the area of applied mathematics. Such responses highlight the mutually inclusive relationship of scientific ideas to academic and governmental institutions. This illustration of mathematics’ development, then, demonstrates the malleability of the boundaries of knowledge.

This dissertation represents a major contribution to the field of STS and the history of mathematics. It brings together in one sustained examination of professionalizing American mathematicians public and private insights into the imagination of mathematical identities. Alma accomplishes this even further while displaying a complex grasp of the questions involved that surpass earlier treatments, incorporating mathematics into STS and history of science literature. Alma’s dissertation, then, should speak directly at once to core audiences for the subject—historians of mathematics and the Cold War most notably—and to other seemingly disparate groups. They will come away from this dissertation with a greater appreciation for the professionalization and development of mathematics, a seemingly unchanging and stable discipline, as contingent on where it is culturally and socially embedded.

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