## Libraries and Mathematics: Rethinking "the Mathematician's Laboratory"

Organizers

Michael J. Barany

University of Edinburgh

Kevin Lambert

California State University Fullerton

Chair

Joan Richards

Brown University

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Session Abstract

According to a biographical sketch made of him by his friend John Aubrey, Thomas Hobbes first fell in love with Euclid "in a gentleman's library." Placing Hobbes in a seventeenth century library studying Euclid might evoke a contrast with the iconic spaces of early modern demonstration and experimentation, but historians of science have recognized libraries and laboratories as kindred settings of knowledge making. Indeed, for mathematics this kinship may be especially close: twentieth-century mathematician Paul Halmos quipped that "The Library is the mathematician's laboratory." In this panel, we propose historicising libraries as places, both material and ideal, of mathematical knowledge production. Four different material and virtual settings, ranging in time from the end of the eighteenth to the early twentieth centuries, demonstrate different relationships mathematicians have had to libraries as research tools, as home-made intellectual resources, and as platforms for articulating communities and values. Presenters will examine personal and institutional libraries as well as publishing enterprises and assemblages of "hints or references" as achievements of collection, curation, and personal and infrastructural configuration. The aim will be to see libraries not simply as stable sources of settled knowledge but as dynamic resources, open assemblies of print and paper as well as other materials and relations, that were used to produce theories, theorists, institutions, and publics. Far from antithetical or complementary to the mathematical ideals of abstract ideation, these paper collection practices and material assemblies will be shown to be integral features of the mathematical enterprise.

Presenter 1

The Malthus Library: The Library as Cognitive Instrument in the Making of the Malthusian Population Principle

Kevin Lambert

California State University Fullerton

Abstract

Thomas Robert Malthus (1766-1834) is infamous for his argument, made in the first edition of his An Essay on the Principle of Population (1798) that population growth would always outstrip food production. In this paper, I will investigate how Malthus's justified his population principle as a universal bio-mathematical law in the larger and more complex later editions of the Essay. Most of the materials Malthus assembled to write the second 1803 edition of the Essay are preserved at the Old Library, Jesus College, Cambridge. Malthus used that assembly of books and maps as an instrument with which to look across the early nineteenth European, American and Pacific worlds. What he had originally only supposed he was now able to present as a universal principle. Assembling materials to provide an empirical foundation for a universal truth would become an established practice in early nineteenth-century Cambridge. Two of Malthus's closest Cambridge friends William Otter and Edward Daniel Clarke were key figures in the founding of the first lasting Cambridge scientific society, the Cambridge Philosophical Society (CPS), a body known for its collecting practices. And George Peacock, a fellow CPS founding member, would justify his principle of equivalent forms as the foundation for English algebra through the collection of materials and reports from around the world. In my paper, I will argue that when Malthus assembled his library of materials to justify his population principle as a universal bio-mathematical law he prefigured what would later become a characteristic nineteenth-century English mathematical practice.

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Presenter 2

Shaping a Model Library in Göttingen: Felix Klein and the Spaces of Professional Mathematics

Jenne O'Brien

Princeton University

Abstract

Mathematician Felix Klein (1849-1925) was known in equal measure as a pioneering researcher and as an institutional reformer. During his tenure as the mathematics chair at the University of Göttingen from 1886 to 1912, he significantly expanded two of the university's existing libraries, the circulating library of the mathematical-physical seminar and the collection of mathematical models and instruments. Almost immediately after arriving in Göttingen, Klein began a detailed correspondence with far flung mathematicians, enlisting them both as advisors to and suppliers of his collection. Soon after, Klein found the circulating library a physical home in the form of a reading room, not unlike the reading room he had previously set up at Leipzig but arguably unlike any other university space in Germany. The reading room became somewhat illustrious in the history of mathematics, and appears occasionally in mathematicians' memoirs. The room was used not only for individual research but for collaborations and social gatherings, and was distinguished by its locked door for which only students in mathematics and natural sciences were eligible to receive keys. Both the reading room and the instrument and model collection exemplified and supported Klein's vision of mathematics in the nineteenth century, manifesting his inclusions and exclusions of books, tools, and people. These libraries, by uniting objects and books from all over Germany and the world, allow us to examine mathematics in the making at the nexus of material and ideal, local and global. Considering these spaces together as libraries-in-the-making cast in relief the dynamics and considerations of a transitional period in the professionalization of mathematics.

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Presenter 3

Having No Books to Speak Of: The Mathematical Self-Education of Oliver Heaviside

Bruce J. Hunt

University of Texas Austin

Abstract

Oliver Heaviside (1850-1925) made major contributions to many areas of mathematics and mathematical physics, particularly those connected with telegraphy and electromagnetic theory. Working on his own in the 1870s and 1880s, mainly while living with his parents in very modest circumstances in London, he developed the main tools of vector analysis, devised powerful operational methods for solving differential equations, and was the first to cast Maxwell's equations of the electromagnetic field into their now canonical vector form. He did all of this with almost no formal education and with very little access to the published mathematical literature. As he told his friend G. F. FitzGerald in 1894, "Having no books to speak of, I have had to do nearly everything myself, sometimes only on the basis of hints or references." This paper will examine how Heaviside came across those "hints" and proceeded to form himself as mathematical physicist-or, as he liked to call himself, a "physical mathematician." In the process, we will shed light on how Heaviside arrived at his distinctive view of mathematics as an experimental science, as well as on how his relative isolation affected both the direction his work took and the sometimes hostile reception it received from more orthodox mathematicians.

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Presenter 4

The Scripta Mathematica Library and the "Survival" of Mathematics in America

Ellen Abrams

Cornell University

Abstract

In 1934, the Scripta Mathematica Library published The Poetry of Mathematics and Other Essays by David Eugene Smith, Professor of Mathematics at Columbia University Teachers College and former president of the History of Science Society. Smith's collection of essays was the first in a series of publications from the Scripta Library meant to communicate the artistry and virtues of modern mathematics to, as Columbia mathematician Cassius Jackson Keyser called them, "intellectual non-mathematicians." Jekuthial Ginsburg of Yeshiva University had founded the Scripta Mathematica quarterly journal in 1932 during a time when many of its subscribers and contributors, including Keyser and Smith, considered mathematical interests in the United States to be insufficiently supported, if not flat-out under attack. In his review of Smith's Poetry, Caltech mathematician Eric Temple Bell explained that mathematicians must make "a compelling case for democratic support... if mathematics is to survive in America."

Around the Scripta Mathematica grew the Scripta Mathematica Library, the Scripta Mathematica Forum Lectures, and the Society of Friends of the Scripta Mathematica. In this paper, I explore the Scripta infrastructure through which a network of mathematicians, many of whom were based in New York City, sought to demonstrate the importance of mathematics not only to various fields of research and education, but also to individual self-cultivation and national pride. How did the Scripta network conceive of their target audience and of their enemies? What was the relationship between the Scripta's promotion of mathematics as a human endeavor and other efforts to promote mathematics as a benefit to industry and a weapon of war?

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