Abstract
Insofar as library science is concerned, modern classification of mathematical subjects occurred within the larger framework of library classification, a vast project receiving sustained attention in the period from 1870 to 1920. The work of the library cataloguers was carried out against the background of a broad nineteenth-century interest in the classification of knowledge. We explore different views during this period concerning the position of mathematics in the overall scheme of knowledge, the scope of mathematics, and the internal organization of the different parts of mathematics. We examine how mathematical books were classified, from the most general level down to the level of particular subject areas in analysis. The focus is on the Library of Congress classification system in its various iterations from 1905 to the present.
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Notes
- 1.
LaMontagne (1961, 208) observes that Charles Cutter “foresaw the continuing growth of the library and knew that each change in the shelving of books entailed the changing of ‘shelf marks’—a long and expensive process. Cutter therefore decided to abandon fixed location ‘and to adopt a method which would allow books to be moved without changing the marks on the catalogues.”’ The part in quotation marks is from (Cutter 1882, 6). Cutter’s “bench marks” are what we refer to today as call numbers.
- 2.
For a general survey of work on classification in the nineteenth century see Dolby (1979).
- 3.
Flint (1904, 222–223 and 308–312) gives accounts of the classifications of Renouvier and Goblot.
- 4.
English translation is by Thomas J. McCormack from the 1893 English edition of Mach’s book, The Science of Mechanics; A Critical and Historical Account of Its Development (Open Court, Chicago).
- 5.
Flint (1904, 277) mistakenly gives the date of publication of Masaryk’s book as 1866. Masaryk was born in 1850 and entered the University of Vienna in 1872.
- 6.
An exception to the prevailing consensus was Karl Pearson, who in his Grammar of Science (1892) put theory of functions and calculus together with arithmetic and algebra, these subjects dealing with quantity, while geometry was classified as a distinct subject area dealing with space (Flint p. 296). Earlier the Paris book seller Jacques-Charles Brunet (1814, 1860) in his pioneering classification scheme placed mathematical subjects in the order arithmetic, algebra, calculus, and geometry. Brunet was presumably influenced by Comte and Ampère. Brunet’s catalogue was exceptional among all classification schemes in placing mathematics at the end of the sciences, following philosophy, physics, chemistry, geology, biology, and medicine.
- 7.
Göbel (2008, 9–13) observes that “Später bildeten diese Abschnitte die Grundlage für den Aufbau einer Mathematik-Klassifikation.” (“These divisions later formed the basis for the construction of a mathematics classification.”)
- 8.
- 9.
While there is a general conservatism among librarians with respect to classification, in the case of the Dewey Decimal system there have been revisions of the classification that have been retroactively applied by some libraries to books in their collections. For example, before 1970 books on analysis were classified by Dewey under 517 (after geometry), whereas after 1970 such books were assigned the classification 515 (before geometry). In the public libraries of Cleveland and Cincinnati the older books retain their original classifications. However, in the library of the University of Illinois at Champaign-Urbana, where the Dewey system is used, the older books on analysis have been assigned the new classification numbers. This is also generally true of the Toronto Public Library.
- 10.
There was not complete consistency in cataloguing during the transition years between about 1968 and 1972. It should also be noted that books on real analysis were sometimes assigned 517 rather than 517.5 (before 1970) and 515 rather than 515.8 (after 1970).
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Acknowledgements
I would like to thank Hardy Grant for advice on an earlier draft of this paper and Matthew Edwards for helpful discussions. I am grateful to two referees for their comments on the paper. I am also grateful to Noah Stemeroff for help with LaTeX and for his careful proof reading of the paper.
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Fraser, C. (2017). Mathematics in Library Subject Classification Systems. In: Zack, M., Schlimm, D. (eds) Research in History and Philosophy of Mathematics. CSHPM 2016. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-64551-3_12
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