4.6 Article

Abstract relations: bibliography and the infra-structures of modern mathematics

期刊

SYNTHESE
卷 198, 期 SUPPL 26, 页码 6277-6290

出版社

SPRINGER
DOI: 10.1007/s11229-020-02683-3

关键词

Bibliography; Infrastructure; Structuralism; Abstracting; Abstraction

资金

  1. Dartmouth College Society of Fellows
  2. National Science Foundation [SES 1826891]
  3. Grattan-Guinness Archival Research Travel Grant

向作者/读者索取更多资源

Mathematical abstracting played a crucial role in reshaping mathematical research and theories in the mid-twentieth century, coinciding with the adoption of symbolic and conceptual abstraction across mathematical fields. The study contextualizes mathematical abstracting within the early twentieth century and explores its impact on the latter half of the century and beyond. My analysis connects the changing social structure of modern mathematical research communities with their evolving domains of investigation and resources for representation and collective understanding.
Beginning at the end of the nineteenth century, systematic scientific abstracting played a crucial role in reconfiguring the sciences on an international scale. For mathematicians, the 1931 launch of the Zentralblatt fur Mathematik and 1940 launch of Mathematical Reviews marked and intensified a fundamental transformation, not just to the geographic scale of professional mathematics but to the very nature of mathematicians' research and theories. It was not an accident that mathematical abstracting in this period coincided with an embrace across mathematical research fields of a distinctive form of symbolic and conceptual abstraction. This essay examines the historical, institutional, embodied, and conceptual bases of mathematical abstracting and abstraction in the mid-twentieth century, placing them in historical context within the first half of the twentieth century and then examining their consequences and legacies for the second half of the twentieth century and beyond. Focused on scale, media, and the relationship between mathematical knowledge and its forms of articulation, my analysis connects the changing social structure of modern mathematical research communities to their changing domains of investigation and resources for representation and collective understanding.

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