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Histories of mathematical practice account for mathematical knowledge and action by interpreting presently-available evidence as traces of the events, contexts, and relations that make up the past. Interpretations depend on the assumptions one makes about how mathematical knowledge works, insofar as it is knowledge and insofar as it is mathematical. Though the specific rules and their meanings can differ from context to context, mathematics is a kind of ruly knowledge, expected to follow orderly patterns and principles wherever it is found. The contexts and activities of mathematical practice--how that knowledge is made, shared, applied, and understood--are necessarily less ruly, and different practices leave or occlude different kinds of evidence for historical interpretation. The apparent ruliness of mathematics can be both a resource and an obstacle for understanding its unruly pasts. Historians' interpretive assumptions and goals have been shaped by centuries of interaction between mathematics research, history, and education. As a guide for mathematics educators and education researchers to historical perspectives on mathematical practice, this article briefly introduces four major interpretive traditions that inform the present discipline of mathematics history. It then illustrates some interpretive approaches and challenges through the history of blackboards in mathematical practice before explaining the two broad kinds of historical interpretation applied to mathematical practices. Reconstruction involves understanding the conditions and contexts of practices in a single historical moment. Genealogy, by contrast, connects elements of the past across time through transmission, interpretation, adaptation, and other kinds of preservation and change.

The article discusses the introductory history of science course at the University of Edinburgh. The course, which has been offered since 1972, aims to provide students with a broad understanding of the history of science and its relevance to their lives. The course is designed to be flexible and allows students to choose their own readings from a curated resource list. The course materials are arranged thematically, covering topics such as cosmologies, abstractions, lives, bodies, quantities, and objectivities. The author also mentions the use of a kaleidoscope as a metaphor for the course, emphasizing the diversity and dynamism of the field of science. The course materials are freely available online under a Creative Commons license. [Extracted from the article]

Nothing ever works quite as imagined. When algorithms and mathematical systems work, to the extent they do, imagination makes all the difference. Work, imagination, and the space between them manifest in mediated practices of conceptual figuration sustained through regimes of remediation: repair, correction, backfilling, but also (as a pun) patterns of mediation and material transmutation. Such remediation links algorithmic practice and fantasy from early modernity to the present, from the elementary to the elite. It makes whole small errors and grand systems alike. I explore these remediations and their relationship to materials, labor, and fantasy through an episodic account of sixteenth-century arithmetic, nineteenth-century blackboards, twentieth-century projects to create global infrastructures and universal foundations, and twenty-first-century tests of the promises and limits of mediated imagination in mathematics. [ABSTRACT FROM AUTHOR]

A recent controversy involving the Notices of the American Mathematical Society and questions of politics, racism, and the appropriate role of a professional mathe- matical organization began with a comparison to events the American Mathemat- ical Society confronted in 1950. A close look at the AMS's own archives for that period shows that the controversies that vexed the society around 1950 do indeed resonate strongly with those of today, but not in the ways recently suggested. Then, as now, the AMS confronted allegations of political and viewpoint discrim- ination in universities, the challenges of structural racism in American education and society, and the proper place of the AMS as a leading national organization in an international community. Then, as now, mathematicians actively debated how their membership in a professional community related to timely matters of social, political, and racial justice. Among the mid-century controversy's legacies is the Notices itself, created in part out of dissatisfaction with communication channels for involving members in political decisions. [ABSTRACT FROM AUTHOR]