The Colonial Legacy of European Mathematics in the Americas: Baroque, Creole, Mixed

• In Event: Unforgetting Settler Colonial Histories of Science and Mathematics Education

Abstract

Objectives
More historical research is needed to understand how European mathematical practices of the 17th century came to be packaged as curricular “compendia” and incorporated into colonial efforts in the Americas. This presentation introduces the concept of a baroque-creole ‘mixed mathematics’ to describe the mathematics archive at the Biblioteca Palafoxiana in Puebla, México, founded in 1646 as the first public library in the Americas, and a crucial historical record of settler mathematical knowledge. We describe various compendia texts written by European and criollo mathematicians (Spanish heritage people born in México) who produced mathematical knowledge for both pedagogical and scientific purposes. Our aim is to show how settler colonial mathematics was a paradoxical mix of practical and speculative practices, where geometric astronomy and the combinatoric mathematics of polyphonic musical instruments served to appropriate Indigenous knowledge as part of baroque-creole perspectivism.

Perspectives
This research is situated within the field of Critical Curriculum Studies (Apple, 2018; Au, 2012; Helfenbein & Huddleston, 2021) and Postcolonial Curriculum Studies (Tuck & Yang, 2012), recognizing that the process of colonization continues through curriculum (Tuck & Gaztambide-Fernández, 2013). Calls to decolonize the mathematics curriculum have multiplied across North America and Europe, but have been challenged by long-standing assumptions that mathematics is independent of place and situated practice (Borovik, 2023). We read the curricular archive alongside historical research focused on Creole cultures (More, 2013; Zamora & Kaup, 2010; Bauer & Mazzotti, 2009).

Mode of Inquiry
We study curricula as an archive of collective practices and ‘major’ ideas endorsed by the state/institutional body, often erasing ‘minor’ mathematical practices (de Freitas & Sinclair, 2020) and eliminating the possibility for other ways of doing curriculum (Appelbaum & Stathopoulou, 2016). Through recognizing curriculum as an alchemical process (Popkewitz, 2004) that transforms knowledge for the purpose of instruction and colonial conquest, this project exposes the ways in which knowledge is selected, revised, combined, and represented.

Sources
Archival research within the Palafoxiana library was undertaken during six weeks of onsite field work, along with consultation of existing information about the movement of books in the Americas at this time (Beristáin, 1816–1821; García Icazbalceta, 1981; de Eguiara y Eguren, 2010; Medina, 1991).

Substantiated Conclusions
This research shows that early colonial mathematics curricular materials in the 17th century mixed geo-political practices (astronomy, cartography, fortress building) with metaphysical assumptions about mathematics as artifice and occult knowledge, linking practical and speculative perspectives. We show how 17th century criolli sustained a paradoxical intellectual space where modern physico-mathematical knowledge was assembled with ancient Indigenous knowledge, as a way of recasting settlers as inheritors rather than conquistadors of the land, and as sovereign actors intent to create an identity distinct from imperial Spain.

Significance
This research is significant for how it exposes the distinctive physico-mathematics curriculum that emerged in 17th century New Spain, as part of settler colonialism. It also develops cross-disciplinary research methodologies in curriculum studies by bringing together historians, archivists, and education researchers.

Authors

• Nathalie Sinclair, Simon Fraser University

• Elizabeth De Freitas, Adelphi University