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Short abstract:

I shall critically interrogate the trope that "mathematics is everywhere" and consider alternative models for public and practitioner understanding of mathematics derived from social studies of the locations of (and processes of relocating) mathematical knowledge and practice.

Long abstract:

The trope that “mathematics is everywhere” has been a pervasive component of both public and practitioner discourses about mathematics, its role in the world, and its claims to sociopolitical and scholarly importance. When UNESCO launched the annual International Day of Mathematics “worldwide celebration” on 14 March, 2020, “mathematics is everywhere” was chosen as the inaugural theme. A contemporary legacy of a centuries-long history of mathematization of the sociomaterial world, this trope and companion discourses (for instance the idea of “hidden mathematics” in commonplace objects and experiences) have misleadingly naturalized mathematical theories and applications while counterproductively distracting from place-based accounts of the production and mobilization of mathematical meaning. I shall offer a critical interrogation of the genealogy and effects of the “mathematics is everywhere” trope and examine how a critical study of the location of mathematical knowledge and practice provides not just a more sociologically and historically appropriate account of mathematics but also a better foundation for public and practitioner understanding of the discipline, capable of speaking to the role of mathematics in the production of social inequality and of social inequality in the production of mathematics. My account draws especially from my research on the history of globalization of mathematics, and of the persistence of place and particularity in the negotiation of putatively universal mathematical knowledges and practices.

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Long abstract:

Calls for the decolonization of mathematics curriculum have multiplied across North America and Europe, both within school systems and at Universities (Borovik, 2023). Debates about the mathematics curriculum are particularly complex as many mathematicians believe mathematics to be a lingua franca (i.e., independent of place and situated practice) and are thus resistant to the suggestion of mathematical pluralism. More historical research is needed to understand how specific European mathematical practices of the 17th-18th century came to be packaged as curriculum “compendia” and incorporated into colonial efforts in the Americas. This presentation reframes the concept of 17th century ‘mixed mathematics’ in the colonial context of 17th century México, expanding the concept to incorporate a larger geo-political perspective on the transit of materials and ideas. As a point of focus, we discuss 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 are interested in various Compendia texts written by European and Criollo mathematicians (Spanish heritage people born and raised in México) who selected, compiled and re-packaged mathematical knowledge for both pedagogical purposes and to support scientific enterprise. We discuss whether this archive offers evidence of a distinctive baroque-creole mathematics emergent at this specific historical time and place (Zamora & Kaup, 2010).

References

Borovik, A. (2023). Decolonization of the curricula. Mathematical Intelligencer. vol 45(2), pp. 144-149.

Zamora, L. P., & Kaup, M. (Eds.). (2010). Baroque New Worlds. Duke University Press.

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Long abstract:

Many scholars have described the formatting power that mathematics has had and continues to have in and on society, shaping technologies and systems and also naturalizing the classification and ordering of humans. As math educators, we often wonder what (else) primary and secondary students learn about/from mathematics when they are learning mathematics in school. One possibility is that how we come to know mathematics, or what we learn mathematics is, structures how we make sense of possible relations. For example, we consider Barad’s treatment of Fernandes’ geographies as a response to Cartesian understandings of identity. Although Crenshaw and other feminists of color have conceptualized intersectionality as dynamic vulnerabilities to power, those of us who have been asked since early childhood to plot points on numberlines (and later, on two- and three-dimensional coordinate planes) might find it more familiar to make sense of identity as the stable intersection of fixed social locations on a set of axes, leading to simplistic notions of hierarchy and oppression.

Could alternative orientations to space (Barad suggests topology) unsettle the mathematical metaphors– dare we say ontologies– that stifle more critical relational possibilities? Can coming to know mathematics differently transform how we are with one another? We bring a collection of empirical examples from education research literature and seek to re-read them with mathematicians and scholars of mathematics to find openings for critical transformations of what mathematics is and how students can come to know mathematics and, therefore, of what relations become possible through these transformations.

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Long abstract:

The goal of this session is to explore the social collaborative nature of mathematical work through a critical examination of the interactions between two professional mathematicians engaged in an afternoon of reading, writing, and mathematical problem solving. Drawing on Goodwin’s (2003) conceptualization of the semiotic body in its environment, my broader work is interested in offering an account of mathematics as an embodied practice that is accomplished through social interaction, the recruitment of tools, the creation of artifacts, and a coordinated assemblage of these tools, artifacts, and actors. Focusing on excerpts of interactions and events from an afternoon spent around the kitchen table with mathematicians Natalie and Usman, in this session we will unsettle normative understandings of mathematics as a non-material, abstract practice, instead making an intersectional queer feminist case for the embodied, concrete, social-relational nature of mathematical knowledge production.

The session being proposed will be run as a data-workshopping session using the methods of collaborative critical Interaction Analysis (Jordan & Henderson, 1995). Together, participants will look at excerpts of video data of the two focal mathematicians working together to develop a mathematical concept for a paper they are writing. We will draw on postcolonial feminist perspectives (Ahmed, 2006) to make sense of how mathematical work unfolds, with the specific goal of understanding knowledge production in mathematics as a result of social-interactional, embodied, and emplaced negotiations.

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Long abstract:

Practices of knowing and making are deeply embedded in their specific cultural contexts. Science and Technology Studies (STS) has leveraged sociotechnical controversies to render this embedding visible. In this paper, we explore a series of scientific controversies that center on an intriguing idea: emptiness. Whether it shows up as zero in mathematics, vacuum in physics, absence in psychology, or nothing in metaphysics, emptiness keeps resurfacing across different domains of knowledge, stirring debate wherever it appears. Rather than mapping these controversies in isolation, we adopt a comparative approach, identifying isomorphisms, or abstract patterns that recur across the cases. Such patterns suggest a recurring motif within the European intellectual tradition, a coherent genre of “empty controversies” characterized by discernible traits. The broad contours of such a genre are already somewhat visible: such concepts encounter resistance when they are introduced, often due to the perceived opposition between emptiness and materialism; the resistance is often accompanied by accusations of mystification, heresy, and obscurantism; if/when these concepts overcome the resistance and integrate themselves into the field, they pave the way for downstream conceptual work. Beyond highlighting shared characteristics and proposing an overarching genre, structural isomorphisms may allow us to translate concepts, problems, and problem-solving strategies across fields in generative ways. The neuroscientist Terrence Deacon, for example, has argued that integrating a concept of absence into the sciences of life and mind will have as seismic an effect as the integration of zero in early modern European math. Such translations can foster interdisciplinary research.

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Long abstract:

Topology is widely used in the social sciences to metaphorically render complex relationalities of individuation and transformation. Cases often involve the invocation of a phenomena which raise specific questions of their continuity over space, time, and experience, and the most direct uses of topology often invoke varied geneaological references to ideas of structure. However, these projections of "topological" qualities often carry with them an affect and analytic of excess - of absolute fluidity, of the absence of fixity, of the arbitrariness of connection. The poetic force such excesses paradoxically elicit raises interesting questions concerning the use of topology as an infrastructure of description, in that it often entails the improper description of model "topological" phenomena. What appear as properties of a properly "topological" object, such as the Möbius strip, often arise from the visualisation of their embedding, or a perspectival interaction between the dimensional properties of a surface and the dimensional properties of the space in which it is rendered, where the object appears as an artefact having given properties in a neutral context. In this paper, I will address the possible implications of taking the elicitation of context as interpretive device in ethnography as a relational objectification of embedding, looking specifically at the relation of self-intersection as marking an infelicitous embedding. In this way, I hope to provide a reflection on the political economies of commensuration that give rise to the intelligibility of perspective as a question of anthropological method.

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Short abstract:

Materiality is an important framework for understanding how knowledge is produced through interactions between mathematicians and their tools and contexts. I use preliminary archival research on Benoit Mandelbrot to consider the political implications of focusing on different forms of materiality.

Long abstract:

Scholars of both mathematics and STS more broadly have brought attention to the material aspects of knowledge production in the sciences. Materiality is an important framework for understanding how mathematical knowledge is produced through interactions between mathematicians and their tools and contexts. Such understandings are a productive step toward recognizing, and, crucially, undoing, connections between mathematics and political violence. In this contribution, I investigate the political commitments and calls to action that come from attending to different materialities. Using preliminary archival research on Benoit Mandelbrot, IBM fellow and “father” of fractal geometry,” I focus on the material aspects of fractal research – the visualization of fractals, the computing resources at IBM, and the ties to extraction industries. With these examples, I ask how we, as scholars, should approach the study of materialities that are more or less explicitly political. What are the stakes, for example, of focusing on the ties between Mandelbrot and weapons manufacturers, or between Mandelbrot and institutions central to the Israeli apartheid regime like the Technion? What about less explicitly political materialities such as fractal visualizations? This methodological question attends to what directions of study are the most fruitful on a scholarly level, but, more importantly, it asks what connections and relationships are most fruitful for enacting calls to action. Through a few examples, I suggest that to only focus on the most explicitly political aspects is a disservice that makes the work of organizers aiming to disrupt mathematical systems of violence and harm more challenging.

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Short abstract:

In this presentation, you are welcome to take a look at the poster which will give you a general tour of the development and transformation of the public engagement of mathematics in China.

Long abstract:

The development of public engagement of mathematics in China has seen lots of vicissitudes. Historically, it evolved from the ancient Chinese mathematics, to the modern western mathematics. The main areas it focused went from politics, agriculture, to industries, economy, and culture. The forms of mathematical engagement are mostly books, lectures, but some are interactive games, competition awards, and few are exhibitions or event venues. In terms of content, introductions to mathematical knowledge, methods, and education views used to be the mainstream, which were relatively simple and narrow, for a single group, mostly teenagers and professionals. Moreover, in this era of fast-paced life, most people like short, entertainment videos, which makes it more difficult for people to calm down and learn mathematics, harder to appreciate the fun in mathematics. However, some work occurred a decade ago including histories and cultures of mathematics, mathematician biographies, and international views, which have re-energised the public engagement of mathematics in China. In this presentation, you are welcome to take a look at the poster which will give you a general tour of the development and transformation of the public engagement of mathematics in China. By discussing relevant topics with the presenter, you may exchange ideas of how to make math more popular to the public.

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Long abstract:

In the early 1970s, almost 95% of all pure math papers were single-authored, by 2010, only 30% of math papers were. Co-authoring has changed how math papers are written over the course of the past fifty years in some patterned ways, most notably offering new forms of divisions of labor, and accompanying labors of division of roles, to the task of writing a math paper. This has, as a consequence, produced a proliferation of role-fractions that can accompany mathematical co-authorship. It has been happening at the same time as changes in NSF and other grant funding bodies evaluation regimes were occurring, creating evaluative practices in grant funding that greatly influenced mathematical careers. Yet all of the changes happening in math co-authorship were made relatively, but not entirely, invisible to interdisciplinary evaluation committees – that is, the academic committees in which the norms of a discipline are often topics of required explication, and can not be presumed to be shared. Why so invisible? Mathematicians practice formal declarations of authorship that conceal, for bureaucratic purposes, the social complexities of the actual authorship practices. In part because mathematicians list their authors alphabetically, and there is a strong norm that no one ever publicly discusses who did what on a co-authored paper. Despite any lived evidence to the contrary, all co-authors of a math paper are taken to have contributed equally significant labor to the text. This paper explores the consequences of the tension between formal authorship and actual practice in theoretical mathematics.