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## Full-Text Articles in Philosophy

Book Review: What Is A Mathematical Concept? Edited By Elizabeth De Freitas, Nathalie Sinclair, And Alf Coles, Brendan P. Larvor

#### Book Review: What Is A Mathematical Concept? Edited By Elizabeth De Freitas, Nathalie Sinclair, And Alf Coles, Brendan P. Larvor

*Journal of Humanistic Mathematics*

This is a review of *What is a Mathematical Concept?* edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms ‘mathematical’ and ‘concept’. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question ‘what is a mathematical concept?’ from the philosophy of mathematics. This review comments ...

Academia Will Not Save You: Stories Of Being Continually “Underrepresented”, Lynette Deaun Guzmán

#### Academia Will Not Save You: Stories Of Being Continually “Underrepresented”, Lynette Deaun Guzmán

*Journal of Humanistic Mathematics*

My entire life I have had to navigate educational structures labeled (by other people) as “underrepresented” in my fields—mathematics and mathematics education. As many people who are similarly labeled in this way know, this meant I had to navigate oppressive structures that positioned me as lesser (e.g., white supremacy, patriarchy). Making sense of these repeated interactions, I wrote my dissertation as a series of three articles, each prefaced with an essay that situated a broader social, cultural, and political context and also connected to my lived experiences navigating academia. These essays were some of my most personal academic ...

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

#### Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

*Journal of Humanistic Mathematics*

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of *qukaq* [center] and *ayagneq* [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry ...

Wabi-Sabi Mathematics, Jean-Francois Maheux

#### Wabi-Sabi Mathematics, Jean-Francois Maheux

*Journal of Humanistic Mathematics*

Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabi-sabi mathematics” by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematics

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

#### Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

*Journal of Humanistic Mathematics*

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was *not* misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the ...