{"id":3632,"date":"2025-01-17T07:37:52","date_gmt":"2025-01-17T15:37:52","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3632"},"modified":"2025-02-10T16:50:46","modified_gmt":"2025-02-11T00:50:46","slug":"the-alchemy-of-mixing-mathematics","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/the-alchemy-of-mixing-mathematics\/","title":{"rendered":"“The alchemy of\u00a0mixing\u00a0mathematics” a one-day workshop in the history and philosophy of mathematics"},"content":{"rendered":"

This one-day workshop assembles diverse perspectives from the history and philosophy of mathematics to examine ways in which mathematics is applied and impure. Topics will range from applications of mathematics in the natural and social sciences to impure proofs that transcend a single mathematical domain.\u00a0<\/span><\/p>\n

Please RSVP here by Monday, February 10th to attend the workshop and identify any dietary restrictions.<\/a><\/p>\n

Location: Avery 201, Pitzer College<\/a><\/p>\n

\n

Schedule of talks<\/strong><\/h2>\n

9:35<\/strong>\u00a0Welcome and opening remarks<\/p>\n

9:40<\/strong>\u00a0E. A. Hunter (University of Chicago) on “Tradition at Play: Reassessing Archimedes\u2019\u00a0Measurement of the Circle<\/i>”<\/p>\n

10:30 <\/strong>Coffee\/tea break<\/p>\n

10:50<\/strong>\u00a0Erich Reck (UC Riverside) on “Structuralist Understanding in Mathematical Practice”<\/span><\/p>\n

11:50<\/strong> Lunch break<\/p>\n

1:00<\/strong> Patrick Ryan (Chapman University) on “Impurity, Simplicity, and Explanatory Proof”<\/p>\n

2:00<\/strong> Claudio G\u00f3mez-Gonz\u00e1les (Carleton College) on “Plants of slow growth: reducing coefficients and sustaining mathematics”<\/span><\/p>\n

3:00<\/strong>\u00a0Coffee\/tea break<\/p>\n

3:20<\/strong>\u00a0Emrys King (Pomona College) on “The Mixing of Eugenics and Statistics in English-Language Pedagogy Across the 20th Century”<\/span><\/p>\n

3:50<\/strong>\u00a0Ainslee Archibald and Jane Panangaden (Pitzer College) on “A Close-Reading of ‘Sterilization for Human Betterment'”<\/span><\/p>\n

4:40<\/strong> (snack) mix post-conference reception<\/p>\n

\n

Abstracts<\/strong><\/h2>\n

E. A. Hunter (University of Chicago) on “Tradition at Play: Reassessing Archimedes\u2019\u00a0Measurement of the Circle<\/i>“<\/strong><\/p>\n

abstract: No other text in the Archimedean corpus has a richer history than\u00a0Measurement of the Circle<\/i>. Such richness comes at a price, however, as many scholars doubt the authenticity of the extant text, citing its seemingly negligent argumentation and the triviality of the second proposition, which also relies on the third’s approximation of pi. These qualities are at odds with our image of Archimedes, leading modern editors to modify the text: E.J. Dijksterhuis relegates proposition two and Thomas Heath omits it entirely.\u00a0This presentation challenges the assumption that the primary aim of ancient Greek mathematicians was axiomatic-deductive rigor. Instead, it situates\u00a0Measurement of the Circle<\/i>\u00a0within its broader literary and intellectual context\u2014one with its own traditions and textual conventions. Through a close analysis of the rhetorical techniques and structural features of the propositions, this presentation reevaluates the text\u2019s authenticity and demonstrates how the propositions function within this framework. While the authenticity of any ancient work will always remain open to debate, a key takeaway is the playfulness present in Archimedes’ mathematical writing. The presentation concludes by reflecting on the fragility of our connection to ancient Greek mathematics and the ways in which modern expectations shape the evaluation of historical sources.<\/p>\n

Erich Reck (UC Riverside) on “Structuralist Understanding in Mathematical Practice”<\/strong><\/p>\n

abstract: When it comes to structuralism in the philosophy of mathematics, the focus is often on metaphysical issues, sometimes supplemented by basic epistemological questions. \u00a0But as I have argued elsewhere, mathematical structuralism had its origins primarily in certain methodological developments, from the late 19th <\/sup>century on, that added up to \u201cmodern mathematics\u201d. \u00a0This brings \u201cmethodological structuralism\u201d into the center of attention.\u00a0\u00a0As a next step, I will now consider how these developments brought with them several distinctive levels or kinds of mathematical understanding. \u00a0For illustration I will go through a number of examples, ranging from Dedekind through Hilbert, Noether, and Bourbaki to recent mathematics. \u00a0In doing so, I will attempt to clarify the sense in which certain kinds of \u201cunderstanding\u201d are important goals in mathematical practice.<\/p>\n

Patrick Ryan (Chapman University) on “Impurity, Simplicity, and Explanatory Proof”<\/strong><\/p>\n

abstract: In this talk, I will argue for an association between impure proofs and explanatory proofs in contemporary mathematics. Broadly speaking, a proof of a theorem \u03d5 is said to be impure if it draws on what is \u201cextrinsic,\u201d \u201cdistant,\u201d or \u201cforeign\u201d to the content of \u03d5. In a similarly broad fashion, a proof \u03c0 of \u03d5 is said to be explanatory if the proof shows why \u03d5 is true, thereby distinguishing \u03c0 from other proofs merely showing that \u03d5 is true. My earlier work has aimed to show how it is even possible for an impure proof to be explanatory. Here, I aim to show how an impure proof can actually generate explanatory power. My contention is that this often occurs because the impure resources produce a particular kind of simplicity that I call \u201cconceptual speed-up.\u201d I justify my philosophical claims via an examination of two central number-theoretic results, Szemer\u00e9di\u2019s theorem and the Prime Number Theorem, and various of their proofs. Finally, I conclude by discussing what my analysis shows about the nature of explanation in mathematics.<\/p>\n

Claudio G\u00f3mez-Gonz\u00e1les (Carleton College) on “Plants of slow growth: reducing coefficients and sustaining mathematics”<\/strong><\/p>\n

abstract: In this talk, we offer a concrete, visual, and historical introduction to resolvent degree (RD), an invariant that aspires to quantify just how hard solving algebraic equations can be. This overview makes contact with the origins of topology, miracles of classical algebraic geometry, and Klein\u2019s \u201chypergalois\u201d program, which dare us to push beyond the solvable\/unsolvable dichotomy. Throughout the talk, we will reflect on the past and future of resolvent problems, institutional processes that shape mathematical consensus, and what we do and do not know about RD. Ultimately, we seek a deeper understanding of how mathematical institutions sustain themselves, particularly in the context of accelerating environmental, economic, and geopolitical crises.<\/span><\/p>\n

Emrys King (Pomona College) on “The Mixing of Eugenics and Statistics in English-Language Pedagogy Across the 20th Century”<\/strong><\/p>\n

abstract: Today, we find ourselves surrounded by statistics and data. However, the omnipresence of statistical methods is a new phenomenon. The first extension of the method of least squares as a means to characterize non-observational error was by Sir Francis Galton, in studies of heredity in the pursuit of eugenics. The initial studies published by Galton were soon extended by Karl Pearson, a professor of statistics and professed eugenicist. I argue that the eugenic beliefs of these men fueled their pioneering studies of linear regression and thus influenced the statistical tools themselves. This merits a further evaluation of the presence of eugenic ideology statistical pedagogy post-Galton. To begin tackling this evaluation, I present a preliminary review of statistics textbooks from 1880-1970, assessed for their citation and\/or approval of eugenic ideology, or lack thereof.<\/p>\n

Ainslee Archibald and Jane Panangaden (Pitzer College) on “A Close-Reading of ‘Sterilization for Human Betterment'”<\/strong><\/p>\n

abstract: The Human Betterment Foundation was a pro-eugenic sterilization think-tank and propaganda organization that operated in Pasadena between 1928 and 1942. At the end of 1929 its founder Ezra Gosney and employee Paul Popenoe published a short booklet entitled \u201cSterilization for Human Betterment: A Summary of results of 6000 Operations in California, 1909-1929\u201d in which they lay out their case for the necessity, safety, and desirability of eugenic sterilization. In this talk we explore differences between the published version of this booklet\u00a0 and an earlier draft with handwritten edits which is located in the Gosney Papers collection of the Caltech archives. We pay special attention to the authors\u2019 use of data and statistics in their arguments while using a variety of archival documents to track their sources and methods of analysis.<\/p>\n","protected":false},"excerpt":{"rendered":"

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