{"id":4031,"date":"2026-03-09T20:55:04","date_gmt":"2026-03-10T03:55:04","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=4031"},"modified":"2026-03-22T21:58:02","modified_gmt":"2026-03-23T04:58:02","slug":"the-alchemy-of-mixing-mathematics-the-second-annual-ccms-workshop-in-the-history-and-philosophy-of-mathematics","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/the-alchemy-of-mixing-mathematics-the-second-annual-ccms-workshop-in-the-history-and-philosophy-of-mathematics\/","title":{"rendered":"The alchemy of mixing mathematics: The second annual CCMS 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 interacts and expands across other fields of study.<\/span><\/p>\n

Please RSVP here by Monday, April 6th to attend the workshop and lunch.<\/a><\/p>\n

\n

Schedule<\/i><\/p>\n

10:00 to 10:05<\/strong> Welcome!<\/p>\n

10:05 to 11:05<\/strong> Ot\u00e1vio Bueno (University of Miami & Tohoku University), “Why there are no styles of mathematical reasoning”<\/p>\n

11:10 to 12:10<\/strong> E. L. Meszaros (Brown University), “Algorithmic translations and interpretations of late Babylonian mathematics”<\/p>\n

12:10 to 1:20<\/strong>\u00a0Lunch<\/p>\n

1:25 to 2:25<\/strong> Jed Buchwald (CalTech), “The winding trail to Newton’s\u00a0Principia<\/i>”<\/p>\n

2:30 to 3:30<\/strong> Mate Szabo (University of Southern California), “Turing\u2019s machines and Max Newman\u2019s symbolic machinery for mathematical physics”<\/p>\n

\n

Abstracts<\/em><\/p>\n

\n

Ot\u00e1vio Bueno (University of Miami & Tohoku University), “Why there are no styles of mathematical reasoning”<\/span><\/p>\n

The notion of style of scientific reasoning has been used as an analytical tool for the characterization of significant features of scientific practice (in particular, by Crombie [1994], Hacking [2002], and Granger [1988]). Styles of scientific reasoning are different from scientific theories in a given domain of inquiry: styles are broader than theories, and they are not so dependent on features of the particular domain. In this work, I have two main goals. I\u2019ll first provide a characterization of the concept of style of reasoning that overcomes some difficulties that have been raised against this tool (by Bolduc [2014]). I\u2019ll then argue that, despite the broad conception of style I defend, there is no suitable way of formulating a notion of style of mathematical reasoning. Mathematics, I\u2019ll argue, is too malleable, and attempts at characterizing a notion of style in geometry, analysis, algebra or set theory end up yielding just more mathematical theories particular to these domains. Mathematical practice is significantly different from scientific practice in this respect.<\/span><\/p>\n

E. L. Meszaros (Brown University), “Algorithmic translations and interpretations of late Babylonian mathematics”<\/p>\n

Initial investigations into Babylonian mathematics as \u201calgorithms\u201d began, intuitively, by interrogating the large corpus of Old Babylonian mathematical texts. Donald Knuth viewed these prose maths problems as examples of algorithms, though many scholars of Babylonian cultures and languages disagreed with this characterization. However, recent studies have demonstrated the value of looking for algorithms among other corpora, particularly astronomical texts. While astronomical procedures demonstrated more algorithmic characteristics, they also highlighted uniquely Babylonian tendencies. Whether these texts can be truly considered \u201calgorithmic\u201d becomes less important than whether the algorithmic lens as a tool of analysis can shed light on new aspects of the science and mathematics contained within the tablets. This talk examines the application of the term \u201calgorithm\u201d to less frequently considered Late Babylonian mathematics. While this corpus remains small, the few examples that have been recovered show characteristic differences from their Old Babylonian counterparts, making it valuable to reconsider the application of the term algorithm and the algorithmic lens of investigation. Beginning with an introduction to the corpus and what makes it different from earlier mathematical texts, this talk then makes the case for viewing these later texts algorithmically. Comparisons to Babylonian algorithmic forms and cultures, particularly arising from the astronomical sciences, will be made and evaluated for use within the field.<\/p>\n

Jed Buchwald (CalTech), “The winding trail to Newton’s\u00a0Principia<\/i>“<\/p>\n<\/div>\n

Throughout the years between his first engagement with mathematics under Isaac Barrow and the production of the manuscript that evolved into Book I of the\u00a0Principia<\/i>, Newton was only sporadically engaged by issues of motion, whether earthly or astronomical. His first concerted interest involved collisions, which he modeled on the material circumstances of a springlike mechanism. In doing so, and in a subsequent turn to circular motion, the young Newton presumed without comment what would later be formalized as the\u00a0Principia<\/i>‘s three laws of motion. He was hardly the only one, at least in England, to make such presumptions. We will discuss this early work in order to unpack what transpired when, in 1679, Newton responded to a letter from Robert Hooke, his former critic in optics. We’ll then consider what in consequence took place following the famous visit to Newton by Edmond Halley in 1684. If time allows, we’ll conclude with a brief examination of the interesting reaction of the mathematician John Wallis to Newton’s manuscript account of fall under resistance, sent to Wallis for comment by Halley two years before the\u00a0Principia<\/i>. In so doing we will see that the fundamental key to the novelty of Newton’s work at that time consisted in the specific manner according to which he discretized motion change.<\/p>\n

Mate Szabo (University of Southern California), “Turing\u2019s machines and Max Newman\u2019s symbolic machinery for mathematical physics”<\/p>\n

While Turing\u2019s \u201cOn Computable Numbers\u2026\u201d from 1936 and its impact is well studied, much less is known about Turing\u2019s early influences. The aim of this talk is to show how Max Newman, who taught Turing in Cambridge and was later his boss in Bletchley Park and at the University of Manchester, influenced his early work. Indeed, Turing\u2019s interest in the \u201cEntscheidungsproblem\u201d stemmed from Newman\u2019s lectures on the foundations of mathematics he attended in 1935. While Newman is known as a combinatorial topologist, he was the first to teach a modern, Hilbert style mathematical logic course in the UK. In addition, he frequently engaged with the Cambridge philosophers during the 1920s and 1930s. His interest in scientific philosophies most likely stems from his visit to Vienna during the 1922\/1923 academic year, where he came in touch with members of the famous Vienna Circle. Indeed, his unpublished dissertation, The Foundations of Mathematics from the Standpoint of Physics (1923), shows strong influences of the Vienna Circle. Newman\u2019s aim in the dissertation is to build up mathematical physics as a \u201csymbolic machinery\u201d for manipulating \u201ca body of ‘logical axioms\u2019 and a set of ‘physical assumptions\u2019\u201d. This leads to the parallel development of an ‘epistemic logic\u2019 to deal with ‘beliefs\u2019 and ‘judgements about sensations\u2019 on the physical side, and the description of logic as acts, performances and processes of symbol manipulation. After a careful look at the dissertation I will bring out the surprisingly strong resemblances (as well as the important differences) between Newman\u2019s treatment of mathematical activities and Turing\u2019s analysis of the human \u201ccomputor\u201d.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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