Seminar 2: Diagrammatization of written mathematical practices A problem about matricesMarcus Giaquinto (University College London)This talk concerns a question about the matrices of linear algebra: What, strictly speaking, are they? This is not a practical problem. If you are familiar with matrices (as I assume), you can recognise presentations of them and manipulate them to solve problems. But there are conflicting views among mathematicians about what constitutes a matrix, as revealed by a survey of their definitions. The problem is philosophical. In what follows I examine Alexander Paseau’s attempt to resolve the conflict and to answer the question in his 2016 paper “Philosophy of the Matrix.” Philosophia Mathematica (III) 25(2) 246-267. (Recommended reading, but not needed for the talk). While initially in agreement with Paseau’s proposed answer and favourably impressed by his case, I became increasingly dissatisfied over time. I will give my reasons for dissatisfaction, argue for an alternative answer, and propose a wider view of mathematical entities than is currently standard. Commentator: Célestin Xiaohan Zhou (Institute for the History of Natural Sciences, CAS, & School of Mathematics, The University of Edinburgh)What is at stake in diagrammatic features of written practices? Views based on Arabic and Chinese sourcesKarine Chemla (School of Mathematics)The talk begins with a discussion of Marcus Giaquinto’s book Visual Thinking in Mathematics (2007, Oxford), and in particular with the chapter dealing with calculation and symbolic manipulation. I rely on Arabic and Chinese sources to highlight that they already show evidence of certain benefits associated with symbolic manipulation in the context of arithmetic computation.Commentator: Zehra Bilgin (School of Mathematics, University of Edinburgh & Institute for the History of Science, Istanbul Medeniyet University) Feb 03 2026 13.00 - 17.00 Seminar 2: Diagrammatization of written mathematical practices Join Marcus Giaquinto (University College London) and Karine Chemla (School of Mathematics) for the second seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. JCMB Room 2901
Seminar 2: Diagrammatization of written mathematical practices A problem about matricesMarcus Giaquinto (University College London)This talk concerns a question about the matrices of linear algebra: What, strictly speaking, are they? This is not a practical problem. If you are familiar with matrices (as I assume), you can recognise presentations of them and manipulate them to solve problems. But there are conflicting views among mathematicians about what constitutes a matrix, as revealed by a survey of their definitions. The problem is philosophical. In what follows I examine Alexander Paseau’s attempt to resolve the conflict and to answer the question in his 2016 paper “Philosophy of the Matrix.” Philosophia Mathematica (III) 25(2) 246-267. (Recommended reading, but not needed for the talk). While initially in agreement with Paseau’s proposed answer and favourably impressed by his case, I became increasingly dissatisfied over time. I will give my reasons for dissatisfaction, argue for an alternative answer, and propose a wider view of mathematical entities than is currently standard. Commentator: Célestin Xiaohan Zhou (Institute for the History of Natural Sciences, CAS, & School of Mathematics, The University of Edinburgh)What is at stake in diagrammatic features of written practices? Views based on Arabic and Chinese sourcesKarine Chemla (School of Mathematics)The talk begins with a discussion of Marcus Giaquinto’s book Visual Thinking in Mathematics (2007, Oxford), and in particular with the chapter dealing with calculation and symbolic manipulation. I rely on Arabic and Chinese sources to highlight that they already show evidence of certain benefits associated with symbolic manipulation in the context of arithmetic computation.Commentator: Zehra Bilgin (School of Mathematics, University of Edinburgh & Institute for the History of Science, Istanbul Medeniyet University) Feb 03 2026 13.00 - 17.00 Seminar 2: Diagrammatization of written mathematical practices Join Marcus Giaquinto (University College London) and Karine Chemla (School of Mathematics) for the second seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. JCMB Room 2901
Feb 03 2026 13.00 - 17.00 Seminar 2: Diagrammatization of written mathematical practices Join Marcus Giaquinto (University College London) and Karine Chemla (School of Mathematics) for the second seminar of the second year of the 'Rethinking the history of mathematical symbolism' project.
