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. Restoring Computational diagrams From Thirteenth-Century Chinese Mathematical WorksKarine Chemla (School of Mathematics)In contrast to the earliest extant mathematical works in Chinese, those composed in the 13th century include what we might call computational diagrams. However, the surviving ancient editions of these works present considerable variations in important features of these diagrams. This talk intends to compare how different ancient editions of the same work diagrammatize the same computations and to examine the extent to which we can retrieve the features of the original diagrams. 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. Restoring Computational diagrams From Thirteenth-Century Chinese Mathematical WorksKarine Chemla (School of Mathematics)In contrast to the earliest extant mathematical works in Chinese, those composed in the 13th century include what we might call computational diagrams. However, the surviving ancient editions of these works present considerable variations in important features of these diagrams. This talk intends to compare how different ancient editions of the same work diagrammatize the same computations and to examine the extent to which we can retrieve the features of the original diagrams. 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.
