Seminar 5: Diagrammatization of written mathematical practices What is at stake in diagrammatic features of written practices? Views based on Arabic and Chinese sources (Part II)Karine Chemla (School of Mathematics, University of Edinburgh & SPHERE)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: Agathe Keller (LTE, Paris Observatory) Iterated exponentials, powers and iterates: Which diagrammatization? Which symbolism?Ivahn Smadja (Nantes Université & Institut Universitaire de France)This exploratory contribution aims at analyzing a significant shift around 1800 in the way some diagrammatic features of mathematical symbolism were addressed, conceived, and exploited in mathematical practice. As a guiding thread into the thick of it, we will first focus on iterated exponentials, tracing the history of the topic from Euler to the British mathematicians of the Analytical Society, and beyond. A broader purpose, however, is to show how this perplexing issue connects with new ways to think about diagrammatization and symbolism, increasingly brought to the fore in the early decades of the nineteenth century.While commenting on the striking analogy between the Bodhisattva’s calculus in the Lalitavistara Sūtra and Archimedes’ Sand Reckoner, in his Mémoire sur la propagation des chiffres indiens (1863), historian of mathematics Franz Woepcke made an interesting observation, suggesting a watershed in the history of symbolism. The numbers attested in these ancient sources are expressed by means of extended scales of numerical names. They may seem huge, but, Woepcke argued, they are far from marking “the limit of the possible in terms of notation”. He hinted at his own mathematical work on iterated exponentials, taking up and clarifying issues that arose decades earlier. These debates hinged on the role of nested parentheses in defining iterated operations, the status of such symbolic expressions as and further the possibility of constructing an open-ended hierarchy of operations. Unfolding this sequence will lead us to look deeper into the meaning and scope of Arbogast’s so-called “method of separation of symbols”, thoroughly discussed by the British Analysts.Commentator: David Waszek (ENS Ulm, Paris) May 05 2026 13.00 - 17.00 Seminar 5: Diagrammatization of written mathematical practices Join Karine Chemla (School of Mathematics, University of Edinburgh & SPHERE) and Ivahn Smadja (Université de Nantes, IUF) for the fifth seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. JCMB Room 5323
Seminar 5: Diagrammatization of written mathematical practices What is at stake in diagrammatic features of written practices? Views based on Arabic and Chinese sources (Part II)Karine Chemla (School of Mathematics, University of Edinburgh & SPHERE)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: Agathe Keller (LTE, Paris Observatory) Iterated exponentials, powers and iterates: Which diagrammatization? Which symbolism?Ivahn Smadja (Nantes Université & Institut Universitaire de France)This exploratory contribution aims at analyzing a significant shift around 1800 in the way some diagrammatic features of mathematical symbolism were addressed, conceived, and exploited in mathematical practice. As a guiding thread into the thick of it, we will first focus on iterated exponentials, tracing the history of the topic from Euler to the British mathematicians of the Analytical Society, and beyond. A broader purpose, however, is to show how this perplexing issue connects with new ways to think about diagrammatization and symbolism, increasingly brought to the fore in the early decades of the nineteenth century.While commenting on the striking analogy between the Bodhisattva’s calculus in the Lalitavistara Sūtra and Archimedes’ Sand Reckoner, in his Mémoire sur la propagation des chiffres indiens (1863), historian of mathematics Franz Woepcke made an interesting observation, suggesting a watershed in the history of symbolism. The numbers attested in these ancient sources are expressed by means of extended scales of numerical names. They may seem huge, but, Woepcke argued, they are far from marking “the limit of the possible in terms of notation”. He hinted at his own mathematical work on iterated exponentials, taking up and clarifying issues that arose decades earlier. These debates hinged on the role of nested parentheses in defining iterated operations, the status of such symbolic expressions as and further the possibility of constructing an open-ended hierarchy of operations. Unfolding this sequence will lead us to look deeper into the meaning and scope of Arbogast’s so-called “method of separation of symbols”, thoroughly discussed by the British Analysts.Commentator: David Waszek (ENS Ulm, Paris) May 05 2026 13.00 - 17.00 Seminar 5: Diagrammatization of written mathematical practices Join Karine Chemla (School of Mathematics, University of Edinburgh & SPHERE) and Ivahn Smadja (Université de Nantes, IUF) for the fifth seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. JCMB Room 5323
May 05 2026 13.00 - 17.00 Seminar 5: Diagrammatization of written mathematical practices Join Karine Chemla (School of Mathematics, University of Edinburgh & SPHERE) and Ivahn Smadja (Université de Nantes, IUF) for the fifth seminar of the second year of the 'Rethinking the history of mathematical symbolism' project.
