Seminar 1: Diagrammatization of written mathematical practices Diagrams in Fibonacci’s Extant WorksJens Høyrup (Roskilde University, emeritus)Using a tolerant understanding of what constitutes a diagram, a first section of the talk looks at the diagrams used in Ibn al-Banna’s Talkhīṣ and al-Qalaṣādī's Kašf, which turn out to be restricted to the writing of fractions and composite fraction lines, and a few other instances linked to the Arabic idiom for fractions.The bulk of the talk looks at Leonardo Fibonacci's use of diagrams. Apart from the notations for fractions and ascending continued fractions, he turns out not to borrow from the “learned” madrasah level of Maghreb mathematics. In all his works, he uses rectangular frames that superficially looks like diagrams but are simply indications that numbers are supposed to be written on a whitened board. Beyond that he uses single-line lettered diagrams and Euclidean-style lettered diagrams; most of these show by their lettering to be borrowed from possibly Greek but at least mostly Arabic sources or earlier Latin translations. When geometric objects or situations are illustrated, they are also mostly diagram-like with no naturalistic pretensions. None of this is sensational, and it is comprehensible that Fibonacci's diagrams have attracted little attention.In the end, lettering of Fibonacci's diagrams is taken up in detail, giving substance to the claim that it is informative about Fibonacci's sources and his use of them.Is the mathematical running text a diagram?Roy Wagner (ETH, Zürich)This year’s focus is on the independence of mathematical notation from spoken language and on non-linear aspects of mathematical notation. While the running text encountered in premodern manuscripts often appears to be linear and to have a close correspondence with straightforward reading, the actual practices of engaging with mathematical texts may deviate from this appearance. In my rather speculative intervention, I will try to show in what ways a linear mathematical running text might be viewed as a diagram.I will start with my own reading practices of mathematical texts as a historian of mathematics reading foreign languages in which I have a limited working knowledge. Using Malayalam and/or Italian examples, I will focus on my philological practices of breaking up the text, identifying key anchors and repeated “formulaic” expressions (in the sense defined by Reviel Netz in The Shaping of Deduction), and resolving embedded syntactical structures. During this analysis, I sometimes reorganize the text graphically and, in some sense, turn it into a diagram. Sometimes, I accompany the reading with ad-hoc somewhat diagrammatic symbolic annotations. I will then raise the question: to what extent can such practices be attributed to contemporary readers of mathematical texts? Our limited knowledge of learning and research practices will allow me to offer only tentative guesses. If time permits, I will also consider examples of the non-linear interactions between a running Hebrew text dealing with operations on fractions and an apparently idiosyncratic calculation diagram that accompanies the text in the original manuscript. Jan 06 2026 13.00 - 17.00 Seminar 1: Diagrammatization of written mathematical practices Join Jens Høyrup (Roskilde University, emeritus) and Roy Wagner (ETH, Zürich) for the first seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. JCMB Room 5323
Seminar 1: Diagrammatization of written mathematical practices Diagrams in Fibonacci’s Extant WorksJens Høyrup (Roskilde University, emeritus)Using a tolerant understanding of what constitutes a diagram, a first section of the talk looks at the diagrams used in Ibn al-Banna’s Talkhīṣ and al-Qalaṣādī's Kašf, which turn out to be restricted to the writing of fractions and composite fraction lines, and a few other instances linked to the Arabic idiom for fractions.The bulk of the talk looks at Leonardo Fibonacci's use of diagrams. Apart from the notations for fractions and ascending continued fractions, he turns out not to borrow from the “learned” madrasah level of Maghreb mathematics. In all his works, he uses rectangular frames that superficially looks like diagrams but are simply indications that numbers are supposed to be written on a whitened board. Beyond that he uses single-line lettered diagrams and Euclidean-style lettered diagrams; most of these show by their lettering to be borrowed from possibly Greek but at least mostly Arabic sources or earlier Latin translations. When geometric objects or situations are illustrated, they are also mostly diagram-like with no naturalistic pretensions. None of this is sensational, and it is comprehensible that Fibonacci's diagrams have attracted little attention.In the end, lettering of Fibonacci's diagrams is taken up in detail, giving substance to the claim that it is informative about Fibonacci's sources and his use of them.Is the mathematical running text a diagram?Roy Wagner (ETH, Zürich)This year’s focus is on the independence of mathematical notation from spoken language and on non-linear aspects of mathematical notation. While the running text encountered in premodern manuscripts often appears to be linear and to have a close correspondence with straightforward reading, the actual practices of engaging with mathematical texts may deviate from this appearance. In my rather speculative intervention, I will try to show in what ways a linear mathematical running text might be viewed as a diagram.I will start with my own reading practices of mathematical texts as a historian of mathematics reading foreign languages in which I have a limited working knowledge. Using Malayalam and/or Italian examples, I will focus on my philological practices of breaking up the text, identifying key anchors and repeated “formulaic” expressions (in the sense defined by Reviel Netz in The Shaping of Deduction), and resolving embedded syntactical structures. During this analysis, I sometimes reorganize the text graphically and, in some sense, turn it into a diagram. Sometimes, I accompany the reading with ad-hoc somewhat diagrammatic symbolic annotations. I will then raise the question: to what extent can such practices be attributed to contemporary readers of mathematical texts? Our limited knowledge of learning and research practices will allow me to offer only tentative guesses. If time permits, I will also consider examples of the non-linear interactions between a running Hebrew text dealing with operations on fractions and an apparently idiosyncratic calculation diagram that accompanies the text in the original manuscript. Jan 06 2026 13.00 - 17.00 Seminar 1: Diagrammatization of written mathematical practices Join Jens Høyrup (Roskilde University, emeritus) and Roy Wagner (ETH, Zürich) for the first seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. JCMB Room 5323
Jan 06 2026 13.00 - 17.00 Seminar 1: Diagrammatization of written mathematical practices Join Jens Høyrup (Roskilde University, emeritus) and Roy Wagner (ETH, Zürich) for the first seminar of the second year of the 'Rethinking the history of mathematical symbolism' project.
