Seminar 1: Diagrammatization of written mathematical practices

Diagrammatization in the Liber abbaci and in abbacus manuscripts: borrowings and/or fresh starts?

Jens Høyrup (Roskilde University, emeritus)

Leonardo Fibonacci informs his readers that he has learned from the environment in Bejaïa, and from numerous other places in the Mediterranean trading network. But he has also contributed with his own inventions. What can be said about his copious diagrams, can we distinguish borrowings from independent ideas?

The abbacus writers do not speak about their sources – the occasional references to Boethius or Fibonacci are not references in the modern sense. Their sources must be identified from the texts, and these normally do not suggest precise links to other mathematical cultures we know about. In any case, diagrams are rare in early abbacus writings, and do not suggest borrowing from Fibonacci or the madrasah-level of Maghreb mathematics. What we find speaks in favour of modest and slow fresh start.

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.