From Diophantine analysis to philology: Contextualizing C. G. J. Jacobi’s late engagement with Diophantus’ text

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• Ivahn Smadja (Université de Nantes)
• Monday 28 April 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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MHMW02 - Modern History of Mathematics: Looking Ahead

In the past decades, a mid-1830s, two-page paper by Carl Gustav Jacob Jacobi on the use of elliptic and Abelian integrals in Diophantine analysis has notoriously offered a debated case in point of interpretive abuse in twentieth-century historiography. Hardly more than a note taking stock of a shifting mathematical landscape, this paper, then largely unnoticed, was originally meant as breaking new ground in mathematics at its peak, rather than shedding light on its remote past. And yet, it was much later used (or rather misused) as allegedly providing evidence that could be read both ways, whether as prefigurative of modern algebraic geometry, or as providing presumably convenient tools for making sense of Diophantus’ ancient methods. As a rule, though, the current historiographic consensus disproved and rejected all such attempts based on unchecked anachronistic projections, consequently prompting new questions. This contribution aims at analyzing and contextualizing C. G. J. Jacobi’s late engagement with Diophantus’ text against the backdrop of his previous mathematical work. Trained in mathematics and classical philology, Jacobi turned indeed to carefully reading Diophantus in the 1840s, chasing Greek manuscripts in European libraries from the Vatican to Wolfenbüttel. His approach, however, strictly complied with prevailing philological standards, never mixing higher mathematics with source criticism. At Alexander von Humboldt’s pressing request, Jacobi jotted down some thoughts on ancient mathematics in general, and Diophantus in particular. These reflections, as will be shown, not only bear witness to Jacobi’s involvement in current debates but also reveal the extent of his debt to Georg Heinrich Ferdinand Nesselmann, Diophantus scholar and a former Königsberg student of his. They also shed light on the way he conceived the relationship between ancient and modern methods.

This talk is part of the Isaac Newton Institute Seminar Series series.

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