Oswald Veblen's 1901 notebook on the foundations of geometry as an axiomatics laboratory

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• Emmylou Haffner (CNRS - Ecole Normale Superieure Paris)
• Friday 02 May 2025, 09:15-10:15
• Seminar Room 1, Newton Institute.

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MHMW02 - Modern History of Mathematics: Looking Ahead

Drafts, notes, notebooks and various archival material kept by mathematicians constitute, one could argue, their personal workshop. They show what happens ‘behind the scenes’ and unveil writing practices designed for the research phase that can differ deeply from the ones observed in publications. Such texts are an integral part of mathematical practice, and indeed crucial to understand the shaping of mathematical knowledge. It is in that framework that I propose to look at Oswald Veblen’s 1901 notebook on the foundations of geometry. Filled with notes taken during a seminar given by E. H. Moore at the University of Chicago, this notebook documents both Moore’s teaching through collective reading of contemporary sources, and Veblen’s personal reflections on the matter. Building from work with J. Lorenat and N. Michel, my focus, in this talk, will be on three aspects: the reappropriation of Hilbert’s and Peano’s texts; the process of selecting axioms and designing a new axiom system; the specific materiality of writing exhibited in the notes and its role in the two previous points.

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

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