BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Veronese Redivivus and the (Re)writing of the History of Fin-de-Si ècle Non-Archimedean Mathematics – What Remains to be Done: Prospects f or Future Historiographical Research - Saša Popović (Mathematical Instit ute of the Serbian Academy of Sciences and Arts (MI SASA)) DTSTART:20250429T081500Z DTEND:20250429T091500Z UID:TALK230347@talks.cam.ac.uk DESCRIPTION:I will indicate and address the main lacunas\, open questions\ , misconceptions\, and misinterpretations in the current historiography of fin-de-siè\;cle non-Archimedean mathematics\, taking the Italian ma thematician Giuseppe Veronese (1854&ndash\;1917) &mdash\; &ldquo\;the chie f modern champion of the infinitely small&rdquo\; (sec. Cajori) &mdash\; a s a particularly illustrative case study. Veronese introduced and develope d non-Archimedean geometry in a series of seminal publications from 1889 t o 1909\, culminating in the Fondamenti di Geometria. Initially\, Veronese& rsquo\;s results were widely discussed by leading mathematicians (e.g. Pea no\, Cantor\, Hilbert\, Poincaré\;\, etc.)\, as well as in major ref erence journals\, mathematical encyclopaedias and lexicons of the time. Hi s work also quickly garnered the attention of philosophers working on the foundations of mathematics. However\, shortly after this initial burst of enthusiasm for Veronese&rsquo\;s new geometry\, already at the beginning o f the 1920s we can see that discussions in both mathematical and philosoph ical circles started shifting to other mathematical subjects and\, consequ ently\, to other authors\, resulting in a somewhat peculiar situation that Veronese&rsquo\;s results seem to be almost entirely unknown by contempor ary mathematicians\, philosophers and historians of mathematics alike. Thi s striking asymmetry in the initial and final stages of the reception of V eronese&rsquo\;s theory will be at the heart of my talk. I will indicate w hat were the key factors that negatively impacted the further disseminatio n and development of Veronese&rsquo\;s ideas\, as well as who were the &ld quo\;main culprits&rdquo\; for what may be considered a damnatio memoriae of Veronese in the actual practice of contemporary non-Archimedean mathema tics and its historiography. In this context\, I will especially focus on the roles of Cantor\, Peano\, Russell\, and Poincaré\; in Veronese&r squo\;s Nachleben. I will also provide a critical overview of the few atte mpts at interpreting some facets of Veronese&rsquo\;s theory that have bee n advanced in the last 135 years\, emphasizing their various shortcomings and omissions. Finally\, I will propose a novel interpretative strategy wh ich\, in my view\, provides us with &bdquo\;un nouvel hommage ré\;pa rateur&ldquo\; of Veronese&rsquo\;s insights\, and allows us to detect and follow a continuous developmental path from Veronese&rsquo\;s geometrical investigations from the 1890s up to late 20th-century non-Archimedean the ories (e.g. Robinsons&rsquo\;s NSA\, Vopěnka&rsquo\;s AST\, or Conway&rsq uo\;s surreal numbers). LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR