220301 Nicolas Michel

Throughout his long and distinguished career, the Danish mathematician Hieronymous Georg Zeuthen constantly contributed to the emergence of enumerative methods in geometry. He did so alternatively as observer, as participant, as professor, or even as referee in the context of the frequent disputes which plagued the early development of this theory. His 1914 Lehrbuch der abzählenden Methoden der Geometrie, the sum of this prolonged engagement, opens on surprising pronouncements: in lieu of first theorems or definitions, we find a philosophical discussion of the "meaning of numbers" and the "relativity of the concepts of general and particular."

Drawing on Zeuthen's holistic outlook on the history and epistemology of geometry, this talk will set out to explain why, to an algebraic geometer at the onset of the 20th century, answering such technical questions of mathematics might first require philosophical detours—and what we might lose by discarding them.