The geometer's gaze: on H. G. Zeuthen's holistic epistemology of mathematics (Q6623921)

In this article the author discusses the epistemology of geometry of the Danish mathematician and historian Hieronymus Georg Zeuthen. He does so, among other things, with regard to the relation between symbolic reasoning, such as we know from enumerative geometry, and what Zeuthen called intuition. Intuition provides a holistic perception of the geometric figures with which we are concerned. This holistic perception is in Zeuthen's view the basis of everything, while without the involvement of intuition symbolic relations such as Plücker's formulas, which relate certain numeric invariants of algebraic curves to corresponding invariants of their dual curves, are easily used beyond their scope of applicability. The author also shows how Zeuthen was influenced in this respect by the work of Harald Høffding and Henri Bergson.\N\NFor the entire collection see [Zbl 1537.01004].