On the impact of History on modern research and teaching

L'impact de l'Histoire sur la recherche et l'enseignement modernes

Satyanad Kichenassamy (1)

1 LMR - Laboratoire de Mathématiques de Reims

We have shown that the works of Brahmagupta, Baudhāyana and Tartaglia spell out not only theorems but their assumptions and the essential elements of proofs in the form of an *apodictic discourse*. To these results, we add three elements. First, the notion of apodictic discourse, absent from Aristotle’s Rhetoric, was not introduced sooner because of the weight given in some teaching traditions, especially British, to Hellenistic Mathematics, leading to an over-estimation of sources in Greek, observed even today. Second, “Modern” Science is partly Indian, for it is the result of an essential reorientation of Mathematics around 1900, influenced by the simultaneous realization that Hellenistic mathematics was not consistent, and that there were other forms of mathematics elsewhere: in India, the Middle East and China, but also in forgotten sources from the Mediterranean world. Third, if time permits, we shall show that tools from History help obtain new results in “Modern” Science, focusing on our very recent results on Wave Mechanics. Other earlier results of ours may be viewed as illustrations of the same approach.

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Géométrie métrique [math.MG]; Relativité Générale et Cosmologie Quantique [gr-qc]

Satyanad Kichenassamy. On the impact of History on modern research and teaching. International Web-Conference on History of Mathematics, Indian Society for History of Mathematics, Dec 2020, Delhi, India. ⟨hal-03088811⟩