Topology and biology: From Aristotle to Thom

Athanase Papadopoulos (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 YMSC - Yau Mathematical Sciences Center

René Thom discovered several refined topological notions in the writings of Aristotle, especially the biological. More generally, he considered that some of the assertions of the Greek philosophers have a definite topological content, even if they were written 2400 years before the field of topology was born. In this article, we expand on these ideas of Thom. At the same time, we highlight the importance of biology in the works of Aristotle and Thom and we report on their conception of mathematics and more generally on science. The final version of this article will appear in the book \emph{Geometry in history} (ed. S. G. Dani and A. Papadopoulos), Springer Verlag, 2019.

Mots clés: stratification; Stokes formula; history of topology; morphogenesis; hylemorphism; 54-03; 00A30; 92B99 Keywords: Mathematics in Aristotle; mor-phology; 01-02; AMS classification: 03A05; history of topology.; 01A20; 34-02; 34-03; René Thom; Mathematics in Aristotle; topology in Aristotle; form; morphology; mathematics in biology

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Philosophie; Topologie géométrique [math.GT]; Histoire, Philosophie et Sociologie des sciences

Athanase Papadopoulos. Topology and biology: From Aristotle to Thom. 2018. ⟨hal-01929108⟩