Topology and biology: From Aristotle to Thom

Abstract

René Thom discovered several refined topological notions in the writings of Aristotle, especially the biological ones. More generally, he understood that some assertions made by philosophers from Greek antiquity have a definite topological content, even if they were stated more than two and a half millennia before the field of topology was born. He adhered completely to Aristotle's theory of form which the latter developed especially in his biological treatises. Thom emphasized the importance of these ideas in biology, and more particularly in embryology, namely, the idea of a form tending to its own realization. In this article, we expand on these ideas of Thom. At the same time, we highlight some major ideas in the works of Aristotle and Thom in biology and we comment on their conceptions of mathematics and more generally of science.