Mathematics and Philosophy

This book explores the major impact of mathematical ideas on philosophical thought. It shows that from Antiquity (Plato) to the end of the Middle Ages (Nicholas of Cusa), philosophy and mathematics have been linked. At the time, visions of the world directly followed the conception of relatively simple mathematical ideas (irrational numbers, squaring of polygons, cubature of polyhedrons, angle trisection, etc.). From the 17th to the 19th Century, increasingly technical domains emerged, leading to the development of algebra, analysis, differential calculus, probabilities, topology, etc. These new mathematical ideas inspired a number of philosopher-mathematicians (Descartes, Pascal, Leibniz, Husserl, etc.), often providing them with new methods or concepts. However, once this discipline reached a certain level of complexity, only professional mathematicians were able to learn from their knowledge. The movement started with Wronski and Clifford, followed by Cantor and Finsler, up to Thorn and Grothendieck. This has led to a situation where philosophy is very often found elsewhere than in literature solely dedicated to the subject. Book jacket.