Abstract

Renewing Foundations-1 This is the first part of a work in progress, which contains Introduction, explaining the whole project, and a chapter on Euclid's "Elements". The idea of the book is to describe foundations in mathematics in their history from Euclid until today and then provide a project of future foundations of mathematics. Further historical parts of the book will contain chapters on "New Elements of Geometry" by Arnauld, Hilbert's "Grundlagen der Geometrie" first published in 1899 and Bourbaki's "Elements of Mathematics". The part of the book describing prospective future foundations of mathematics will be on Category theory.