Abstract
From different viewpoints, in the last few IACME-CIAEM conferences the author has been formulating a global approach to Mathematics, its Epistemology, its History and its Didactics: "The Chronotopy Program". The Chronotopy Program intends to analyze the introspective syncretic totality we might call "my personal, private spatio-temporal experience", to try to capture some characteristics of the construction of my own mental space-time I name "my chronotope". This lecture synthesizes some advances achieved up to now in this Research Programme —in the sense of Lakatos, Baltzer, Moulines and Sneed— in order to develop an academic discipline that would be named "Chronotopy". The Chronotopy Program intends to reformulate Mathematics itself, in particular, ancient Astronomy, Geometry and Arithmetic, and the whole formal theory of processes and systems with their substrates, structures, and dynamics, in order to reorient accordingly its Epistemology, its History and its Didactics.