A FUNDAMENTAL REVISION OF THE FOUNDATIONS OF MATHEMATICS: THE IRT PARADIGM.Survey manifesto :

This work proposes a radical restructuring of mathematical knowledge based on a single primitive object — the isosceles right triangle with legs equal to 1 (IRT). It is shown that the classical branches of mathematics — arithmetic, geometry, algebra, analysis, and topology — are different projections of a unified theory of IRT mosaics. The analysis of structural connections has been deepened, and traditional contradictions between the discrete and the continuous, the algebraic and the transcendental, have been eliminated. All of mathematics is derived as the fractal dynamics of self-similar IRT configurations. The essay contains a concrete program for redefining foundations, key theorems of unity, and practical resolutions of well-known problems. Additionally, the following are detailed: the constructive building of numbers, the geometric nature of algebraic structures, topology as a homotopy theory of mosaics, and the universal dynamics of striving towards minimal asymmetry. IRT models of computation, information theory, fundamental physics, and cryptography are introduced.