General Mathematics

    

On Babylonian Mathematics and Real Numbers

Authors: Lucian M. Ionescu

Babylonian Algorithm for Square Roots is a precursor of Newton-Cotes numerical method for finding roots, as numerical approximations(perturbative method)."What is a number?" has two complementary aspects: axiomatic viewpoint and as a tool in applications, via mathematical models.Modern 21-st century Mathematics regards Real Numbers as part of Complex Dynamics, in terms of Newton flow, Fatou and Julia sets and fractals, pointing towards their role as trajectories in Dynamics. A brief account is provided.Their relation to Number Fields, theory resulting from the work of Galois and Artin, starts to be apparent via Dirichlet Unit Theorem and the concept of uniformizer (Power Series/Diff. Eq.), extending the correspondence between Number Fields and Function Fields of Algebraic Curves.

Comments: 21 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar Sept. 18 2025.

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[v1] 2025-09-19 18:16:03

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