Evolution of the Paradigms of Mathematics

Abstract

The development of mathematics has been driven by various phenomena and needs throughout history. From its primitive use to quantify the surroundings to the scientific revolution of the Modern Age, mathematics has been fundamental in science and technology. Today, one of the biggest challenges is its role in prediction processes, both past and future, in fields like astronomy, climatology, economics, and biology, especially in complex and chaotic dynamic systems. Predicting these systems is limited by uncertainty and chaos, posing significant challenges for long-term modeling.