👉 Non-Bernoulli mathematics (NB math) is a broad, interdisciplinary field that extends beyond the traditional confines of classical mathematics, particularly focusing on realms where conventional probability theory, rooted in Bernoulli's laws, falls short. It encompasses areas like non-standard analysis, which introduces infinitesimals and infinite numbers to provide a more intuitive understanding of calculus and analysis; generalized probability, which explores alternative axiomatic systems for modeling uncertainty, such as those involving non-Bernoulli distributions; and category theory, which offers a unifying framework for understanding mathematical structures across diverse disciplines. NB math also delves into topics like free probability, which generalizes classical probability to analyze random matrices, and stochastic processes with non-standard stochastic calculus. By broadening the mathematical toolkit, NB math aims to address complex problems in fields like physics, computer science, and economics where traditional methods may be inadequate.
