The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to these equations correspond to observed mathematical and physical behaviors (Wolfram 2021).
The mathematical paradigm has proved extremely successful over the last 300 years in describing and predicting real-world systems and phenomena. However, it has proved less successful in some types of phenomena, particularly those associated with complex systems. In such cases, Wolfram (2002, 2021) has advocated the use of a "computational paradigm" in which simple programs rather than mathematical equations are used to model a system's behavior. Such an approach can be effective as a result of thet fact that even simple rules can manifest immensely complex behavior when iterated. This can be understood in terms of concept of computational irreducibility, which posits that there may be no faster way to find out what a system will do than just to trace each of its computational steps.
More recently, in the course of the investigations of the Wolfram Physics Project, Wolfram (2021) has advocated moving beyond the computational paradigm to a multicomputational paradigm.
