p-Adic mathematics and theoretical biology

Abstract

The principal objective of this article is a brief overview of the main parts of p-adic mathematics, which have already had valuable applications and may have a significant impact in the near future on the further development of some fields of theoretical and mathematical biology. In particular, we present the basics of ultrametrics, p-adic numbers and p-adic analysis, as well as insight into their applications for modeling some cognitive processes, genetic code and protein dynamics. We also argue that ultrametric concepts and p-adic mathematics are natural tools for the viable description of biological systems and phenomena with a hierarchical structure.

Keywords: Biological complexity; Biological information; Cognition; Genetic code; Hierarchical systems; Mathematical biology; Protein dynamics; Theoretical biology; Ultrametrics; p-adic modeling; p-adic numbers.