# $p$-Adic Mathematical Physics: The First 30 Years

## TL;DR

This paper reviews 30 years of $p$-adic mathematical physics, highlighting its development from non-Archimedean models of spacetime and strings to applications in biology, emphasizing recent advances and future prospects.

## Contribution

It provides a comprehensive overview of key achievements and recent developments in $p$-adic mathematical physics over the past three decades.

## Key findings

- Significant progress in modeling spacetime and string dynamics using $p$-adic methods
- Extension of $p$-adic techniques to biological phenomena
- Identification of promising future research directions

## Abstract

$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of $p$-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.