p-adic analysis is a branch of mathematics that studies numbers in a different way than traditional analysis. Instead of focusing on the usual distance between numbers, it uses a concept called p-adic valuation, which measures how divisible a number is by a prime number p. This leads to a unique system of numbers that can be used to solve problems in number theory and algebra. In p-adic analysis, functions are examined in the context of p-adic numbers, which form a complete field. This allows mathematicians to explore convergence and continuity in a new light, providing insights into various mathematical structures. The approach has applications in areas like algebraic geometry and cryptography.