P adic numbers application What is the application of p adic numbers. I have tried thinking a lot but do the p adic numbers have a real world application? 
 A: As in many areas of mathematics: p-adics don't have a direct application to the real world, but they're an indispensable tool in studying things that have indirect applications to the real world.
One obvious answer: p-adics and related number systems are incredibly important in number theory, and number theory finds a lot of direct modern applications in computing and cryptography.
To go one step further down the rabbit hole: there are a few subtle number-theoretic considerations in the study of dynamical systems, PDEs on surfaces, homotopy theory, and the like, all of which have their own (direct or indirect) applications.
Questions like this are generally very hard to answer for a number of reasons, but an important one among them is the observation that applications of pure-mathematical theories almost always come after the theories are sufficiently developed. No doubt there are plenty of "useless" theories that have since become redundant or been discarded too, but even these may have had their own historical significance in pointing mathematicians in the right direction to develop better theories. It's hard to disentangle any individual part from the whole.
