Station 10EWho Really Cares about Ten-adic and other “adic” Number Systems?
If one conducts an internet search on the topic of “p-adic numbers” (here “p” stands for prime) one will see the extent to which mathematicians care about these number systems. As I mentioned before, they seem to provide a powerful tool for analyzing multiplicative properties of numbers in basic number theory: the properties of prime numbers and prime factorizations of numbers. So many basic questions about numbers and basic arithmetic are still unanswered!
But perhaps the most surprising application of p-adic numbers I’ve seen is an application to geometry.