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About your difficulty to see the application of theoretical math, often times even the people developing the theories have no clue. GH Hardy, one of the most prominent figures of Number Theory in the 20th century, was famously proud of its pureness and lack of applicability in the outside world. He was a strong pacifist living in the beginning of WWII, so he was particularly proud that it would have no military application whatsoever.
Fast forward 80 years, and Number Theory is being used literally billions of times per second in our world: it is the basis of public key cryptography. As you can expect based on that, it has military applications. But the funniest thing is that it only took a few years for Number Theory to be fundamental in cracking the Nazi Enigma codes during WWII. See more on that in Wikipedia: https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology
I would say that most of what drives research in mathematics (and sometimes in other sciences as well) is pure curiosity and desire to know, with no consideration about the aplicability of any of it. But then it sometimes turns out that even the most esoteric parts of math end up being useful in describing the real world.