Every time someone wants to explain the importance of pure mathematics they then will start to state that usually lots of them just doesn’t have any immediate application, then give an example of logic and number theory from 19th century than suddenly become much more important with the rise of computers in 20th century. Then I think about it a little more and u realize there’s not really any other example beside it. All other applied mathematics are founded after they are needed, so they are created to solve existing problem.
Is there really any other example? The one I found closest is that I’ve heard that quarternion may be surprisingly useful in quantum theory but I heard that it’s still speculative so far.