If I know that I am not going to make any new discoveries about it, is there anything else I can do by learning topology?
There's also quite a large body of (academic) work applying topological methods to robotics. Robots have complex configuration spaces and apparently topological methods can help us understand those spaces.
Similarly, matrices existed way before QM was even formalized but now it heavily relies on Matrix Algebra.
Number Theory had no usage whatsoever until it suddenly had in cryptography. Therefore, nowadays, I have begun to think of any new mathematical inventions as a possible prelude to the future.