It can be difficult to predict whether a given research topic will be useful or not in the future. It's easy when something is developed with an application in

It can be difficult to predict whether a given research topic will be useful or not in the future. It's easy when something is developed with an application in mind. It can be far more difficult for "pure math". There are plenty of examples of math that we don't have an application for today becoming very relevant in the future. For example: - Fast Fourier transform (Gauss discovered and didn't publish it b/c he thought it wasn't very useful. Others rediscovered it later.) - Number theory was considered useless for a long time, now it's used for cryptography