"The interesting thing is that stuff from pure maths ends up being useful anyway, even when they were studied just because they were interesting at the time."

"The interesting thing is that stuff from pure maths ends up being useful anyway, even when they were studied just because they were interesting at the time." I agree with this statement. In fact, I am inclined to believe that it is not by chance that the results in pure mathematics become useful in the real world. Much of math is dealing with hypothetical situations before they arise. These hypothetical situations may have real world analogs, or they may just be solutions to other abstract problems. While its real world utility is often obscured due to the lack of an immediate direct application, the truth is that by definition, the results derived will be useful if and when an apt situation arises. Granted, many results may never see the light of day, but are still potentially useful in inspiring solutions that require a novel way of thinking. To judge mathematics based on its current real-world utility would be extremely short sighted. We probably would not have much of the technology we have today if mathematicians in the bygone era decided that they would stop developing it due to the lack of a real world application. Now there are definitely certain things which can in no conceivable way be applied to the real world, such as the concept of infinity, but those concepts seem to complete a comprehensive framework for us to think about problems.