Given the proximity to physics, that is very often untrue. Because of how abstract logic and maths are, analogies from maths often inform us about the physical world.
Much of cutting edge physics doesn't have practical applications either, whether it's dark matter and string theory, early universe cosmology or astrophysics. =)
Are you really suggesting that the majority of current research in pure math has practical applications in physics or other sciences? I just don't think that's true.
