This won't be popular [1], but research breakthroughs in theoretical mathematics seem to be often useless in a way that useless science is not. Scientific breakthroughs are also often useless (nothing practical is gained from the first detection of a gravitational wave, or from finding out how flight first evolved in insects) but scientific insights still have more information content: they tell us facts specifically about our world, while mathematical proofs merely tell us about all possible worlds. About some consequence of made-up assumptions we happen to find interesting.

It's a bit like finding the fastest way possible to beat Super Mario Bros 3 while collecting the minimum number of coins. A solution to a neat puzzle, but it doesn't carry the epistemic weight of finding out how the universe works, even if both pieces of knowledge are equally useless.

1: And of course this point doesn't apply to applied math.