Some things are valuable, because they keep people alive and healthy in the short term. Some are valueble, because some people find them inherently valuable. Pure mathematics is in that category. And then there is bureaucracy.

Bureaucracy has no direct value, but it may have indirect value, if it helps us achieve things that are more directly useful. Pure mathematics has had a lot of indirect value until now. It turns out that training people to do mathematics for the sake of doing mathematics, at any level from schoolkid to mathematics professor, teaches skills that transfer to other domains. If human thinking becomes obsolete, that indirect value may be gone, but the direct value will remain.

The results in pure mathematics are largely irrelevant, except as means of acquiring transferable skills. Sometimes they have practical implications, but such situations are exceptional. And there is not much correlation between the practical value of a result and its value as seen by mathematicians.