Science often discovers and quantifies natural phenomena that are useful outside science. Whether pure math dealing with gazillion-digit-long primes can be of any use outside of satisfying curiosity is unclear.
Aren't some modern digital cryptography methods based on exactly that?
I do agree on the view that science often discovers useful phenomena. What I tried to stress was that basic research does not, by definition, aim for such utility. Especially with pure math, whether there are any applications for new, even groundbreaking discoveries, is often very unclear. And when there are, they might be only utilized decades or centuries after the initial discovery.
We’re really bad at handling large, complex structures.
Mathematics dealing with large primes and their complex structures is likely to find applications in other complex structures, eg in physics or computer science.
Mathematics is modern ontology: even when its self-investigation is not directly applicable, the vocabulary and semantics developed is often useful for articulating other truths.
