I asked my math teacher for applications and she just mumbled something, embarrassed. Took me until a while later to realize that most of my teachers had never stepped foot outside a school in their entire life.

Later at university I complained about the lack of applications in the textbook, and my classmates became very upset. One of them responded, "we are mathematicians, we do not concern ourselves with applications."

That's a bit of a caricature, but would you ask the same of an English major or an art historian? Math is an intellectual activity that's about sharpening and chiseling the mind, and the satisfaction of figuring things out and seeing things fall into place neatly. Thinking about real things out there in the world in math ways (~= applications) can also be fun.

Just look at software. It's undeniably useful with many applications. Still, some people treat it playfully and in an enjoyable way, they learn about algorithms they won't ever use, just for the elegance, read Knuth, even if reading some React handbook may be more useful for their day-to-day. There are more considerations than "but how will this make my employer richer?"

Posing was the application for them :)