The study of calculus that you’re referring to is real analysis. Never quite thought of it as pure math though as it’s very applicable to many things - hence th

The study of calculus that you’re referring to is real analysis. Never quite thought of it as pure math though as it’s very applicable to many things - hence the “analysis.” Number theory is actually an example of pure math having real world impacts despite its nature. It’s very much about studying math for maths sake - though there are also people interested in it for their own applications. They’ve gone the brute force route with number theory because proving things in it is hard - in the sense that a hard number theory problem takes centuries to solve otherwise.