[ta123456789]

I don't think this is accurate. For example square root of -1 was motivated by clear applications in mathematics, it was definitely not just idle leisurely math. Most of important pure math has not been leisurely or recreational in any sense in its origin

[beatley]

Before the 19th and 20th century, much of the basis of modern math was entirely leisurely and recreational. Even today that still rings true. I recommend reading Barry Mazur's "Number Theory as Gadfly" to add some context to that claim.