[beatley]

A lot of modern technical marvels were built on top of the leisurely work done by people who were just playing.

"I wonder what would happen if the square root of -1 existed"

"I wonder what happens if numbers were cyclic"

"Can you actually cross all the bridges of Köningsberg without walking any of them twice"

The impetus to solve these problems was that they were fun to think about, not that they a century or several centuries later would enable us to do harmonic analysis, invent the basis for cryptosystems or spectral graph theory. Which are billion or even trillion dollar inventions.

[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.