I’m sure not only “elite” mathematicians intuit the interest of problems like the unsolvability of the quintic. That one can prove a construction impossible, the very concept of an invariant, is startling to the uninitiated. So many classic problems of this nature are held up as paradigms of beauty—the Konigsberg bridge problem, ruler and compass constructions of cube roots, the irrationality of sqrt(2),..
I’m sure not only “elite” mathematicians intuit the interest of problems like the unsolvability of the quintic. That one can prove a construction impossible, the very concept of an invariant, is startling to the uninitiated. So many classic problems of this nature are held up as paradigms of beauty—the Konigsberg bridge problem, ruler and compass constructions of cube roots, the irrationality of sqrt(2),..