> And of course it is historically backwards; groups arose as people tried to solve problems they were independently interested in.
Reminds me of the joke that philosophy students university learn the work of people who didn't go to university.
Would a text written by the discoverer of a field be more interesting?
I've found important papers easier to read than textbooks covering them... OTOH the original paper can be too close to their own motivation, and not treat - or yet be aware - of its general significance.
A motivating problem doesn't have to be practical or relatable... it just must lack obvious solution. A puzzle.
Good example of something (although it's perhaps a bit trivial) that is a puzzle that seems to make even non-mathematicians curious is the 'justification' for greco-latin squares.
The idea is that you have 6 files of 6 men. Each is of a different regiment, each is of a different rank. Is it possible to arrange them so that no row and no file have two men of the same rank or from the same regiment?
You can mention this in your first lecture on algebraic geometry (or, for that matter, combinatorial geometry i.e. matroid theory) and then come back to it when you talk about projective geometries.
Reminds me of the joke that philosophy students university learn the work of people who didn't go to university.
Would a text written by the discoverer of a field be more interesting?
I've found important papers easier to read than textbooks covering them... OTOH the original paper can be too close to their own motivation, and not treat - or yet be aware - of its general significance.
A motivating problem doesn't have to be practical or relatable... it just must lack obvious solution. A puzzle.