How an unsolveable problem taught 3Blue1Brown about topology

In the video above, 3Blue1Brown explained the inscribed square/rectangle problem which asks whether all closed continuous curves can make an inscribed square or rectangle with any four points on the curve. As you might have guessed, this hasn’t been proved yet in a general sense (there are some specific proofs) but in exploring the problem, 3Blue1Brown found out more about topology and what it really means.

My knowledge of topology goes as far as the coffee mug donut joke. But, of course, there is so much more to it and one problem like this can open so many doors.