Comment Re: Travelling salesmen (Score 2) 51
I don't think squaring the circle is a good example here, since the problem isn't so much a find the number problem, but a find the answer while restricting yourself to a few specific operations problem. So the non-algebraic solution doesn't count because it doesn't follow the rules. People knew what the answer was as a number that you can calculate for ages. They weren't sure if you could do it while following the arcane rules of ancient compass and straightedge constructions. It's turns out that the answer is no.