Laura HelmuthResidents of Königsberg asked Leonhard Euler to figure out whether it was possible to walk a path across all 7 city bridges only once. Euler dismissed the problem as banal and non-mathematical—but then got hooked and invented the math to solve it https://www.scientificamerican.com/article/how-the-seven-bridges-of-koenigsberg-spawned-new-math/
John Carlos Baez@laurahelmuth - I didn't know he initially dismissed it! That makes it more exciting. Thanks!
The article says nothing about how Euler solved the problem, except for inventing the concept of graph. He showed a more general result: you cannot walk across all bridges and get back where you started (another condition in the original puzzle) if one vertex has odd degree - i.e. one land mass has an odd number of bridges leaving it.