(Moved from PractitionersRejectFormalMethodsDiscussion)
A chemist, a physicist and a mathematician are stranded on a desert island, and all they have to eat is a can of beans, but nothing sharp enough to open it with. They each in turn set about devising a method to open the can.
The chemist comes up with a method that involves making seawater acidic enough to get the top off, and then neutralizing the acid with some basic coconut juice from a nearby tree to avoid ruining the food.
The physicist comes up with a complicated stick and rock momentum-leveraging apparatus to basically smash open the can.
The mathematician scratches his head, and walks around the beach for a while considering the problem. Finally, he comes and sits down next to his fellow castaways and says, "Assume a can opener..."
Would that be a perfectly spherical can opener of infinite density?
{Somewhere there is an allegedly real story about a farming productivity simulation that turned out wrong because it assumed spherical cows.}
We can extend this: