Sometimes it works the other way round. One professor solved an equation in a class by integrating with respect to pi. The students could not believe their eyes

Sometimes it works the other way round. One professor solved an equation in a class by integrating with respect to pi. The students could not believe their eyes: "You can't do that!", they said; "pi is a constant!". The professor explained that once you have expressed your problem in a formal system like mathematics, you can do anything that is allowed in the rules of that system, even if the intermediate stages make no sense with respect to the original problem, and still obtain a correct answer. [This story is from E T Jaynes 'Probability theory, the logic of science'. But I don't have it to hand, so I may have the details wrong (and I can't remember who the prof was - it wasn't Jaynes).]