The point was to realize precisely that some problems might have analytical solutions, but they would take too long. If you’re solving problems on pen and paper

The point was to realize precisely that some problems might have analytical solutions, but they would take too long. If you’re solving problems on pen and paper nowadays, you’re most likely looking for an approximate answer anyway. Maybe I should add that, as long as the answer was within a specified margin (say 5%), the answer was considered correct. If you saw that your calculations started to become way too complex, you had already missed something.