Are there any situations where you can only memorize rather than understand? I realize that you should understand theorems, equations etc. rather than just memorizing them, but are there any circumstances where memorizing in necessary? (I have always considered math a logical subject, where every fact can be deducted using logic rather than through memory)

If there are any, I'm certain that humans haven't discovered them. If there truly is a situation in mathematics where you can only memorize and there is no logical reasoning you can use to get there, then there comes an interesting question: how do we know that this formula is true? Everything we know about in mathematics we know from reasoning. If we can't figure it out with reasoning, then we simply can't figure out what there is to memorize.
