Kant asks the question "How is pure mathematic possible?". I think that he when he says that you need to know A priori information to know any kind of mathematics. So i think the answer would be no mathematics is not pure someone is always going to have to figure it out. You cant just know what the answers are.
Also you cant just have math in your head. You have to at least have some type of picture before you can figure out what the answers to the questions are.
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