Problem Solving Skill vs. Mathematical Knowledge Here goes more of my mathematical musings: Problem Solving Skill vs. Mathematical Knowledge. Which is more important to you? Spending time to improve one will cost you time to improve the other. You must excel at both to become a mathematician, but while you are still developing, which do you place more emphasis on? By the way, you should not be counting assignments that are forced upon you, unless it is something you know you would want to do anyway. In other words, which do you try to develop more during your "free math time?"