Ok, this may sound like a stupid question, but I really, really need to know. How much more mathematical knowledge does a typical mathematician have than a math specialist student who has just finished fourth year university math courses? Before you criticize my question, let me explain why I ask. I want to become a mathematician, so I need to get a feel of how much knowledge I need to acquire before I can become one. Now, I know that knowledge is not everything. Indeed, it is problem solving skills and generation of ideas that makes a true mathematician. I agree! Nevertheless, one must have immense prerequisite knowledge before they can come up with original ideas and solve open problems. If the answer is, say, 3 times as much. Then I can focus on my problem solving skills, read thoroughly the proofs of theorems, etc..., and build my knowledge at the pace of a regular student. If, however, the answer is, say, 100 times as much, then I will know that I have to step up on my reading. So this question, I think, is important in order for me to get a sense of how much and in what manner I should self-study. My guess is that a typical mathematician has 50 times as much knowledge as a math student who has just graduated from university. Any other ideas? A mathematician's honest answer would be greatly appreciated (and I won't think you are being arrogant).