Sorry in advance if this question doesn't belong here. I know it walks the line of what kinds of questions should be asked, but I'm really interested in what the community here has to say on it. Knowing this, I won't be offended if people vote to close it.
This question is meant as a companion to previously asked questions like Proofs every mathematician should know.
More and more I'm beginning to see that there is just too much math to learn. Additionally, there is far more math that I'd like to learn then is covered in my undergrad. So, my question is, what math should every person that titles him/herself as a mathematician, or math-capable know? For example, to say that you play hockey, you should at least be able to skate forwards and backwards, stop, take a pass, shoot, ect. If you say you're a hockey player, but can't stop.. well then..
At the same time, I'd like to have a comprehensive understanding of the math I "know". To give clarification of what I mean by this, I reference the turtles standing on turtles analogy of how any proposition requires justification. In the case of math, I'm hoping that this isn't an example of infinite regress as in the case in science (it's the main reason I study math instead of science). Using the turtle analogy for math, I'd like to know what the stupid turtles are standing on.
Sorry again if this question isn't suitable for this site. I just really respect the amount of knowledge some people in this community have to offer, and would really just like some advice.
Thank you for reading.