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Edit: I have taken away my comments comparing my experience in mathematics and math ed departments. I still think there is something true about the kind of character that emerges from working on hard problems which demand a certain kind of rigor, and I also think there is something special (and not known to the general public) about the strong social bonds that exist in the mathematical community, but I don't think that one needs to contrast math and math ed groups to make that point.

Edit: I have taken away my comments comparing my experience in mathematics and math ed departments. I still think there is something true about the kind of character that emerges from working on hard problems which demand a certain kind of rigor, and I also think there is something special (and not known to the general public) about the strong social bonds that exist in the mathematical community, but I don't think that one needs to contrast math and math ed groups to make that point.

My short answer (to which Gil alludes below) was: Persistence and humility.

Though I'm not sure this applies only to mathematicians, but in general to people who work on hard, and perhaps in some ways technical, problems.

Short answer: Persistence, humility.

Longer answer: I have worked in both mathematics departments and math education departments, and I think there are a few striking differences:

1. Department meetings in mathematics are much more concise.

2. Disagreements among my math colleagues tend to be much more about issues, among math ed colleagues things tend to get personal.

3. For some reason, the math groups I have been with are much more social; and have much better habits, such as afternoon teas; and meet socially outside of the university.

4. Mathematicians tend to be better at asking and receiving help. (Perhaps because of 1-3 above? Also perhaps because at the end of the day are actually are right answers :-))

Edit: I have taken away my comments comparing my experience in mathematics and math ed departments. I still think there is something true about the kind of character that emerges from working on hard problems which demand a certain kind of rigor, and I also think there is something special (and not known to the general public) about the strong social bonds that exist in the mathematical community, but I don't think that one needs to contrast math and math ed groups to make that point.

I have worked in both mathematics departments and math education departments, and I think there are a few striking differences:

1. Department meetings in mathematics are much more concise.
2. Disagreements among my math colleagues tend to be much more about issues, among math ed colleagues things tend to get personal.
3. For some reason, the math groups I have been with are much more social; and have much better habits, such as afternoon teas; and meet socially outside of the university.
4. Mathematicians tend to be better at asking and receiving help. (Perhaps because of 1-3 above? Also perhaps because at the end of the day are actually are right answers :-))

Short answer: Persistence, humility.

Longer answer: I have worked in both mathematics departments and math education departments, and I think there are a few striking differences:

1. Department meetings in mathematics are much more concise.

2. Disagreements among my math colleagues tend to be much more about issues, among math ed colleagues things tend to get personal.

3. For some reason, the math groups I have been with are much more social; and have much better habits, such as afternoon teas; and meet socially outside of the university.

4. Mathematicians tend to be better at asking and receiving help. (Perhaps because of 1-3 above? Also perhaps because at the end of the day are actually are right answers :-))