So, quick background information. I am a PhD student in mathematics going into graph theory. I hope to either do a post-doc or (hopefully!) get a tenure-track position at a research-oriented university after graduation. I don't have a super high mathSE reputation, but it has been steadily increasing from answering questions.(I have only asked a few, but I answer a lot.)
While I don't think it would be a good idea to put my mathSE reputation on a CV(or am I wrong?) I could potentially see myself mentioning SE at an interview. While I know answering questions on MathSE isn't anything like publishing original research, I think it shows a dedication to mathematics and teaching.
What I want to know(hopefully from people who do interviews, but all answers are welcome) is if something like that would ever make a difference?(especially if it would be frowned upon similar to having trivial papers on your CV.)
Note: answering questions on MathSE is something I do in my leisure time or times when I cannot work on my course work/research such as while I am on my daily bus ride to campus, so I don't need to see answers that say "spending the time studying/researching would be a better use of your time"
Edit: my main concern is in an interview setting. Only if you have reason to believe that it would be good to put on a CV am I interested in that as I already had a feeling that it would not be well suited for a CV.
Answer
I have seen Math.SE and MathOverflow activities mentioned by both grad students and faculty in connection with various applications and promotion-related materials. I don't see this as anything to scoff at; personally I find it intriguing and consider looking up someone's SE profile(s) a great way to get some insight into their mathematical personality (note that there can be a potential downside if said personality turns out to be uninteresting or unimpressive). With that said, I think this is only worth mentioning on your CV if it represents a major activity, say if you have been active for at least 1-2 years and have dozens of answers including a good number of highly voted ones. I wouldn't specify the reputation points as that seems like a silly thing to (admit to :-) ) be concerned about. And there can be a better place to mention it, e.g., in a research/teaching/personal statement.
As for mentioning this in an interview, like many other things this can be a good idea if done tactfully (in a no-big-deal, casual sort of way that shows a sense of proportion), or a horrible idea if done untactfully (saying it and expecting fireworks or a round of applause).
Finally, I wanted to mention that I noticed from questions such as this one that there is a common belief in the Grand Principle that for academic (and specifically math) jobs one should hide any information about oneself that attests to one being interested in anything other than doing math research all day, every day, and that any decision about what to put on one's CV or what to mention in an interview/personal statement should be considered in the light of this Grand Principle. I can't say if this is true or false as a general rule, but it's categorically false for me: personally I'm delighted if a job candidate tells me they are interested in archery, or chess, or surfing, or playing piano, or whiling away their time answering elementary questions on Mathematics StackExchange. Think about it this way: given that I already know the level of research they do (which presumably must be pretty good if I'm interviewing them), any evidence that they have other unusual skills or abilities outside of math research can only raise them in my estimation. Besides, when you hire someone you get a complete package, mathematician/academic+human being, and personally I rather like being surrounded by interesting human beings and not just paper-writing robots. But maybe I'm weird and it's just me who thinks this way, so handle this advice with proper caution.
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