Why don't mathematics professors use social media to promote their work? I notice that many computer science professors do a great job of self-promoting; they are very active on Facebook, Twitter, Quora, and many of them have tens of thousands of followers.  They post their papers on social media, give updates regarding their research group's progress, talk about interviews they recently participated in, and some even comment about their political preferences and views on current events.  By now, it is also well-known that many of the best CS professors get poached by industry giants, e.g., Google, Facebook, Uber, which at least one professor thinks is beneficial to both academia and industry:

https://techcrunch.com/2016/04/26/it-isnt-just-uber-carnegie-mellons-computer-science-dean-on-its-poaching-problem/

However, I don't see much self-promotion going on from mathematics professors on social media.  Many that I know of - both young and old - either do not have Facebook accounts (or they are completely private on Facebook), do not have Twitter, nothing on Quora, except for maybe some conversation on mathoverflow.net.  On their school websites, math professors give relatively minimal information - office location, publications, course notes, a resume.  Sometimes they will say whether they are going to some conference to give a talk.

Main question:
Why don't mathematics professors advertise themselves more on social media?
Is it perhaps frowned upon by the math community, and that they would come off as "less serious" about academic research?  Is it some traditional, philosophical reason for not publicizing one's work for the non-math world to see?  Of course, an extreme example that comes to mind is Grigori Perelman, who turned down the Fields Medal and never gave an interview about his important work.

Secondary question: Don't they also want the chance to be poached by an industry giant and make a few million dollars for a couple years of work - and then return to academia?
[It's hard to imagine an answer that isn't somewhat speculative, so let me give a somewhat speculative one.  A lot of what I will say is more or less the same as various commenters already said.]

For context, I am a pure mathematician working in the UK, but I did postdocs in the US and in Europe. Here are some reasons I can think of that a mathematician would not use social media to promote themselves in the way you describe. 

First, motivation. It takes a lot of work (as well as good fortune) to become a mathematics professor. It's safe to assume that almost everyone who achieves this goal actually wants to be where they are. (Initially, at least.) If we all wanted to work in the tech industry, we would have made a different choice at some point in the past. But we want to do math, and teach math. 

The contrast with computer scientists should be clear: it's plausible to think that a computer scientist could move from academia to the tech industry without changing their research focus too much, and then come back to academia if they change their mind. For most mathematicians, though, this move would mean no longer being a mathematician, and most of us don't want to do that.

Second, nobody is going to poach you! (Probably.) This has already been well-covered in the comments, but it's worth repeating. The idea of a mathematician being poached by a tech company on the strength of their research is not very realistic in most cases. 

Despite what we write in grant proposals, a lot of the research done by academic mathematicians does not have much relevance for the "real world" outside math. (Even in what is usually called "applied math", my personal impression is that many people are more interested in the research itself than in possible applications.) Of course there are exceptions, but even among these, many people are working in fields not relevant to the tech companies that you describe as doing the poaching.  Other industries may have use for the outcomes of mathematical research, but not the resources to employ dedicated mathematical researchers. 

In particular, the scenario you describe of "mak[ing] a few million dollars for a couple years of work - and then return[ing] to academia" is wildly unrealistic for, I would say, the vast majority of mathematicians. To me your second question feels a bit like asking "Why don't more mathematicians spend more money playing the lottery? Don't they want the chance to win millions of dollars?" 

Again, by contrast, it seems very plausible that an academic computer scientist might be working on something that is of immediate relevance for a large tech company, so poaching is a realistic prospect here.

Finally, mathematical culture. OK, but even if being poached is not a realistic goal, or not even desirable, why don't mathematicians promote themselves more on Facebook, Twitter, and the like? Don't they at least want to boost their profile and get a bit more recognition? I think the answer to this involves, more than any philosophical reason as you suggest, the norms of mathematical culture. (To repeat, I 'm a pure mathematician, so my point of view is heavily slanted towards this part of the discipline.) 

In my experience, mathematicians as a community tend to be extremely sceptical of anything they regard as boasting or exaggeration of one's achievements. The norms of our culture teach us that self-deprecation and understatement are the appropriate attitudes to adopt, at least in public. (Real example: a seminar speaker writes his big theorem on the board, then says to the audience apologetically "Now, this is not entirely trivial...") In this context, using social media to "promote" your work might have the opposite of the intended effect. Instead of people reading, and respecting, your work more, people might start to think of you dismissively as "that Twitter guy".