Previously, I ranted, just a bit, about the suggestion that there are more linguists than languages. I guessed that, in fact, this may not be true. Thanks to the LSA update email that was just sent out, I was able to follow up a bit. That email referenced the results of the American Academy of Arts and Sciences’ survey of linguistics departments (pdf, it doesn't load every time, so repeated clicking might be warranted). Table LN1 (below) gives an estimated 1630 faculty member in linguistics departments across the United States. That strikes me as a fair base to start a back-of-the-napkin estimation of total linguists worldwide (I noted in my previous rant the problems with defining a linguist, but I'll take this survey as my authority for now).
Let the number games begin. First, let's assume that this initial estimation is conservative. I'll throw in another 10% to make up for that. Let's assume there are about 1793 linguists in the US. I think it's fair to assume there are about as many linguists in Europe (though you'd never know it by the poor rate at which American linguists cite Europeans, but that's another rant). So that's another 1793 for Europe. I'd wager that there are at best an equal number of linguists in the rest of the world as in either the States or Europe, so that's another 1793.
By this estimation, there are approximately 5379 linguists in the world (1793 x 3). That sounds about right to me. And if this is correct, then my original point stands, there are NOT more linguists than languages.