Personally, I like both math and learning languages but I'd like to believe it's no more than a coincidence.
None of my English teachers were too keen on maths and vice versa.
What is your experience? What other fields may be connected to language learning?
I excel at languages and tangible logic...but am horrible at math. Great at grammar...can't do geometry. My school couldn't believe that a kid could get an A in German and Latin, but an F in Algebra. They accused me of not trying and getting bad grades (marks) on purpose, which was not true.
One of the things I find very restrictive about math is that there is always an absolute answer. 2 + 2 = 4. Always. This isn't the case with language. There's more than one way to say something, and you can use different grammar forms to say the same thing or to get the point across.
That allows for creativity, personal expression and freedom within a set framework. Something I think mathematics completely lacks.
Many people who love math love it for exactly this reason. The answer is absolute. No grey zones. No doubts, no worries. Whereas those who thrive in the grey zones feel stifled by the "fascism of numbers". This could be more the answer for why there seem to be two groups, even though the cognitive function might be very similar.
As for another field....I'd say detective work and con-job criminality would be related to languages. Some of the best con-artists are fantastic at languages (creativity within a framework) and a detective puts together clues to figure out "what happened", that is, what parts are related to other parts to create meaning...subject + adjective + verb = Mr Green did it in the library with the lead pipe!
Grammar is kind of like math. So, it stands to reason that people who are good at math would be good at grammar and vice versa.
On that note, I hereby conjecture that the communicative language teaching was invented for the purposes of weeding math people out of language courses.