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.
Servus Tom! Here my hypothesis about the correlation between languages and mathematics. I read that the abilities for both branches of knowledge co-variate until the age of 12. Smart kids are good at both until the beginning of adolescence, more or less. After that, there is a kind of specialization. Most people are either good in one domain or in the other. But of course there are exceptions. I was talking about smart kids, if we take into consideration the groups of SMARTER kids, you will find people who are exceptionally good in both.
As for me, I always had a preference for languages and literature, though I was and still am curious about many things. At college, I found that statiscs were fun but I didn’t excel in it. They were just useful.
I think it's not a coincidence. When you communicate in foreign language your brain has to an analysis of the sentence, like it does while solving the math problem. On the other hand building the sentences is similar to solving problems using earlier known templates (like doing an exercise similar to one you did before).
The logic is a field of knowledge which refers to both: language and math. You try to be precise while building the sentence, to avoid misunderstandings. Using the programming languages is a nice training how to use the logic to communicate precisely with the computer. I think we use a lot of logic while learning human languages too (maybe some people learn it other way - those who hate math).
On the other hand there are languages which seem to ignore (or suspend) some laws of logic. I haven't see Slavic and Romance languages among languages you speak and I don't know how it is in Hungarian, but in most (maybe in all) Slavic and Romance languages there are double negations (when 'NOT ... NOT' is not 'YES' but still 'NOT'), which make all English teachers angry.
For example we can say in Polish "nie robi nic' or in Italian "non fa niente' what in literal translation means 'doesn't do nothing' what is obvious logical error in English and other Germanic languages.