Not necessarily, though it does seem that often people excel in one "camp" and don't in the other. I of course have chosen the English/linguistics/history camp over math/science, but I always did well in math and science in school, and I have a casual interest in them.
I did well in English (though you can't tell it from my posts here) and sucked in math. I transpose numbers and always had a very low but passing grade in math.
It is quite common to find mathematically-minded people are weaker at languages, or (like me) vice-versa; but that does generalise and there are plenty of highly educated people who are as fluent in English as they are numerate.
Interesting point, Thriftymaid, about whether we use all of our abilities to the full. Obviously no-one can be a complete polymath, and there are those who are not interested in being even a "unimath", so to speak; but I believe each of us has a certain limit of ability in any academic field or creative skill we attempt. You cannot force people to learn anything, and certainly beyond their natural ability; but even voluntarily, with the best will, enthusiasm and opportunity in the world none of us can proceed beyond our personal limits.
I believe in what I call my 'Buckets On A Beach' mental capacity model. One factor in my concocting it, is the contrast between my father and me.
Dad held a BSc, was a Chartered Electrical Engineer - not a wire-man although he was very able practically and re-wired our house to the proper standards among other things - and used his education and charter professionally, as a Civil Service scientist. Therefore, as an Engineer, his work would have been mainly mathematical; and electrical principles are chock-full of trigonometry and 'complex numbers' (in maths jargon).
Possibly to my parents' disappointment, which didn't bother me much then let alone now as it's my life not theirs, I proved a slow learner in anything and everything, but especially Mathematics and French. Yet, and perhaps surprisingly, I had been "diagnosed" as unusually highly intelligent at a young age - ordinary IQ tests show only puzzle-solving, not learning, ability. You need high analytical skill to understand hence learn, Maths; and a prodigious memory for the rote drudgery of the arcanities of gendered nouns and umpteen irregular verb tenses. I left school with mediocre GCE exam results and embarked on a "career" of impressive ordinariness, much of it as a semi-skilled factory hand.
Now, Dad himself found his own levels in an unexpected way. Our Mam was always the musical one of the family - played piano, sang in amateur choirs - but Dad bought an electronic organ kit made by the German firm, Wersi. The instructions were entirely in German, but he understood circuit-diagrams and electronic theory, bought a German-English dictionary to help, and built the instrument to his usual very high craft standard. However, playing it was a different matter, and he admitted ruefully he'd reached a level where he could play simple tunes from the scores, but was unable to progress however hard he tried.
I think Pearl has summed it up very neatly: it depends on the individual.
Benedict Arnold 