Emirikol said:
1. High intelligence score but very low education
My father never got past 9th grade, but his personal reading library puts mine to shame. He routinely reads encyclopedias, National Geographic, and is as addicted to the History Channel as I am. This is called "Independant Scholarship". He was also a truck driver; If I told him I was going to such-and-such address in whatever town, USA, 9 times out of 10 he could get me within 10 blocks of the destination.
Another example is my mom, literally grew up in the woods (my grandfather built the house himself about 10 miles from O'Hare International Airport... Except it was only a single strip of dirt at the time and he had to chop down a mile-long strip of trees to make a "road" to the house) and existed on a High School diploma for nearly a decade. She finally got tired of "drone work" and went back to school to become an LPN. Of course, she's still frustrated, so I'd say she should have gone to med school... Certainly would have kept her out of my hair.
Then there's my uncle... Well, not really my uncle, only that his farm (now a State Landmark in Wood Dale, Illinois) was the only other farm within 3 miles of my mom's home, so his family is kinda attached to our family... At any rate, never got passed high school, and isn't much of a reader (literate, yes, but not well read). However, if you got a car problem...
any car problem... You take it to him. Diesel truck broke down? Take it to him. Rewire the entire friggin' house? Call my uncle.
And, of course, my Grandfather... I doubt he got past 8th Grade (though I might be wrong), but he was one of the best Operator-Engineers ever to work excavation in the Chicago region. Built his own house, constantly called Architects to let them know that
they screwed up the foundation of a building or a field survey, had every major US battle from WWI to Viet Nam memorized to heart (at least, as memorized as disclosed public documents would allow), and could recite German history (as well as our related family lineage) back to the 1300s (and was well versed in the mythology of the preceeding eras). He also had acommidations from the US Army (circa WWII) for things like "original thinking", "improving performance" and "updating standards and maintaining high efficiency ratings" (on top of his Purple Heart).
Given these real-life examples, I would say that High Intelligence/Low Education would be a misnomer. Rather, it's a lack of "formal" education. Such characters would be most knowledgable in those things that have actually had importance in their life while also having knowledge in those subjects that they pursued as a matter of personal interest rather than "graduation requirements". An alternate would be someone who's extra Skills are put mostly into life-necessities but is frustrated by their past inability to achieve some degree of mental/scholarly achievement.
2. High education but very low intelligence
Like my brother... Went to school full time for five years to get a three-year degree. Struggled for a year to get his Real Estate license, but never paid for the license and thus didn't get it. Went to Dealer School and found out that running a Blackjack Table really was work so never did anything with his certification. Purchases a $600 you-can-make-a-fortune-in-computers software education package and then never removes the shrink wrap.
Hmmm... Okay, maybe his Wisdom's a tad low, too. Closest representation I can think of, though.
Oh, no, wait... The girl's brother in
The Mummy (alchohaulism optional). Lots of information in his head but little ability to actually recall it without being reminded about it by his sister, book, or wall enscription. Such a character would probably be prone to saying something akin to "I just remembered that..." about 30 seconds after it would have been ideal to know it.
Then again, he might just be a star athlete that got preferential treatment from his University of Choice and doesn't know much beyond throwing a ball and downing a beer-bong.
