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Source: https://writers.stackexchange.com/a/27120
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

In the real world, especially before the internet, technical expertise and education correlated heavily with economic privilege and access to resources. If the character isn't formally educated, there's little hope for him being academically intelligent. He/she (more likely he, given medieval gender roles) can be skeptical, he/she can have a sharp wit, he/she might even be able to read. Keep in mind, however, that literacy was a [rare ability](https://www.quora.com/What-were-literacy-rates-in-Medieval-Europe-How-did-they-compare-to-literacy-rates-in-the-Roman-Empire) in medieval societies.

One alternative is to have a society that is _aesthetically_ medieval but _functions_ as might a society from a different era (not necessarily a _better_ era, just an era where it is more feasible for a peasant to be educated. If this means the protagonist is a slave whose job is to write down what elites say, well then, you have a society that functions in some ways like the Roman Republic.) For instance, a society with the governmental quality of a [republic](https://en.wikipedia.org/wiki/Republic) or maybe a [constitutional monarchy](https://en.wikipedia.org/wiki/Constitutional_monarchy) or at least some semblance of [egalitarinaism](https://en.wikipedia.org/wiki/Egalitarianism) and [humanism](https://en.wikipedia.org/wiki/Humanism) would make the kind of protagonist you're talking about more feasible. Even if it comes packaged with a set of social ills separate from those seen in real-life medieval societies. Mixing and matching your government types with varying levels of egalitarianism, humanism, [secularism](https://en.wikipedia.org/wiki/Secularism) and [mercantilism](https://en.wikipedia.org/wiki/Mercantilism) can result in entirely unique fictional societies which, while they never existed in the real world, are not necessarily unfeasible. The aim is to create a society where the reader can experience sufficient [suspension of disbelief](https://en.wikipedia.org/wiki/Suspension_of_disbelief) within the scope of your story.

On the flip side, keep in mind that socioeconomic status is not a guarantee of illiteracy so much as it is a decent predictor. Consider, for instance, the escaped American slave [Fredrick Douglass](https://en.wikipedia.org/wiki/Frederick_Douglass#Life_as_a_slave), who against all socioeconomic odds managed to be more literate and intellectual than the average free man at the time. This shouldn't be regarded as surprising, but it should be regarded as unique, and difficult to attain.

If your protagonist is in a downtrodden position, he will likely require the help, unwitting or not, from people in a higher position.

If you desire even less fidelity to history and more creative freedom, systems of magic and superhuman abilities provide all you need. A character can be graced by the God or Gods with the wit of solomon, Can be given psychic powers which allow for heightened empathy and sensitivity, can decode alphabets of foreign languages without the help of native speakers, can slow down their own perception of time to prolong important decisions.

If you go with a magical system always have a way for your character to become exhausted or less sane with the execution of each "spell" so that their heightened abilities come at a price which increases narrative tension.

A good and increasingly popular example of the sort of character you're setting out to create is [Kvothe](http://kingkiller.wikia.com/wiki/Kvothe) from the [Kingkiller Chronicle](https://en.wikipedia.org/wiki/The_Kingkiller_Chronicle). I would also like to mention [Will Hunting](https://en.wikipedia.org/wiki/Good_Will_Hunting) who, while not a fantasy character, is a lower-class Bostonian janitor who is a genius at math despite being the kind of guy who sometimes gets into street brawls. His character, to me at least, manages to be convincing and compelling despite not necessarily being realistic.

Original score: 3