[quote=@0 Azzy 0]
Under a section labeled "Character strengths"  he has written "He is amazing at everything he tries. If needed, he could learn and entire language in a day and a half or get officially certified as a musician on a lute with a broken string.".  
[/quote]
That's better than some power players I've known, sadly enough. 

If we're going to use the RPG comparison, I think the difference between being a power playing Gary Stu and just high leveled is the explanation behind it. For instance, I can see Matrim Cauthon in WoT being a good staff fighter with a high charisma modifier and bluff skill, but it was the DM's that gave him his A class strategy mind by leading him through the the doorway in Rhudiean (if that is the reasoning. I'm rusty). And he got the cool anti-magic medallion. These being given to him through the DM's story, so to me it's not so much of a Gary Stu problem because it had to be earned and experienced.

Ran I won't even touch, and Mat/Perrin are Ta'veren so they're lucky in general, but I do feel like the latter two had some of their abilities explained and [i]gained[/i] throughout the story. Same with Egwene and...well maybe not Nynaeve. 

My question is, did Kvothe ever have his abilities explained or gained, or did he start out great at everything?