None of these subjects are simple, but this is more problematic than most, although I think the line is pretty far from what many traditional GMs consider a good place.
Some years back I was in a short campaign or maybe scenario is a better description. I was playing an anthropolist. Someone who was actually a professor of the subject and had pretty good knowledge of it. It was a mystery game and one of the clues was a song. The key was to figure out the language used in the song.
So, I (as the player) checked a list of European languages (as it was clearly western European, although not one I would have readily recognized). So, I spotted some languages on Wikipedia it might have. I’m not sure, but lets say it was one of the Gaelic languages, so I went to find an example of what it would sound like sang… and I immediately found the song used by the GM.
I understand the GM didn’t really like this, because I went outside the rules to do this. On the other hand, because of my characters expertise, he should have recognized the language immediately. From my point of view, I was trying to play my character better, because I wanted to have access to knowledge the character would have. This particular GM does have a very dictatorial way of running games, so he didn’t like anything outside of his control, or which he hadn’t planned for. If you’ve read my stuff before, you know this doesn’t work between us.
Anyhow, in this case I wasn’t apparently allowed to do this in order to get into the head of my character, but that very same GM doesn’t like people using Persuasion skills, because he would much rather have players play these situations out. Okay. I get that, but this is an idiotic approach. I’m not my character, even if I want to get into the head of my character. If my character is quick-witted and charismatic, how am I supposed to play that? Okay, that was just a bit of self-irony, I am very quick-witted and some people do develop a weird respect or fascination for my persona, so I guess I have some charisma as well, but anyway, is everyone supposed to be as quick-witted as the person they play?
This is comparable to having weights in the room and asking the players to raise them whenever their character wants to do something that requires strength. If you don’t do that, all physical abilities are always going to be inherently better than social and intellectual ones, because they don’t actually count, if you still have to do all the work yourself.
Of course, you don’t want everything to be just a series of rolls either, but it doesn’t have to be. The key is to leave all decision to the player. As long as the player can’t just roll to find out what the character should be doing, there is no problem. However, there are other ways.
One of things I like to bring up, which is often forgotten, is the genre (and I’m not talking about setting). Genre should be the deciding factor on how the players can approach these things. Do you want to emphasize social interactions or puzzles? You shouldn’t let the characters only get out of it with a roll, but at the same time you shouldn’t punish the players awkwardness either (and let’s face it, many of us are awkward). If they’ve put points into a skill that makes their character better negotiators, than their character should be a good negotiator, even if the player can’t really play it through. As long as they try to, it should be good enough.
Same with the intellectual stuff. Rolls shouldn’t clarify everything (unless its that kind of a game), but you should get clues and so forth. If there is an intellectual puzzle, a character should be able to figure it out somehow. After all, within the fiction its supposed to be the character doing it, not some avatar of the player.