I have long thought the book description of Intelligence (and to a lesser extent Wisdom) should be junked.
Str, Dex, Con, and Cha determine your chances of success for a given task. You, the player, can have your character try anything you can think of; if your stats are unsuited to the task, you'll probably fail, but you can still make the attempt. However, because of the way the book describes Int and Wis, a lot of people see them as limiting what the player can do. If you the player come up with a brilliant idea, but your character isn't as intelligent as you are, you have to forget you ever had that idea. You can't act on it.
For most D&D players, all the things that Int purports to measure, we excel at. By any reasonable standard, the majority of players are Int 16+. So, if you want to "roleplay your character," you have three choices:
1. Constantly second-guess your decisions. Whenever you have an idea that you, the player, think is really clever, it's likely too smart for your PC. Forget it.
2. Play a wizard.
3. Play a non-wizard, and put 16+ in Int.
If I had my way, Intelligence would be renamed Lore, and it would represent simply your knowledge of the game world. You decide for yourself how smart your character is, without reference to the rules. You roll Lore skills to question the DM about things your character knows but you don't, just as you roll Perception to question the DM about things your character sees. If you have a low Lore, your character can be whip-smart, but you're uneducated. Anything you want to know about the game world, you have to find out in-game.