Oh, and to actually answer the original question:
You present a 5th level wizard with (+6 Int modifier) + (8 ranks) + (1 from trait) = +15 bonus
If this character takes Dragonfire Adept for level 6 (hey, breathing fire at will is cool) and takes Draconic Aura (Insight) as his level 6 feat, that increases his Knowledge bonus (assuming no antimagic field) by +7, so maxed out Knoweldge skills would be
(6 Int)+(9 ranks)+(1 trait)+(6 invocation)+(1 aura) = +23
He could also make untrained skill checks at +14 if he didn't have any ranks in the subject.
At level 7, the bonus from the aura scales up to +2, giving +25 to maxed out skills and +15 to untrained skills. Unless your 7th level is in akashic, in which case you double the Int bonus and so reach a bonus of +31 for maxed out skills and +21 for untrained skills. (Without the headband, it would be +29 and +19, respectively.) Plus first level akashics gain the ability to add a +2 bonus to any skill check once per day. That would make 2 levels that weren't advancing your spellcasting, but boy would you know a lot.
