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I feel like so many ppl probably brush Erwin's achievements under the rug cuz Isayama didn't spend an entire manga focusing on them. Like people out there REALLY think a newbie is smarter than the 13th Commander of the Survey Corps who guided the course of the story until RtS.
It really don't make sense. No hate on said newbie though. But I guess that's why this is a shounen series, and since most of us were exposed to the main trio more than the vets, we're just conditioned to think about things that said main trio did instead of thinking critically.
The adults legit had YEARS to do things that the kids JUST started doing. Experience is a big variable when it comes to smartness. As I see it, Zook, Hans and Erwin will always be smarter than Armani for me. I'd explain exactly why but I don't feel like wasting my time on that.
(But if you still wanna ask me, I might link you to a very ranty tunglr reblog I made more than a year ago when I'd had it with the Erwin slander. I'm not VERY proud of the tone I used in it, but I still stand by the points I was making... So ask at your own risk.)
Although Hans is, according to Isayama, one of the smartest, I think they lack elsewhere, which is why they're in such a state right now in the series. I think their intelligence might not be cut out for strategy-based decisions (remember they are a researcher first).
(That being said, you can pry "Awesome Commander Hanji finally realizing their potential for real and kicking ass" from my cold, dead hands.)
Zook and Erwin are close competitors for me. Obviously I prefer Erwin because of my bias, but thinking more on it, I think Zook's tendency of letting his emotions sway him is where he's put at a disadvantage, while Erwin, as we all know, is king of compartmentalizing emotions.
I'm not too proud of Erwin's ability of putting his emotions and morals aside to get shit done, but it's certainly something I admire him for. He might not be the most intelligent (tho I think he is) but with how the series went, he still comes off as the smartest imo.
Anyway, I'm not challenging anybody. I'm just putting my own thoughts out there to make sense of WHY people would be so convinced that a 15 yo is smarter than three whole adults who've been known AND shown/said to be the smartest people around.
Another reason why I think it's safe to assume that Erwin is the smartest within the series' proceedings is because I have unfailingly always been more interested in characters who are the smartest (strategist) of the lot 
