I like this show (and its second season) a lot. Pretty much one of the very few 2011-2012 anime shows that I really am looking forward to watching almost every single week.
Out of the many shows that Sunrise have made, I think Phi Brain is somewhere at the top, because it's not about Gundams and physical fighting. There's also a certain air of unpredictability when it comes to this series.
You have to keep in mind, Phi Brain was made for NHK Educational channel, which is an offshoot of NHK. It's intended to encourage/motivate Japan's youth to challenge themselves. On the official Phi Brain website, for every new episode that airs, they post the accompanying puzzle that showed up in the episode. What's pretty amusing is that the anime stars characters, who are not exactly good candidates for being on an educational channel.
The show's setting, itself, cannot exactly be taken seriously as it takes place in a reality where puzzles are essentially EVERYTHING. In that world, being super good at a puzzle essentially makes you a celebrity or a target of a some kind of organization. However, if you've played a lot of Professor Layton games, you will get use to this kind of setting in no time. That's what makes that kind of reality unique, in a sense. Not every day will you come across a show that focuses on puzzles, and not about who's being number 1 master/champion of the world.
Story ~
I was expecting a lot of filler throughout most of the show along with the POG people challenging each of the main characters, which would be atypical of a shounen show set up. HOWEVER, it never ended up the way I was expecting as there are plenty of random things that do go on in the show. In the end, the story is no longer just about puzzles and how wrong it is to make them dangerous. It's about friendship, childhood trauma, emotions, and the true meaning of trust. That's what I admire about it.
Puzzle-wise, I enjoyed several of them. The show started off with ones you would sort of expect, but then, some of them do become ridiculous hard to your brain. They don't always explain how the puzzles work, but I don't mind that at all. You can always try it yourself online. (And this clearly improves with the second season.)
The first OP was awesome. May'n's Brain Driver was a pretty solid and fitting song towards the animation direction that the OP presented itself with. However, the 2nd OP for the second season, if you ever get there, it just blows May'n's away. (Overall though, they're both good.) ED wise, I like both first and second season's EDs.
Art ~
Kind of what I expect of Sunrise animation. Nothing too spectacular, but it's good enough as it is. They did a lot of good research behind puzzle designs and did pretty well on conveying the character expressions.
Sound ~
I think it speaks for itself. Sunrise does their sound and music like any other anime companies. I already put my input as to what I said about the OPs and EDs so no further comment is necessary for those.
Character ~
Out of the zillion anime character archetypes to use, Phi Brain puts together a: semi-grouchy puzzle prodigy, a photographic memory tomboy (-yandere-ish as some call her?), a baby face computer genius, a super convincing cross-dressing artist, a high strung tough crazy/sadistic(?) biker guy, and eventually, an apple juice loving student president. (And then, Kaito's childhood friend who is....*spoiler* so I won't be saying anything about him.) These guys are just lovable in their own ways. All their personalities are different as well as their antics. Even if some of them display, er.... "fan-service"-ish qualities, I pretty much disregard it because it's not bad compared to the shounen manga/anime that displays fanservice purely for guys. =__=;;
I initially wasn't sure what to expect from these characters , but the people behind the show, were able to play with these personalities in order to make the show engaging. Sometimes, they used the characters to poke fun at their own selves so I like that. ^_^ So much for some cliches....
We're also able to get into a backstory with some of them, even though, Kaito's past is the main focus. I think season 2 will continue with flexing out some of the other characters' pasts, from the looks of it, even if it's still Kaito past-focused. The side characters, for this show, are never forgotten in any way. They each get a role to shine in, whether it's a backstory or not.
Side note: A lot of people wonder what's wrong with the main character, Kaito, and why he treats all these other characters, supposedly his friends, the way he does. There is a reason for this and it's all part of his character development. People need to be patient about him, because his original personality was really.......*spoiler spoiler*
Enjoyment ~
If you've reached this far in my review, you can clearly tell that I have enjoyed this show immensely right into the second season. Things got pretty good by the end of the first season, and the second season just leaves the main characters without too much break/mercy.
Overall ~
If you can understand that this show....
+ Shouldn't be taken too seriously, while it still has its serious parts (that reminds me of Poke'mon Black/White, the game, just a little bit).
+ Don't expect the puzzles to be fully explained out or solved slowly, at least in season 1.
+ Don't mind a cross-dresser, who is soooo convincing that even after you know the truth, it's still hard to believe.
+ Don't mind the antagonist to be a bit "creepy" with Kaito and probably some other people.
+ Isn't all black vs. white. There are a lot of gray areas with the characters.
+ Kaito's own actions are influenced by "something".
Then, this is a show that's worth a shot. It's not exactly the level of "Fantastic Children", but, it's one of the better shows for me, at least, as oppose to a show full of harlems, stupid fanservice, pointless comedies,pointless fighting, undeveloped characters, and magic girls.