They have no interest in ever being a child. They eschew toys in favor of books and beginner scientific equipment. They immediately and eloquently denounce the logic of Santa Claus. They may insist that their parents read the classics to them as bedtime stories and thus scoff at the books meant for their age. Or they just read the classics -- or, better the encyclopedia -- to themselves purely for fun. They would rather discuss world events than... play (How childish!). They may even already have a distinct, philosophical worldview, never mind that they haven't lived long enough to see enough of the world to form such a view. And so on.
One common effect of this "adult-in-a-child's-body" phenomenon is that characters who act their intellectual age have no interest in kids who are their actual age. They may look down on kids their own age as savage or barbaric, and would rather associate with their intellectual peers, even if those peers are 4 or 5 times the character's age. Strangely, in the world of TV and media in general, neither party seems to care about the age difference, and the kid genius in question thinks nothing of it to discuss the latest political development with someone old enough to be their father/mother. Thus, of course, they are likely to be construed as teachers' pets in any academic setting. This aspect is only occasionally Truth in Television, as there are many cases of highly intelligent students deliberately dumbing themselves down in order to fit in.
Often, a character who acts their intellectual age is, supposedly, more sophisticated than the adults, even the educated ones, and will not hesitate to point out grammatical errors, logic flaws or to criticize behavior. Often may grow into an Insufferable Genius, if they are not one already. If they're lucky, they may instead outgrow their uptight arrogance and wind up a recovering Insufferable Genius.
Note that this refers to kids who more or less behave like adults while still functioning in the world of kids, and having a normal childhood (or as close as a Child Prodigy can get to normal). If they are highly intelligent but thrust into an adult role, or otherwise traumatized into maturity, then they are Wise Beyond Their Years.
Somewhat Truth in Television, but reality is more complicated. Gifted children are usually all over the place in maturity, acting their intellectual age in some aspects, their actual age in others, and in between in other ways. And in some ways they may be different from non-gifted kids of any age. Emotional maturity is usually at age level or only slightly advanced. This makes finding friends tricky, since older kids see them as immature, while same-age kids don't understand them. (An amusing anecdote is a highly gifted 4 year old who wanted to leave a note for her same-age friend, before remembering with disappointment that her friend couldn't read!)
- Detective Conan's Ai Haibara is an eighteen year-old prodigy who has been shrunk down physically to age six or seven. Since she puts no deliberate effort into acting like a child, she tends to come off this to people who aren't aware of this fact. The degree to which this is true has dwindled with her Character Development as she's Took a Level in Cheerfulness over the course of the series. Even before she was shrunk down, Ai studied biochemistry in the United States and started working for the Black Organisation before she was thirteen.
- In The Mage Will Master Magic Efficiently in His Second Life, Zeff acts his appropriate mental age in comparison to, say, Milly, who is a year older physically but an actual Child Prodigy.
- Ace Attorney has the first introduction of Franziska von Karma, who, with perfect sentence structure, says she will be tutoring Edgeworth. At the time, she is about two or three.
- Throughout his long career as a superhero, Billy "Captain Marvel" Batson has been all over the map with regard to this trope. Averting this trope is generally regarded as an important part of his characterization, and was certainly part of the character at his conception. Billy is a 12-year-old boy who becomes a superhero in an adult body, and acts like it, reacting to the strange things he encounters with childlike enthusiasm. Various authors have forgotten this feature and played the trope straight, turning the adult Captain Marvel into someone with a personality indistinguishable from Superman. These runs are generally regarded very poorly by fans.
- Still, possessing the Wisdom of Solomon while in Captain Marvel form can help justify more adult behavior. Or at least a more adult level of awareness.
- Amethyst, Princess of Gemworld is a more subtle case of averting the trope, and then playing it straight, than Captain Marvel. Like Marvel, she was a 12-year-old who gained powers and age when she travels to a magical kingdom. Played less childishly than Captain Marvel, Amy still had a tendency to be emotionally immature at certain moments, and the original creative team had to remind certain readers in the letters pages that it was because Amy was still emotionally a 12-year-old, whatever she looked like. And then the creative team was kicked off the book and the "Amy Winston" aspect of Amethyst's character was basically dropped.
- Kid!Loki after his old self's consciousness took over his body began acting like this (see Young Avengers) not only more mature but also troublingly unchildlike. He even drank and flirted, which the others didn't take seriously because, well, he looked around 12. On the other hand he still didn't act the age appropriate to his actual age probably thanks to being a Manchild even as an adult.
- Harry Potter and the Methods of Rationality: Harry James Potter-Evans-Verres. And most of the other children, who act 3-10 years older than their physical age, depending on just how much training they've had.
- A cycle of Discworld fics have Ponder Stibbons lucking out and meeting a girl. She is an Assassin by qualification and circumstance, an educator at the Guild school, and by vocation and temperament is a good enough zoologist to earn a doctorate for it. This marriage of academic minds creates three daughters. The youngest of the three is frighteningly intellectual. At eight, she is taking home worksheets in mathematics designed for the average third-grader and answering them as if she was in the eleventh. She even speculates on what circles and spheres would look like if viewed from higher dimensions of space-time, and has a fair stab at working out the theoretical physics. Her class teacher in maths had to be taken away by kindly friends for a reviving drink. Ponder resorts to inventing "Take your Daughters To Work Days" and has Ruth spending time with her father at Unseen University. Where she starts to outclass her father's undergraduate Wizard students. Read more in the works of A.A. Pessimal.
- Charles Wallace from A Wrinkle in Time, which leads to him overestimating his capabilities, and gets him ensnared by IT. Charles Wallace is a little different, though. He wishes to be accepted by his peers, but finds that he cannot hide his intelligence, and gets bullied for it.
- Artemis Fowl... most of the time. Subverted in the beginning of The Lost Colony, when among his greatest nemeses is the distraction that is puberty.
- One of the first novels to feature a Child Prodigy was The Hampdenshire Wonder in 1911. The protagonist is not only a genius, but a truly superintelligent little kid who judges the whole human culture an "elementary, inchoate, disjunctive patchwork"... at age four and a half.
- Lord Peter Wimsey graduated from Balliol College, Oxford with a first-class degree in history, and knows a great deal about incunabula and criminology. He also played high-level cricket for Oxford, and in his 40s takes regular exercise with a fencing master and judo teacher.
- Wensleydale in Good Omens: His parents "called him 'Youngster'. They did this in the subconscious hope that he might take the hint; Wensleydale gave the impression of having been born with a mental age of forty-seven." His favourite "comic" is Wonders of Science and Nature, and he insists on being the Only Sane Man in the face of Adam's ideas.
- Aaron Fidget in Hogfather:
Aaron: Let's be absolutely clear. I know you're just someone dressed up. The Hogfather is a biological and temporal impossibility. I hope we understand one another.
Death-as-Hogfather: Ah. So I don't exist?
Aaron: Correct. This is just a bit of seasonal frippery and, I may say, rampantly commercial. My mother's already bought my presents. I instructed her as to the right ones, of course. She often gets things wrong.
- John Green's An Abundance of Katherines has Colin Singleton, who started reading at 3, loves anagrams, and creates a mathematical theorem to detail his relationship with all of his 19 girfriends (all of whom are named Katherine).
- In This Is Not a Werewolf Story, Mary Anne, who's probably supposed to be about 10 or so, seems to be trying to act more mature than her age, like when she brings up "the social contract" to tell Raul off. She has a fair number of Not So Above It All moments, though, particularly regarding her neglectful parents. An angry Raul takes a bit of vicious pleasure in one, glad that she occasionally gets reminded that she really is just a troubled kid like the rest of them.
- River Tam from Firefly is a subversion. She's shown, in flashbacks, to have been so smart that she could spot flaws in the textbooks Simon was studying from and uses surprisingly advanced terminology ("that whole section is fallacious"). It comes up because she's engaging in age-appropriate activities (like pestering her brother while he does his homework, and playing pretend that he and she are Alliance soldiers who have gotten cut off from their squad when the Independents brought in dinosaurs. Then suggesting they must resort to cannibalism).
- Manny from Modern Family. In one particular episode, he has been having conversations with a grown woman online and arranges a date, neither suspecting an age difference. "He's an old soul."
- Micah in Heroes.
- The "Dakota Fanning" series of skits on Saturday Night Live is made of this trope. An actress portraying a fictionalized version of Fanning behaves this way.
- In an episode of The WB show Everwood, Ephram talks about a young child and notes that she's mature "but without having that creepy Dakota Fanning '45-year-old-lady-trapped-in-a-10-year-old's-body' vibe."
- Star Trek: The Next Generation's Wesley Crusher is actually an aversion. Although he is a technical genius who understands the Enterprise as well as many of the crew, his emotional maturity is more like a typical teenager. This combination, along with the allowances Captain Picard gives him, are probably what made him so annoying to many viewers. However, he is one of the more believable depictions of a gifted child in fiction.
- Sheldon Cooper in The Big Bang Theory was this. When he was young, he had a diary of his toilet training, and was angry when his parents got him a motorized dirtbike instead of a titanium centrifuge for his birthday. He still had some childish traits, like his imaginary friends, only he called them imaginary colleagues and sent them home at the end of the day.
- Zig-Zagged by Calvin of Calvin and Hobbes. He's incredibly intelligent, well-spoken, and has a very solid grasp of concepts and ideas that many real-world adults struggle with, but at same time, he frequently uses his enormous vocabulary and razor-sharp wit to express the kind of thoughts any regular six-year-old would have. He also has a heavy case of Brilliant, but Lazy, especially when he's forced to do something (like schoolwork).
- In Arcadia, Thomasina functions as a child with regards to romance and sex, and an adult with regards to intellectual matters (Classics scholar, mathematical genius). Which serves as a reflection of the Central Theme of the conflict between Romanticism and the Enlightenment.
- Van from Harvest Moon: Animal Parade prefers studying to playing, and always wants to know if your kid likes to read/go to school/do homework. He even teaches some of the other kids during events!
- Min-Jeong in Renowned Explorers is the youngest character you can add to your exploration party. She's also a prodigy, serving in the Scientist role. In events, she generally acts composed and skeptical, closer to Agatha than anyone else her age. She even gets the "led by a child" debuff if Hildegard (who is two years older than Min-Jeong) is chosen as captain.
- This is one of the biggest differences between Molly and Golly in The Inexplicable Adventures of Bob!. Both are superhumanly intelligent and much younger than they look, but while Molly is perfectly content to alternate between reading Stephen Hawking and Dr. Suess, Golly works very hard to look mature and sophisticated at all times (to mixed results).
- The Whateley Universe has several examples. Ayla is a self-acknowledged one, and Jobe is one who doesn't realize it. Ayla's reaction to realizing this is to try and bring his friends up to his level, so that they can at least understand why some things bug him so much. ("Why would I blow money on an expensive stereo system that's going to be outdated in three months' time, or on clothes that are going to be out of style in two weeks?")
- DSBT InsaniT: Even though Snake is the same Vague Age as Bear, Duck, and Balloon, he is far more mature and sensible than they are.
- Huey Freeman of The Boondocks has elements of this in both his comic and animated incarnations. As an example, in one episode of the animated series, his friend Jazmine says something about the Tooth Fairy. Huey responds by saying that the Tooth Fairy isn't real, the world is a hard and lonely place, no one gets anything for free, and everyone she loves will be dead one day.
- Egghead, Jr. in the Looney Tunes Foghorn Leghorn cartoons. He was always reading books and otherwise acting in an intelligent manner, and didn't want to do the childish things Foghorn Leghorn wanted him to do.
- Subverted with Polly from Stickin' Around. She plays off this trope accordingly, though it doesn't stop her from playing with the other kids.
- Stewie in Family Guy tends to zig-zag this trope.
- Dexter in Dexter's Laboratory adheres to the trope, except that his attitude toward girls remains entrenched in normal 9-year-old mode.
- Lampshaded in an American Dad! episode with a flashback of Steve's friends as toddlers:
Young Barry: Interesting how we've developed such a sophisticated hierarchy at this young age.
Young Steve: Shut up, Barry.
Young Barry: (enthusiastic) I'm at the bottom!
- Daria generally manages to play this fairly realistically: Daria is smarter than most of the adults she knows, but she is still lazy and pretty immature at times, particularly with her own emotions (which she'd rather just repress). The episode "Boxing Daria" has flashbacks to her younger days; Helen describes her as acting like a miniature adult, and unable to connect with other children, but even then her six-year-old reading material is Black Beauty rather than, say, Homer in the original Greek.
- Zig-zagged by Lisa Simpson of The Simpsons, Depending on the Writer. She's a Child Prodigy who is usually far more mature than other children or even than most of the adults around her, identifying with world-weary jazz musicians and quoting existential philosophers. Every once in a while, though, the audience will be reminded that she's still an eight-year-old girl with details like her constant yearning for a pony or her subscription to Non-Threatening Boys Magazine and precocious crushes on teen heartthrobs named Corey.
- The title character of the very short-lived and critically-blasted Allen Gregory is an example gone awry, in that he was supposed to be extremely mature for his age, and promos made him seem like a tiny Frasier Crane. In practice, though, he was the other kind of "mature," and came off as a smug, creepy, unlikable sociopath.
- Mr. Cat from Kaeloo possesses the intelligence of an adult, and acts like one too. He's far more mature than the other characters, who are also kids, and typically refuses to play children's games. In one episode, he was stated to have possibly "lost his inner child".
- Lisa from The Loud House is a super genius 4 year old. She has a hard time interacting with other kids because of her maturity.