Recently, in a review of the third Percy Jackson book, I accused all the women in the series of being "Faux Action Girls" -- women whose prowess and usefulness in a given situation is more of an Informed Attribute than anything that the reader ever gets to see. What was interesting (and frustrating) to me at the time was that a lot of the tropers on TV Tropes didn't really see it the same way -- sure, the Annabeth character in the movie was a Faux Action Girl, but the one in the book is smart and intelligent and her advice saves the day more than once in the series. That makes her useful, right? Wrong.
The problem, at least in my opinion, is that being the Smart Girl in a novel doesn't make a female character strong, useful, and meaningful to the story -- it makes them less so.
The Smart Girl, as a character, is useful only to the author. She serves as a plot exposition device; such as when Annabeth explains all the plot-relevant Greek myths to Percy, even well into the later books when he really should have brushed up on his mythology by then. Why should he expend effort to learn the myths? From a literary standpoint, the more ignorant Percy is, the more ignorant the audience can be -- Annabeth is right there to pipe up and explain things to Percy and the audience. She becomes the narrative voice that is so hard to achieve in a first-person novel, and her purpose as Plot Exposition Voice doesn't make her smart or strong or useful -- it renders her into the same role as an author's footnote.
The Smart Girl is not, ultimately, smart at all. Never does her vast encyclopedic knowledge help her avoid an obvious trap -- to do so would be to avoid literary tension and exciting adventure, and no one (most especially not the audience!) wants that. Annabeth, Thalia, Zoe, Bianca, and every other girl in Camp Half-Blood stumbles blindly into the same traps that snare the admittedly ignorant Percy; despite every possible warning sign, the adventurers only notice the trap once it has sprung. Then, and only then, can the Smart Girl start spouting plot exposition and analyzing the obvious nature of the trap. "I've been so stupid!" she may cry, and the audience is forced to agree: the Hero may be ignorant, but the Smart Girl is stupid... and ignorance is a curable condition.
Even when the trap has been sprung and the Smart Girl's brain is allowed by the author to start working, the Smart Girl will not be the one to get the heroes out of the trap they find themselves in. She will be called upon to provide exposition, backstory, and relevant weaknesses of the monster/trap they are facing, but the actual solution will be hit upon by the young, plucky, male hero. Once again, this adds tension to the novel at the cost of reducing the Smart Girl to an even more useless character: it wouldn't be interesting if the person with all the knowledge immediately solved the trap, so instead the new "everyman" protagonist that the reader is intended to identify with should hit upon the solution in a moment of inspiration. If it is a literary law, though, that the ignorant character must provide the solution, it follows therefore that the Smart Girl can never solve the problem. Thus, we come again to the crux of the problem: the Smart Girl never does anything that could be deemed by the audience to be actually smart.
The Smart Girl is not a strong character even when she saves the Hero from harm. When Annabeth tackles Percy to the ground to save him from the manticore's poison spines, the reader doesn't appreciate how smart this plan was because the reader instinctively understands that Percy was never in danger. Once again, the Smart Girl is really only useful to the author as a narrative device; if Annabeth hadn't saved Percy in that moment, then something else would have -- a blast from Poseidon, an arrow from Artemis, a well-timed trip in the snow, whatever. Since the reader knows that the first-person protagonist is inherently protected from serious harm, thus any smart plan by the Smart Girl to save his life is ultimately pointless because his life was never in any serious danger. On the other hand, a smart plan by the Smart Girl to save the lives of others would in fact be quite meaningful, but Smart Girls don't get to save anyone but the hero -- the other characters must either be sacrificed to cause angst for the hero or saved by the hero to illustrate what a heroic hero he really is. The Hero saves others; the Smart Girl saves the Hero. The problem is, since the Hero is never in credible danger of losing his life, the Smart Girl's actions are ultimately meaningless and without tension or appreciation.
The Smart Girl is smart so that she can be bested by the brave and plucky Hero. She has a high Int score and can provide necessary plot exposition, but every other stat is ultimately her dump stat. She isn't as strong as the hero and will frequently bring a knife or a bow to what is clearly a sword fight, as we see in the many, many battles where Percy's sword is the one weapon that dishes out serious harm to the monsters they face. She isn't as fast as the hero, and can't take as many hits as he can -- expect to see her flung across the room and knocked unconscious at least once per book while the hero can take similar hits and keep going by the Power of Pluckiness. She's not as charismatic as the hero -- a point that will be explicitly called out in text when someone wonders why Ignorant McKnowsnothing is the leader instead of the Smart Girl; the handwave will be that he alone has a hero's heart and the masses will follow only him because of it. And though she is smarter than the hero, she will never be wiser than him; her "book smarts" will leave her cold and unable to follow her heart and make the right choice that the Hero will know instinctively to make.
When the book is over and the Hero has won, the future is bleak for the Smart Girl. Now that she is no longer needed as a plot exposition device, she will be downgraded to a trophy for the Hero. At best, she will be allowed to use her smarts to help the new world order; she will be an adviser, a vizier, a source to be listened to when convenient and ignored when not. At worst, she will be nothing more than the Wise Wife, useful only for soulful pillow talk where she soothes her kingly husband after a long day and provides lovely heirs that are smart and male -- the best of both their parents' attributes, of course.
Over and over in literature, we see the bare fact of the matter that Plucky Protagonists are interesting and Smart Second-Strings are not. Take Kathryn Lasky's Guardians of Ga'Hoole series: in "The Capture", Gylfie may be the one who figures out the moon blinking brain-washing techniques and how to prevent it, she may be the one who infiltrates the crucial hatchery and library and learns their secrets, and she may be the one who identifies which owl can be safely approached to help them learn to fly and escape from their captivity, but she is not the hero. Soren is. Soren, who is younger, who is more ignorant, and who is (to most young readers) more easily identifiable with. To be sure, Soren has some wise moments, such as when he realizes that they are being hypnotized with their names, or when he invokes the Ga'Hoole legends to save their sanity when in the moon prison, but these moments are moments of wisdom, when his "gizzard" instinctively guides him. Once again, the (female) character with the reams of knowledge and loads of intelligence takes a literary backseat to the (male) character who is regularly ignorant but yet is granted important flashes of inspired wisdom.
The Smart Girl effect is so well-established that when it is subverted, it's immediately noticeable. Take David Handler's "A Series of Unfortunate Events" series. Violet, the eldest, is a smart girl, but she is not a Smart Girl. She is smart and plucky and clever, and she invents ingenious devices to save her siblings from danger time and again, but she does not exist solely to spout book smarts and provide plot exposition. If anything, her younger brother Klaus fills that role, but Handler is quick to lampshade the entire concept -- much of Klaus' "plot exposition" is word-for-word repetition of what Handler has already revealed in a Snicket Aside to the reader. The trope is thus subverted and lampshaded at the same time. When Klaus isn't being used for ironic plot exposition, he still manages to avoid the Smart Girl curse because his knowledge does allow him to recognize and avoid traps, and when the children are trapped anyway his intelligence does work to get the children out of danger. Violet, Klaus, and Sunny share the spotlight and each of their strengths are used in turn to avoid death and danger; none of the characters exist solely so that the other characters can outshine them. They are smart children, but they are not Smart Girls.
The Smart Girl effect is so common in fiction that I think as a culture we have become almost blind to it. Any female character that has the Informed Attribute of "smart" and exists to spout plot exposition is automatically considered to be a Strong Female Character without any real analysis of what that might mean. We don't notice as a culture that the Smart Girl never really saves the day, and never really uses her "smarts" in a useful way, because we instinctively understand that the Hero must save the day instead. It's not that the Smart Girl is dumb, the tropers will insist, it's that she's handicapped by the demands of the plot; it's not that she's not a Strong Female Character, it's just that she's not the Hero. It's not the Hero's fault that he always wins, right? And yet we never really question why the male Hero "must" save the day each and every time.
In my opinion, good heroes aren't always right. Contrast the Percy Jackson series with a series like The Hunger Games. Katniss is a Strong Female Character and the Hero, a rare enough phenomena in modern YA publishing. Like most heroes, she's the Plucky Protagonist who acts on her gut impulses instead of following her calmer instincts. She's smart about certain things, like hunting and surviving in the wild, but her most defining moments are moments where she acts "stupidly" and yet captures the hearts and minds of the oppressed in her country.
Yet despite following the established Plucky Protagonist trope, Katniss is a hero who doesn't always win. Sometimes her impulsive acts work in her favor; but other times her rash actions cause herself and others to be unnecessarily hurt. Though she follows her heart and her gut, she is sometimes noticeably wrong instead of being magically always right. She isn't a one-woman army, and for as many times as she rescues her friends and loved ones, she in turn will have to be rescued as well. Like Percy Jackson, she's a first-person protagonist, but unlike him, she's not present for every plot-critical moment, and she isn't the savior of every situation regardless of circumstance. She occasionally takes a backseat while other characters save the day or provide insight into the plot, and she's a stronger protagonist because of it.
Katniss is a very human mixture of smart and stupid, of false bravado and true bravery. She's neither a Smart Girl nor a smart girl -- she's just human. Annabeth, and Thalia, and Zoe, and Bianca, and so many other of Riordan's female characters, on the other hand, noticeably aren't human -- they don't have personalities at all besides a collection of informed attributes designed to propel Percy into the most heroic position possible.
Ultimately, the curse of the Smart Girl isn't that the character is or isn't smart, and it's not even that she's never the protagonist. No, the curse of the Smart Girl is that she is neither human, nor relateable, nor important to the plot. She's a trophy to be won, a measuring stick to be surpassed, a plot exposition voice to provide narration in a first-person story. She's an object in a story otherwise populated by people, and her Usually Female status gives the uncomfortable impression that all females are objects, and only males can hope to be people. The Smart Girl is a bane to the female reader, a reminder that her best achievements will ultimately only be measured in terms of how much they helped the male protagonist to shine as the Designated Hero.