Surpassed the Teacher

For most of the career of a student, The Mentor overshadows the student in terms of ability. This is certainly justified, since it is the intention of a student to become more skilled by learning from a more experienced mentor.

However, there often comes a time when the student surpasses the mentor in ability. It is at this point at which the student reaches his full ability and becomes a master of his trade. This may result in the mentor becoming an Obsolete Mentor. If the student is arrogant, when he proves he is superior, he often utters a Stock Phrase or some variation thereof from which the trope name originates: "The student has surpassed the teacher."

If the mentor is the nice type, he will often be highly proud of his student. If the student has surpassed his mentor but hasn't reached his full potential, his old master may tell him to find a new master who will teach the student more. having passed himself and reaching full potential.

If the mentor is the jealous type, he may be quite jealous and resentful of the student's ability, and in extreme cases, the mentor may become the student's enemy. For when both the teacher and the student are evil, with the student learning the ways of evil from the teacher, the student often proves his superiority by killing the teacher.

Anime and Manga

 * Yuuno from the Lyrical Nanoha franchise is technically Nanoha's teacher in magic. In practice, however, she learns everything he can teach her within three or four episodes.
 * In Magical Girl Lyrical Nanoha A's, Chrono defeats Aria and Lotte Liese, his combat magic instructors, and explicitly tells them that he has become stronger than both of them.
 * As part of Jin's backstory in Samurai Champloo,
 * Fatal Fury: Tung Fu Ru reunites with Terry and Andy on the ten year anniversary of their father's death, during which, he tells them their skills have already surpassed Jeff's. However, only one could become his successor. Adding that the one he chooses would have to surpass his own ability. Guess which one pulls it off?
 * Played with at the beginning of Dragon Ball. Goku's mentor, Master Roshi, disguises himself to participate without getting known at a tournament. The viewer expects this trope to appear, as Goku manages to evade all of Roshi's tactics to defeat him. However, despite Goku having managed to succeed to all of Roshi's attempts, the author introduces an Ass Pull and makes Roshi win a leg clash, Hand Waving it by saying "his legs are shorter are mine, therefore they're weaker". Even though a common aesop that appears all throughout Dragon Ball is that having a bigger size that doesn't mean being stronger. Nevertheless, by the time of the next tournament Goku has completely surpassed Roshi, and by Dragon Ball Z Roshi's an Obsolete Mentor.
 * Averted in Rurouni Kenshin, where the title character cannot ever surpass his mentor Hiko, because he simply does not possess the physique to fully use the Hiten Mitsurugi style. Doesn't stop him from being awesome, though.
 * Naruto perfected Sage Mode, which Jiraiya wasn't able to do. And in a way he surpassed Kakashi, because Kakashi, like the Fourth Hokage, wasn't able to add element manipulation to the Rasengan (which is why Kakashi made Chidori).
 * Domon Kasshu in Mobile Fighter G Gundam surpasses his teacher, Master Asia, in the final climactic battle of the 13th Gundam Fight.

Comics

 * Wally West was once the first Kid Flash, the Sidekick to the second Flash, Barry Allen. After Barry's death, Wally was depowered due to events during the Crisis on Infinite Earths, but he eventually surpassed Barry in terms of speed and accomplishments, becoming the first speedster to enter the Speed Force and come back.

Film - Live Action

 * Darth Vader provides the quote in Star Wars Episode IV: A New Hope when he meets and kills his old master, Obi-Wan. It's subverted, however, in that Obi-Wan intentionally lost in order to merge with the Force, and Vader is disappointed that he didn't put up a fight.
 * In Attack of the Clones, Dooku tries to pull this against his old master, but ends up retreating and distracting his former master to survive.
 * Star Wars in general has many cases of this. The entire Sith philosophy of the Rule of Two is meant to lead into the apprentice betraying his master once he has learned everything that his master knows, ensuring the next Sith masters can only become stronger.
 * Highlander did this, the end of the training montage with Connor and Ramirez has Connor finally besting Ramirez and disarming him.

Literature

 * In Tarnsman of Gor, Tarl learns the sword from a man also named Tarl, whom he refers to as "the Older Tarl." At every sparring encounter the Older Tarl beats Tarl and says "You are dead." At one point Tarl finally gets through the Older Tarl's defense; the Older Tarl cries out with delight "I am dead!" and clutches Tarl to his bosom, "proud as a father who has taught his son chess and has been defeated for the first time." Speaking of which...
 * In Assassin of Gor, Tarl teaches a slave girl to play the Gorean equivalent of chess, which slaves are forbidden to learn. He finds that she's a natural, and stops giving her advice on her game in order to concentrate on not losing too badly.
 * Mentor in Lensmen flat-out says the Children of the Lens (the five Kinnison children) have gone beyond the Arisians.
 * In Matilda, it is clear from very early in the book that Matilda has intellectual capabilities that are certainly beyond that of her teacher, Ms. Honey.

Live Action TV

 * Played with in late season 7 of Buffy the Vampire Slayer: Spike confronts Giles with words along these lines, saying that one of the reasons that Giles turned on Buffy was that Giles was jealous that Buffy had surpassed him in her abilities.

Religion, Mythology, & Folk Lore

 * In Classical Mythology, the great inventor Daedalus had a nephew/apprentice named Perdix who was an even better inventor than he was (he invented the saw, among other things). Daedalus got jealous and plotted to kill Perdix and claim his inventions as his own. As it happens, one day the two were walking by a cliff when Perdix asked how Daedalus's son Icarus died. Daedalus responded by throwing a valuable object over the cliff, and Perdix, struggling to save it, fell to his death.

Tabletop Games

 * A rare but possible result in Dungeons & Dragons basic set's weapon proficiency. By default, there's a 1% chance of doing so if you train with a teacher as skilled as you are. It's possible to boost it to 11% by training with another teacher, but it's more efficient to find someone sufficiently skilled.

Video Games

 * In the Street Fighter canon, Akuma killed his master, Goutetsu, in a fair fight to show that he [Akuma] had truly mastered the power of the Satsui no Hadou. Goutetsu was actually proud of his student for having defeated him in battle.
 * In The Elder Scrolls, you can find trainers who can automatically increase your skills for money (rather than grinding). However, each skill has a trainer for each rank of experience in that skill and can only train you five times. If you ask for training when you're too high level, then they'll say something to the effect of this trope.
 * In Metal Gear Solid 3: Snake Eater, Naked Snake finally surpasses his former mentor The Boss in a final confrontation where he had ten minutes to defeat her or else the area would be napalmed. Amazingly Snake is able to actually defeat her despite earlier not even being able to harm her in hand to hand combat, for the first time in the game Snake can actually counter his mentor's CQC attacks and respond in kind showing a vast degree of improvement in his skills from earlier in the game when she handed his ass to him. For his efforts Snake is awarded the title of Big Boss, showing that in the U.S. military's eyes he had surpassed his mentor.
 * In The Legend of Zelda the Wind Waker, you can undergo a minigame involving sparring with your former instructor in the art of swordplay. If you get a score of 1000 points, he responds in this manner.

Webcomics

 * In this Xkcd comic, Elaine the hacker progidy trumps Donald Knuth, her mentor.