Youthful idealism can be a beautiful thing. There are few things audiences love more than the idea of a gifted teenager (or sometimes simply a young adult) who can see what's wrong with the world and, after initially feeling overwhelmed and powerless in the face of a Crapsack World, deciding that they need to do something about it.

In some cases, may obtain or be born with some special power to help them achieve their goal. Whether they do or not, the key difference between The Alexander and The Hero is that instead of fighting crime on a case by case basis or having to face an already existing Big Bad, they have a much bigger vision and will try to Take Over The World in a belief that Utopia Justifies The Means. However, if these ideas are already a quick way for adult characters to go merrily Jumping Off The Slippery Slope, being a young, frustrated rebel, complete with the standard emotional immaturity and sometimes flat-out childish fantasies you'd expect out of someone this age only makes things worse. Consequently, they often end up as a Well Intentioned Extremist and end up on the Sliding Scale Of Anti Heroes, unless they are a(n) (Anti)Villain Protagonist.

In addition to differing from the typical hero in vision - or ends - they will also differ in the means used. In contrast to the Idiot Hero, The Alexander will have a strong dose of Intelligence Equals Isolation, which may cause them to be quite prideful. And instead of a typical hero who reacts to the nefarious plans of the Big Bad and fights with brawn, they use brains to come up with their own schemes, often being either The Chessmaster, Manipulative Bastard, Magnificent Bastard, Mary Tzu, or all of the above, capable of cooking up a Xanatos Gambit or Xanatos Roulette just as good as or possibly better than your standard Big Bad. As such, they are often subversions or inversions of The Law Of Bruce, which is one of the main reasons why these characters are so unique and intersting.

If they're targeted by bullies, expect them to later gloat Who's Laughing Now?, though when they realize the extent of the damage they've caused, they're especially prone to wondering My God What Have I Done and going through a Heroic BSOD and/or Heel Realization, assuming their Ubermensch mentality cracks enough to let them see it. These characters often die young, seemingly "burned out" by their own genius, though an Alexander who lives to adulthood can either continue down their path to Anti Villain status (or sometimes simply become The Big Bad, deluded by their own idealism), or they can become a mentor who issues Jacob Marley Warnings to other youngsters in their former position.

Named for Alexander The Great, who became a military commander at the age of 16, became king and began his conquest of the known world at the age of 20, and died emotionally and physically burned out at age 32 with his plans completely unfinished with no successor to leave them to.

Examples:

• Death Note: all of the four main characters have the mental qualifications to be this, but only Light is idealistic enough to follow this route.
• Code Geass: Lelouch vi Britannia. Probably the Most Triumphant Example.
• Monster: a story where the main villain, Johan, has all the qualifications, but rather than changing the world, wants to destroy it, just because he can. Unlike For The Evulz types who want to watch the world burn, he doesn't seem to get much satisfaction out of the horrible things he does: he just wants to set it on fire. And is very good at it.
• Enders Game: gathers many of these tropes, but the protagonist wasn't so much a revolutionary as a Tykebomb, yes?
• Legend Of Galactic Heroes: Reinhard von Lohengramm is a textbook example. Luckily he has Kircheis to watch his back, both physically and morally.
• Akumetsu. He acts like a goofy Idiot Hero, but he is actually very cunning and resourceful. He is also much more physical than other examples of this trope.
• Naru Taru: there was a character like that.
• The protagonist of Lost Brain.
• Dune: Kwisatz Haderachs Paul Atreides and God Emperor Leto Atreides. Probably Trope Codifier.
• In Harry Potter, Voldemort, Dumbledore, and Grindewald are hinted to have been this, for a start.
• Naruto has Pein/Nagato, who learned ninjutsu in his youth with his Nakama and afterwards started a group with them to create a better world and was given the Rinnegan. After being forced to kill his best friend, he commits bloody vengeance on his betrayers and plans to create a super-weapon that will scare the other villages into stopping all war.

Real Life:

• Napoleon Bonaparte (borderline: he wasn't a teen anymore, but he was quite young).
• Alexander The Great: Trope Namer and Ur Example (probably)
• Evariste Galois... for the world of mathematics at least.