Peter is a bully, Eric is kind of a sociopath, but the real big bad in Divergent is Jeanine Matthews. Why? Because she's smart one.
We hear about Jeanine a long time before we see her, and the first thing we hear about her is that she's a bit of a genius: "Jeanine Matthews is Erudite's sole representative, selected based on her IQ score. My father complains about her often" (4.43). Okay, so let's revise: the first thing we hear about her is that she's smart and troublesome. That's our first impression of her. Actually, that's just about our only impression of her.
See, whenever the topic turns to Jeanine Matthews, all we hear is that she's smart, like "a walking, talking computer" (25.8) according to Will (who was in Erudite with her). What does Jeanine enjoy? Well, what does your computer enjoy? It's hard to say, isn't it? Jeanine is the mastermind who wants to destroy the Abnegation government and take over the city… so maybe she enjoys power? Or maybe she enjoys helping people and thinks that her vision of the city would be better for everyone? (Her vision of the city is basically "cars for everyone" or as she puts its: "wealth, comfort, and prosperity" (34.24). That doesn't sound so bad.) Or maybe she enjoys hurting people? Or maybe she enjoys gathering knowledge?
Again, just as with Eric, Peter, and other villains, because we see this book through Tris's eyes, we don't get a lot of info on Jeanine, her motivation, or her past. When Tris is face-to-face with Jeanine, Tris gives her summary judgment on Jeanine, which is "She is more machine than maniac. She sees problems and forms solutions based on the data she collects" (34.38). So she's very smart and very logical—like an evil Spock. Basically, she sees—in her opinion—a problem like the Abnegation government or the Divergent people, and she goes about trying to fix it… in the most violent way possible (which isn't super smart but makes for a more adventure-filled book).