Carter visits the Air Force Academy, where she takes a brilliant but rebellious young cadet named Jennifer Hailey under her wing. Meanwhile, O'Neill and Teal'c are tasked with overseeing a team of scientists on an offworld research base.
"Prodigy" provides examples of the following tropes:
- Alien Sky: The Planet of the Week is actually a moon orbiting a gas giant, resulting in this. Carter points this out to Hailey when the latter complains that it doesn't look much different from Earth.
- Always Someone Better: Hailey feels this way towards Carter, complaining that people have been comparing them since she started at the Academy. Carter tells her to get over it.
- Bully Hunter: It's mentioned that Hailey broke another cadet's nose for harassing an underclassman.
- Bunny-Ears Lawyer: Lampshaded in O'Neill's case:General Ryan: Got your hands full with that one, eh, George?
- The Cameo: The then-Chief of Staff General Ryan makes a brief appearance As Himself at the beginning of the episode.
- Cruel and Unusual Death: Dr. Thompson is stung to death by a swarm of energy-based alien lifeforms.
- Energy Being: The aliens are tiny balls of light that can pass through solid matter and are capable of intelligent thought, though they behave like insects.
- Is It Always Like This?: Hailey asks this at the end of the episode.Carter: No. Sometimes it gets really exciting.
- Jurisdiction Friction: The scientists clash with the military personnel over who should have authority on the research base.
- Military Maverick: Deconstructed with Hailey, since her teachers at the Academy maintain that no matter how brilliant she is, if her insubordination continues she won't be able to have a career with the Air Force. Carter asks them to give her one more chance, hopeful that if she's aware she could have a future with the SGC she'll be able to get her act together.
- On Three: Before Teal'c zats O'Neill, O'Neill tells him to give him a warning, suggesting to go on three. O'Neill starts counting "One" before Teal'c zats him.
- One Steve Limit: Averted with Dr. Bill Lee and Dr. Bill Thompson.
- Permission to Speak Freely: Hailey asks for this before dismissing her latest assignment as "lame".
- "The Reason You Suck" Speech: Carter delivers one to Hailey over her attitude problem:Carter: Who the hell do you think you are?Hailey: Ma'am?Carter: Do you think you're better than we are? Do you think you're too good for the Air Force?Hailey: No, ma'am.Carter: Oh, come on. All those little rules and regulations, they don't really apply to you, right? Let's face it, what's the point of a chain of command if none of your superiors are as smart as you are?Hailey: I don't think that way, ma'am.Carter: Oh, I think you do. And I think deep down, you wanna leave. Let me do you a favor. Door's open. Why don't you just quit and go home?
- The Swarm: The aliens form one to attack the research base, effectively trapping its occupants inside.
- Too Clever by Half: Hailey is explicitly described as being "too smart for her own good".
- Written-In Absence: Dr Jackson is stated to be off-world with SG-11.