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.
- Ambiguous Ending: Carter and Hailey both have different theories that either the bugs are angry at being misused by the scientists or they are more aggressive since the moon is passing over the planet's pole. They never figured out which was the answer.
- 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.