You know those jokes about how the Professor in Gilligan's Island could build anything out of coconut shells and sand? This is when you have a character (or group of characters) who can actually do stuff like that. It's Played for Laughs, but in-universe they aren't joking; the character or group really is that good.
Sometimes a characteristic of an Omnidisciplinary Scientist, Evil Genius, or The Smart Guy. Might involve Bamboo Technology. See also The Spark of Genius, Mad Scientist. Overlaps with It Runs on Nonsensoleum if the parts or the principles involved are sufficiently ridiculous. If it's made clear that the character's invention only works because they're making it work with magic or superpowers, that's Magic-Powered Pseudoscience.
Niece-trope of The Ace. While The Ace can accomplish any feat imaginable because he's Just That Awesome, these characters can do physically impossible feats of engineering and construction because they're Just That Smart. They may casually dismiss such feats as being (from their perspective) pathetically easy. See also Testosterone Poisoning, for characters who are Just That Manly. Compare Techno Wizard, and see Charles Atlas Superpower for the super-strength version of this.
- In All Fall Down, both IQ and IQ Squared are these. The former built doomsday weapons, the latter created a software empire worth billions.
- Iron Man: Tony Stark builds an arc reactor in a crude workshop in a cave, using parts that are little more than a box of weapon scraps. Other engineers state that only Tony Stark could do such a thing.
- Inverted in Discworld by the inventor and architect B. S. Johnson, who was so transcendentally incompetent that reality itself wasn't safe from his bungling. Crowning achievements include Empirical Crescent, an Eldritch Location where any given door will probably open into the right room in the wrong building; a mail sorting machine built around a flywheel with a pi value of exactly 3, which brought down the post office by retrieving mail from random points in time; and cast-iron garden furniture that spontaneously melted on at least three occasions.
- The Smarty-Pants from Gordon Korman's Nose Pickers From Outer Space books. The final exam for admission to their ranks includes memorizing the infinity times-table, and they've harnessed the power of the coleslaw molecule.
- Willy Wonka has harnessed nonsensoleum to such ends as creating a television-based teleporter and a flying glass elevator that is kept aloft by "candy power" and/or "skyhooks" and can function as a spacecraft if necessary.
- If there's an alien baddie threatening lives, you can be sure The Doctor will use his incredible scientific genius and planning to stop it, and save the day. That said, by the standards of his own race, he's nothing special. Kind of. He is a mad genius in his own specific ways and he is often stated (by other Gallifreyans) to be able to do impossible feats which defy logic and laugh at the Laws of the universe. His plans usually work because he doesn't think they wouldn't work.
- MacGyver, although his reputation of "aren't you that guy that can build a time machine out of three paperclips?" was far less realistic than the actual character.
- MythBusters has tested a number of myths of this sort. In a number of cases they actually succeeded in accomplishing the seemingly unlikely in Real Life, for example, building a rope out of toilet paper, but usually only after days of work using large amounts of raw material.
- The resident genius character in any Power Rangers series can veer into this territory. Billy's a Teen Genius who graduated high school one year early, but normally, when a Monster of the Week's magical effect isn't something that requires a quest for the necessary Eye of Newt or exploitation of the Curse Escape Clause, the solution is, "Billy goes into his perfectly normal garage and whips up a device that can stop it." (This means Trini counts too; she was always his helper and understood what he was doing, even if she didn't go in for his Techno Babble and Sesquipedalian Loquaciousness.) But the biggest might be Cam from Power Rangers Ninja Storm. The Zords are losing? Well, he comes in to the rescue in his own helicopter Transforming Mecha... and the two copies of it that he whipped up in only minutes. Somehow.
- The Doctor from Star Trek: Voyager. Chakotay's mind has become detached from his body? The captain and the helmsmen have devolved into amphibians? Just another day in the life of an unappreciated Emergency Medical Hologram.
Torres: How did you manage to reintegrate his consciousness?
EMH: It involved three neural transceivers, two cortical stimulators and fifty gigaquads of computer memory. I would be happy to take you through the process, but it would take at least ten hours to explain it all to you. Needless to say, it was a remarkable procedure. I would consider writing a paper about it if there were a convenient forum in which to publish it.
- Dawn of a New Age: Oldport Blues:
- Ivy's superpower turns her into a Gadgeteer Genius that's capable of phasing parts between each other and making them perform functions that would be impossible for a regular modification.
- Benedict's superpowered intellect is to such a degree that he can upgrade a piece of technology to far beyond its realistic capabilities.
- Genius: The Transgression has players take the role of Mad Scientists who are capable of this at the cost of risking Science-Related Memetic Disorder.
- Anyone with Quick Gadgeteer advantage in GURPS.
- The Izzet League from the Ravnica setting of Magic: The Gathering are portrayed like this. Niv-Mizzet himself takes it up another order of magnitude.
- Magic items in Pathfinder are, well, magic. It takes a spellcaster to create them — or a Master Craftsman, who can be a complete muggle but can coax magic out of ordinary materials by being just that good.
- Ork Mekboyz from Warhammer 40,000. They are able to take scrap metal from junkheaps and turn it into crude but effective Powered Armor, assault vehicles, and Humongous Mecha. It's part inherent engineering know how hardwired into them by their creators the Old Ones and part the reality warping Ork gestalt psychic field making their machines work better.
- Casey and Andy can build anything that does anything, as long as you describe it as a "[main purpose or function]-o-mat". At one point, Quantum Cop asked for their aid and described what he wanted the device to do; they refused since the idea was impossible. They had no problem at all when he corrected himself and just asked for the appropriate -o-mat.
- Girl Genius has Sparks, hyper-geniuses that regularly laugh in the faces of all laws, human or natural, with their wacky creations.
- Molly from The Inexplicable Adventures of Bob! combines this with being a Robot Master. She once built a super-strong sentient robot, overnight, out of a farmer's milking machine (who has since become a regular character); and built two (nonsentient) steam-powered robots out of snow (they both melted quickly). It was her first time playing in the snow, and she wanted to have fun. One of the snow robots could transform into an ice ballista.
- Basically any mad genius in the Narbonic/SkinHorse universe. In one memorable instance, one makes a subspace teleporter out of all of the coat hangers in a walk in closet. It's powered by "Spring Power".
- Gadget from Chip 'n Dale Rescue Rangers. She can build pretty much anything a situation calls for out of scraps and bits of garbage lying around, and on the spot at that! Like a rocket sled thrown together from a shovel, blowtorch and c-clamps in the middle of a chase scene.
- Looney Tunes: Egghead Jr., the small chicken in Foghorn Leghorn cartoons. In one episode, Foghorn was babysitting Egghead, so they're playing hide-and-go-seek. While Egghead is counting, Foghorn hides himself in a nearby trash can, chuckling that "he'll never find me in here". Egghead then pulls a pencil and some paper from Hammerspace, does some calculations, and proceeds to dig Foghorn out of the ground. He is absolutely shocked, and rushes over to the trash can...and then decides against it, saying that he "just might be in there too".
- Og in Mike, Lu & Og only needs to be described a modern-day device in order to build a replica of that device using parts found around the tropical island where they live. In other words, he can build nearly anything out of the jungles and beaches around him with no effort—he just needs ideas to start from.
- Phineas and Ferb: The main characters can build anything from roller coasters to time machines in under a day. Dr. Doofenshmirtz has this same ability, though he's too much of a Ditzy Genius for it to be of much use.
- Rick from Rick and Morty once described his abilities and limitations as "can do anything, but only if I feel like it". His intellect has allowed him to, among other things, invent Casual Interstellar Travel, open a Portal Door to Another Dimension, create his own universe inhabited by sentient life, and turn himself into a pickle and back. Notably, this stuff comes so naturally to him that constructing a sentient robot from bits of junk he had to hand just so he can ask it to pass him the butter is less effort for him than just getting up from his seat and fetching the butter himself.