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.
- Marvel Cinematic Universe: In a universe filled with genius scientists, Tony Stark is constantly shown to be leaps and bounds smarter than almost every other character. His own movies have him accomplish impossible feats of engineering in unfavorable conditions (miniaturizing the arc reactor in a cave with a box of scraps or improving Extremis while blackout drunk) and he continues the tradition in other movies. Avengers: Endgame has him inventing time travel after dinner and building a functional Infinity Gauntlet with nanotech, a feat that previously took Asgard's personal blacksmiths working with a forge powered by the dying heart of a neutron star.
- In Perturabo In Remnant, Perturabo is more or less without equal in terms of genius on Remnant. Most of the stuff he creates is utterly beyond the comprehension of even the smartest of his mortal peers. Even his fellow Primarchs are hard-pressed to understand the underlying principles of his inventions.
- 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.
- Leonard da Quirme (Expy of Leonardo da Vinci, of course) is constantly in the process of inventing or researching something, often times becoming sidetracked in the process, resulting in him setting up to create a toaster and ending up drawing numbered schematics for a flamethrower. Most of his inventions are usually quite close to modern devices while he lives in a fantasy setting (he built a perfectly functional pedal-powered submarine, an espresso machine, a gun, ...). Vetinari once reflects that Leonard would probably be extremely dangerous if he could focus on a given problem for more than one hour, as a lot of Leonard's inventions usually have horribly efficient military applications (for his part he believes nobody would stoop so low as to use them to kill other people).
- 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.
- Sherlock Holmes: Professor Moriarty, Sherlock Holmes archenemy, is the Deconstructed Character Archetype of Impossible Genius, a genius so great that he surpasses the scientific community of his time: An Eduardian mathemathician whose last book, "The Dynamics of an Asteroid", is so difficult that nobody in the scientific press can criticize it. This work means the end of Moriarty's scientific career: in a world without computers, his theories cannot be proved nor disproved, and Moriarty realizes that further math investigation is meaningless because there is literally not another human being who can understand it. His genius is so great that it makes him Powerful and Helpless. Is it any wonder that Moriarty decides to turn his intelligence to other activities, like being a Diabolical Mastermind?
- The Parahumans universe has this in two flavors, the "tinker" and "thinker" power classifications.
- Tinkers seem to have The Spark of Genius, but by Word of God (and in-story information of the type which would require Self Fulfilling Spoilers) they ultimately do utilize science with key details omitted from their conscious awareness. One of the PRT's first rules for handling a captured tinker is to keep them far away from anything that could conceivably be used to make anything else.
- Thinkers, on the other hand, have exotic mental capabilities and senses allowing them to casually execute impossible-seeming feats like Awesomeness by Analysis, Rube Goldberg Hates Your Guts, Sherlock Scan, and Break Them by Talking. In a world where Flying Bricks are commonplace, Thinkers are considered The Dreaded.
- Second Apocalypse: The Dunyain are a race of warrior-monks who pursue the Absolute, a state of being in which they divorce themselves from all influences of the world around them to become self-moving souls. To pursue this end, they've subjected themselves to a millennia-long breeding and training program that gives them superhuman physical and mental abilities. They can read a man's thoughts simply by looking at his face, predict the future by entering the Probability Trance, and master virtually any vocation in a fraction of the time it would take a worldborn human. Anasurimbor Kellhus is able to become fluent in a language in only a few days and begins inventing new theorems while still in the process of being tutored in mathematics.
- 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 Proud Scholar Race, he's nothing special. Of course, this is the species that casually tracked every bit of energy in the universe, mastered time travel, and was the reason for the prevalence of Human Aliens (though it's more Time Lord Aliens - Time Lords came first), so 'average' by their standards is still smarter than almost everyone else in the universe.
- It's also worth bearing in mind that while in terms of pure brainpower, the Doctor is probably a little above average at most, and Book Dumb at that, he's got a couple of advantages. First, he's far more creative than other Time Lords are, with a talent for lateral thinking on a level previously undreamed of. Second, his travels mean that he's got far more 'in the field' experience when dealing with the rest of the universe than even very senior and very book-smart Time Lords. As a result, he is often stated (even by other Time Lords) to be able to perform 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.
- Star Trek: Voyager: The Doctor. Chakotay's mind has become detached from his body? The captain and the helmsmen have devolved into amphibians? A patient transported to Sickbay with their body in different time zones? 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.
- Pathfinder: Magic items 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.
- Warhammer 40,000:
- Ork Mekboyz can 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.
- Jokaero are by all appearances just orangutans, and act like them in all regards except for their seemingly supernatural affinity for technology — they can take the most rudimentary of technological salvage and turn it into frighteningly effective pieces of functional technology that may not even resemble the bits it's cobbled together from. Left to their own devices, a group of jokaero can turn a pile of junk and broken machinery into anything from a working starship to a laser cannon to an antimatter weapon capable of leveling cities.
- 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.
- The Inexplicable Adventures of Bob!: Molly 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.
- Narbonic/SkinHorse: Basically any mad genius. 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". The first clue that Dave was a latent mad was when he "repaired" a death ray that was actually a mail-sorting machine.
- 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.