Sometimes, in order to establish how special or powerful something is, writers just take the easy way out and say that "science can't explain it!". It can be anything, from magic to ghosts to miracles to superpowers to whatever. One common tie-in statement is that it is made of no known chemical element.
Sadly, when this is done wrong, it seems to imply that science is only for mundane things.
A note on the most common usage of this: even if magic does not work via our universe's physical laws, in many works it follows its own rules and therefore can be observed, experimented with and theorized about. It might require a new branch of science, but if it can be observed and experimented with, then science can comprehend it. Sometimes magic will be a jerk and break patterns only when someone is actually looking for one, just to invoke this trope. If the scientists persist in offering "scientific" explanations that don't correctly explain the phlebotinum, then this idea has turned into the rather closely related idea that Science Is Wrong.
- In Death Note, after L and Light capture the Death Note in episode 24, Light suggests analyzing it. L replies that the Death Note is the kind of thing that can't be analyzed. He is later confirmed when they do try to analyze it and are unable to determine what it is made of.
- Averted, however, when Light uses his brain as opposed to gizmos to analyze the Death Note and determines what it can or cannot do. Ryuk wasn't even aware of some of these things.
- Averted further when L decides the responsible thing to do with the notebook is acquire a better understanding of it, namely by systematically testing every rule written in it rather than take them on faith. This is the critical point that would have fingered Light as Kira (Light intentionally wrote fake rules in the book to exonerate himself once L found it), forcing Light to finally kill L before he's caught.
- In The Happening, the mass genocide of humans by plants is described by Elliot Moore as something that just "happened", rather than the unprecedented biological phenomena that it actually was. The film goes further than this as the lead character is a science teacher that "teaches" that nature can not be explained by science and that any explanation given by the scientific community is only a "theory".
- Invoked in Primer, where residue on solid evidence is taken in for some formal analysis and they discover it's Aspergillus Ticor: basically, fungus that accumulates everywhere. The device they built a few days ago was caking with the stuff and they had just been wiping it off every five days or so, unaware that the amount they had wiped off up to this point would have required many years to accumulate to the level that it did. The scientist who identifies the fungus for them thinks this must be a bad joke.
- Faster-Than-Light Travel in Harry Turtledove's The Road Not Taken appears to be this for dumbfounded humanity when an alien invasion force attacks that operates on 18th century tech levels. The subject turns out to be more complex once the aliens are interrogated; anti-gravity is so simple a principle that most races discover it before gunpowder. They don't progress from there because anti-gravity has no side applications aside from FTL in stark contrast to electricity. Too bad for the aliens they attempted to conquer Earth 20 Minutes into the Future.
- Played with in House of Leaves. When material samples from inside the house are analysed, the summary is that they're nothing out of the ordinary, chemically speaking. Oh, and by the way, that's a fascinating range you've got there. The oldest samples must have come from meteorites, because they're older than the solar system. Where did you say you found all these, Antarctica?
- Dresden Files plays with this. Magic has a tendency to screw with any kind of mechanical and electrical devices, in particular anything made from WWII onwards, so most methods for documenting magic just don't work, despite Dresden's attempts to go public. None of this stops Butters from trying, and he makes some noticeable strides. Wizard longevity is (probably) due to a lack of telomere shortening, for instance.
The metaphysical rules governing magic change over time, possibly even in response to human beliefs. For example, strong magic users used to cause flames to burn odd colors and milk to sour back before technology. This would make it very difficult to quantify how magic works under prevailing scientific paradigms, although not impossible if new ones could be developed for that purpose and magic's effect doesn't "catch up."
- The eponymous object in The Accidental Time Machine is this for a very long time. Averted in that it is eventually figured out, once technology has progressed for a couple billion years.
- The squeezer in Red Thunder can't be duplicated by anyone other than its inventor, despite being made from off the shelf parts. The perfectly hard, perfectly reflective bubbles it produces stymie any analysis they are exposed too.
- In Sphere, all the chaos erupts because of the scientists accidentally using the eponymous alien device improperly. By the end of the story, they never have figured out how to use it right or even what it's actually supposed to do, let alone how it did what it did.
- H.P. Lovecraft's The Colour Out of Space applies this to the meteorite the titular color came to Earth in. The meteorite is ridiculously malleable, hot upon landing (real ones aren't, and the characters know this), dissolves into the air within a few weeks of landing, and has a strange bubble of something like a color inside it which pops when hit with a hammer, all of which confuse the geologists looking at it greatly. (The color is some sort of Starfish Alien Energy Being-type thing that sucks the energy out of its environment until it returns to space, killing any living thing in the area affected down to germs and turning anything that tries to live there gray and brittle.)
- One example from House has a priest who has lost his faith. His first symptom is a hallucination of a floating Jesus, followed by more life-threatening symptoms. House tries to find a single diagnosis that accounts for everything, but the real disease eventually accounts for everything except the visions. The priest concludes it must have been a genuine miracle which led him to seek House's help. Overlaps with Maybe Magic, Maybe Mundane in this case because he may have been hallucinating due to his alcoholism (an early theory that was ruled out when he presented other symptoms).
- On Stargate SG-1, Tollan technology is so advanced, it contains no apparent circuits, wires, or moving parts. Earth scientists have no hope of reverse-engineering their devices.
- Not that it matters much, as they have the entirety of Asgard technology and more. The Ancients also had phasing technology, but only Janus was shown using it. Apparently, Ancient, Asgard, and Goa'uld technology is much easier to figure out than that. Which is strange, as the Tollan are human, while the others are alien. You'd think they would have similar thought processes.
- The only other tech they have trouble with is Wraith biotech. This is because you need a mix of McKay and Beckett.
- One of the standard pieces of equipment on The Middleman is a B.T.R.S. scanner, which looks for things Beyond the Realm of Science.
- A good portion of the items being hunted and hoarded in Warehouse 13 fall under this trope.
- One of the main sources of Tension and Drama in Genius: The Transgression. All attempts for the Wonders to be analyzed actually causes it to stop working and/or go haywire.
- Both played Straight and Averted in Shadowrun. There are two main schools of thought when it comes to magic in the Sixth World. Shamanistic, which believes magic is an art that you feel rather than analyse. And Hermetic which believes that even Magic can be analysed to the smallest detail and can fit into a grand unified theory. Needless to say there are some tensions between the two schools of thought.
- A key part to Tharan Cedrax's characterization in Star Wars: The Old Republic. He is a freelance scientist and gadgeteer, specializing in lost or obscure technology. Despite being personally fond of Jedi Council member Master Syo (and potentially just as fond of the Consular), he does not trust the Force, and gets annoyed when the Consular suggests using it to solve problems over mundane, practical solutions. He has an especially intense dislike of the Jedi Mind Trick.
- In Gunnerkrigg Court, it's revealed that a Blinker Stone cannot be explained by scientific methods. The divide between magical beings and scientists is a critical point in the comic, to the point that the latter dislike even referring to the former as "Magical." They prefer the term "etheric sciences."
- Want to scientifically analyse the world of Tales of MU? "Well, this is where a lot of the unique undead, cursed artifacts, and tainted lands come from. This is how magical abominations are created."
- Averted by the SCP Foundation. If the Thing Man Was Not Meant To Know doesn't force them to terminate it first, Man's determined to keep poking it until he Knows it anyway.
- Failing that, Man will just keep poking it with various things and record the effects in Experiment Logs. If it's deadly enough, they dump it with the resident immortal Omnicidal Maniac and see what happens.
- Played straight in-universe. If an SCP is analyzed to the extent where it can be entirely explained by ordinary science, it's no longer considered paranormal, and the Foundation will arrange for everything they learned about the former SCP to be released to the general public. It's only things which don't play well with reality that the Foundation contains and covers up.
- The researchers in The Sick Land try to study the eponymous Eldritch Location. They aren't very successful.
- In the My Little Pony: Friendship is Magic episode "Feeling Pinkie Keen", Twilight Sparkle runs herself ragged trying to analyze/disprove Pinkie Pie's "Pinkie Sense". In the end, she gives up and admits that maybe the "Pinkie Sense" can't be analyzed (which turns out to be the "doozy" that Pinkie predicted would happen).
- It's explained in the same episode that magic in the general sense in My Little Pony is comprehensible by science, so most of the series averts this. Pinkie Pie and her "sense" still plays this trope straight, as whatever she's doing is still a unique form of "magic" in the series itself.
- In Jackie Chan Adventures, Captain Black insists on trying to fight magic with science. Uncle insists this is impossible, and since he gets more screen time...