Mathematics, and in particular calculus, is treated as arcane knowledge known only to the very smart or professional mathematicians, and opaque/useless to everyone else.
Writers Cannot Do Math. Whether due to lack of interest, poorly taught classes or an actual inability to handle higher mathematical concepts, many writers took as little math in school as possible. For most, the moment mathematics becomes an optional subject is just about when calculus is taught, so for anyone who
quit the subject at the first opportunity, it's simply the hardest topic
they're familiar with.
Because of this, in media works "calculus" is often used as shorthand for "brain-hurty smart people stuff." This is somewhat of an exaggeration—beginning calculus is not particularly difficult as mathematics goes, and is the foundation for much of the true higher maths and physics. And everyone's brains use the processes represented by calculus in their everyday lives (for example, tracking the rate of change or finding the total distance traveled); what makes it difficult is substituting number-crunching for intuition. However, there are different kinds of intelligence, and mathematics that seems simple to one person can be entirely opaque to another.
Compare
E = MC Hammer, which is when mathematical equations (often gibberish) are displayed to imply that math is occurring, and
Mouthful of Pi, where brilliant mathematicians know pi to a ridiculous number of places. See also
Formulaic Magic.
Examples:
- In Questionable Content, while Raven is working out the topology of Marten's penis and jeans on the board, Faye mutters "is that calculus?"
- In an episode of Dexter's Laboratory, Dexter quips "this will be easier than calculus!"
- Big Bang Theory. Four of the five main characters know advanced physics, and the math behind it. But most non-scientists on the show seem not even to have gotten to linear algebra.
- One of the things that, canonically, Chief Engineer Commander Tucker cannot do in Enterprise.
- Inverted in the Itazura Na Kiss episode, "The Crucial Moment! Class F's Winter Battle", where every high school student tutored by Irie over a very short time period, even the usually dimwitted Kotoko, manages to pass their Calculus section of the college entrance exam. Everyone, save Kinnosuke, who was too proud to get tutored.
- In Kim Possible, the Mathter, despite being a mathematics-themed villain, seems to possess no knowledge of any math above basic algebra. He is understandably beaten by Ron Stoppable's father, who is an actuary and thus actually has knowledge of math of calculus level and beyond.
- Paranoia supplement Acute Paranoia. In a section on mathematics tests, calculus is given as an example of "Very Complex Mathematics". The only category higher than that is "Impossible Mathematics", such as "What is the final digit of pi?"
- From the song "White and Nerdy", by "Weird Al" Yankovic: "I do vector calculus, just for fun."
- In an episode of Futurama, "The Duh-Vinci Code," Professor Farnsworth says something along the lines of, "Oooh, I'm going to go listen to that calculus lecture!"
- Total Drama Revenge of the Island has the Jersey Shore reject character, Anne Maria, mention that she's "no algebra whiz" when referring to a numbers code clue.
- Family Matters also did this in one episode, where Laura complains about how difficult her Calculus test was. And Urkel, of course, rants about how easy Calculus is.
- In the English language version of Tintin, we have Professor Calculus, apparently named so to indicate just how brilliant he is as the direct translation "Professor Sunflower" just wouldn't have the same ring.
- The Major General in The Pirates of Penzance cites calculus as part of his educated background in his opening song.
- In Mass Effect, the biologist Mordin Solus uses a species' ability to preform calculus as a rule for ethical experimentation. Any species that can is off limits.
- Joke: Two professors are arguing in a restaurant about whether calculus was obscure or rather well-known. The "obscure" professor went to the men's room. The "well-known" professor asks the waitress to help him play a joke on him — when he came back, he would call her over, and ask her a question, and she should answer "one half x squared." He comes back, the professor asks him if the waitress knowing calculus would prove it, and the "obscure" professor agrees. He calls over the waitress and asks for the anti-derivative of "x". She answers, "one half x squared — plus a constant." ^{note }That is, the "well-known" professor got it wrong, and the waitress corrected the answer he told her to give! (For those of you who have not taken calculus — it is remarkably easy to forget the constant. Just about everyone who has has gotten back a test where all the problems lost one point for forgetting it, and it is completely plausible that the professor forgot.)
- "Look lively, people! Spot calculus check!◊" Bob the Angry Flower uses calculus as a measure of whether someone's smart enough to be worth his time (given how often he's been portrayed as a Mad Scientist, it shouldn't be suprising that Bob knows higher mathematics). Notice that, while other people seem to have half-forgotten their calculus, they still have studied it at some time in the past.
- In Neal Stephenson's Baroque Cycle, calculus is arcane knowledge — because two of the main characters^{note }Sir Isaac Newton and Gottfried Wilhelm von Leibniz, who did independently invent calculus in Real Life are actively engaged in inventing it. Separately.