By dkl9, written 2023-172, revised 2023-295 (5 revisions)

These are all original, devised by me. Some may have been independently discovered by others.

Some credit also to one of my maths teachers for (implicitly) encouraging me to keep making these and collect them into a book (this is my closest approximation, sorry).

Most of these are puns. Here's how I make those (I think).

Click a hidden punchline to reveal it.

*Devised 2023-293*

"Are you a large hyperbolic triangle?"

A triangle in hyperbolic space can have arbitrarily acute angles, more so the larger it is. The largest possible triangles in a given hyperbolic space are called ideal.

*Devised 2023-233*

You get to a save point at which you solve the travelling salesman problem.

Save points in Undertale (a video game) come with messages ending with "... fills you with determination." The travelling salesman problem, being NP-hard, requires non-deterministic polynomial time to solve.

*Devised 2023-223*

What did the doctor suggest when the patient came in, pathologically oscillating as if going around a circle?

"Sine" is a function closely associated with circular motion, and a sinecure is a job with negligible work and high pay.

*Devised 2023-163*

Suppose `M` = `S`_{n}, i.e. the `n`th symmetric group. Then the set with `n` elements is neurodivergent. (Why?)

Aut is an abbreviation for the group of automorphisms, which, for a set with no additional structure, is the corresponding symmetric group. "Aut is `M`" resembles "autism", a form of neurodivergence.

*Devised 2023-155*

Don't study integral transforms too much, or you might get tied to your chair. (Why?)

The Laplace transform is an integral transform.

*Devised 2023-086*

Small sets of vectors of high dimension like to swim straight across pools, far from the entrances. (Why?)

A set of vectors may or may not be linearly independent, and is more likely to be if there are fewer vectors and more dimensions. Far from the entrance of a pool would be the deep end.

*Devised 2023-060*

All surfaces with boundaries are burning, but if they're flat, it's biofuel on them that's burning. (Why?)

A reference to Stokes' theorem and its two-dimensional (flat) special case, Green's theorem, which are both applied to surfaces with boundaries. Biofuel is thought of as "green" (i.e. environmentally friendly).

*Devised 2023-060*

There is only one subprime mortgage.

1 is the only natural number less than (sub-) any prime.

*Devised 2023-047*

Adding up the force around the edge of a piece of lettuce matches the amount of swirling in the force across the surface. This also works for many other vegetables. (Why?)

Green's theorem relates path integrals to double integrals roughly as described. Some vegetables (such as lettuce) are called "greens".

*Devised 2023-046*

What do you get when you integrate force of habit over a path?

Work is the path integral of force.

*Devised 2023-040*

Force = mass · acceleration. Differentiate both sides. Force-change = mass · acceleration-change + mass-change · acceleration. Assume constant mass. Force-change = mass · acceleration-change = mass · jerk. Thus ...

Self-explanatory. Look up the terms.

*Devised 2023-033*

Why do parts of the American right wing oppose gay marriage?

"Conservative" is a term both for an American political ideology, closely associated with the right wing and a type of vector field. The latter has zero curl/is irrotational, which we may loosely interpret as "straight".

*Devised 2023-031*

You should only group data into one of a discrete set of options if you wish that everyone does that. (Why?)

A variable in data is categorical iff it is one of a discrete set of options. The categorical imperative states that you should only do that which you would want everyone to do by a corresponding law.

*Devised 2023-025*

What kind of people drink, drank, are drinking, and will drink?

The conjugate of a complex number in complex analysis is sometimes notated as `z̅` ("`z`-bar"). "Drink", "drank", "are drinking", and "will drink" are conjugations of "to drink".

*Devised 2023-024*

Every video game is an open-world game. (Why?)

"Open world" is an actual characterisation of some (but really not all) video games. Topologies (the structure, not the subject) are defined with reference to "open sets". One of their axioms is that the entire topological space (i.e. the world) is an open set.

*Devised 2023-023*

What do you call a categorical arrow from one short and fat person to another?

Endomorphisms are an actual type of morphism (categorical arrow). "Endomorph" is a somatotype, i.e. a classification of physique, which refers, essentially, to the short and fat.

*Devised 2023-019*

Singular matrices have free will. (Why?)

Singular matrices actually have a determinant of zero.

*Devised 2023-012*

What do you call it when a category theorist hunts down a map showing a route to their workplace?

Self-explanatory. Look up the terms.

*Devised 2023-012*

How do you convince people to study game theory?

Schelling points, with a name amusingly similar to "selling point" are a prominent idea in game theory.

*Devised 2023-010*

The Unix operating system was designed to diagonalise matrices. (Why?)

Unix was an operating system developed in the 1970s, with the PDP-11 as one of its first targeted machines. Matrix diagonalisation is a procedure whereby a matrix typically notated as `A` is converted to a form typically notated as `P``D``P`⁻¹.

*Devised 2023-009*

Notice that the thigh can be raised, forming an angle with the vertical axis (the torso). That angle is, in spherical coordinates, φ (phi). Thus ...

The bone in the thigh happens to be the femur.

*Devised 2022-364*

What do you call a storebought slice of pizza in an exterior algebra?

Self-explanatory. Look up the terms.

*Devised 2022-358*

What topological relation connects dwarf planets in the Kuiper belt?

Haumea is a dwarf planet in the Kuiper belt, and homeomorphisms are a type of topological relation.

*Devised 2022-358*

They used to sell alcohol near arithmetic means, but not anymore. (Why?)

The arithmetic mean of `x` is notated as `x̅`, pronounced "`x`-bar".

*Devised 2022-354*

What colour do matrices see?

Eigengrau is the colour people typically see in the dark. Matrices have many associated concepts with names starting with "eigen-".

*Devised 2022-354*

Immanuel Kant used commutative diagrams to figure out morality. (Why?)

Kant actually *did* describe a categorical imperative. Commutative diagrams are a type of visualisation mainly used in category theory.

*Devised 2022-354*

Why do mathematicians always build roads thru empty regions of land?

"Field" is a term both for an empty region of land and a type of algebraic structure. "Commute" is a term both for what one might do on a road and a property of a mathematical operation, required in a field.

*Devised 2022-350*

Why is the military led by invertible matrices?

Rank is a number associated with a matrix, which (for a given size of matrix) is highest for invertible matrices.

*Devised 2022-349*

How do posets prepare their coffee?

"Filter" is a term both for a type of subset of a poset and a tool used in actual coffee preparation.

*Devised 2022-348*

Why do we have to pay basketball players so much?

In the matrix form of a system of linear equations, a pivot corresponds to a bound (non-free) variable.

*Devised 2022-343*

The result of any double integral is `x`² + `C`.

"Double integral" properly refers to an integral of a two-input function over a two-dimensional domain, but here I deliberately misinterpret as "integral of double", i.e. integral of the doubling function `f`(`x`) = 2`x`.

*Devised 2022-341*

Why are there so few couples in rings that aren't fields?

Rings and fields are both algebraic structures. They mainly differ in that fields require multiplicative inverses (reciprocals), but rings do not.

*Devised 2022-340*

Why is it so impractical for the British to build apartments?

"Flat" is both the British term for an apartment and a synonym for a Euclidean subspace, which is necessarily of infinite size (examples include lines and planes).

*Devised 2022-338*

Why shouldn't you trust groups on differentiable manifolds?

Groups on differentiable manifolds are called Lie groups, pronounced /li/.

*Devised 2022-334*

Why did Grigori Perelman examine rivers in maps written in Chinese?

The Kunyu Wanguo Quantu was a map in Chinese made by Matteo Ricci, who has no actual relation to the Ricci of Ricci flow.

*Devised 2022-333*

What kind of automobile can mathematicians get cheaply?

The Corolla is an actual automobile. A corollary is a result that can be proven easily (cheaply) from some other result.

*Devised 2022-332*

How would a category theorist describe the process of breaking a semisolid into a liquid?

Forming a liquid into a semisolid is coagulation. Category theory uses "co-" to indicate (roughly) the reverse of something (e.g. product vs coproduct). A category theorist might then interpret "coagulation" as "co-agulation", that is, the inverse of "agulation".

*Devised I don't know when*

Why can't you grow trees on hyperbolic cosines?

Hyperbolic cosine has roots (inputs resulting in output zero) only at (`π`/2 + `π``k`)`i` for integer `k`, all of which are imaginary.

*Devised I don't know when*

Why did the farmer allocate 17 square kilometres for a new crop?

Self-explanatory. Look up the terms, and notice that 17 is prime. (Also technically incorrect, but that's a pedantic detail.)

*Devised 2022-323*

If a set of vectors addicted to drugs quits, their withdrawal symptoms will increase by a constant amount per day. (Why?)

Dependence to a drug is that state which leads to withdrawal upon quitting. A linear function has an output which increases or decreases at a constant rate. Linear dependence is an attribute that may apply to a set of vectors.

*Devised 2022-323*

Why do holomorphic functions always follow the rules and never rebel?

Self-explanatory. Look up the terms. (Holomorphic functions, amusingly, also happen to be well-behaved in the mathematical sense.)

*Devised 2022-320*

If we can't compute partial derivatives of φ with a Turing machine, how *do* we compute them?

The partial derivatives of φ (Greek letter phi) are expressed with the del operator. A mechanism to compute values incomputable on Turing machines is called an oracle, while the Oracle of Delphi was an oracle in the typical sense.

*Devised 2022-316*

Why do doctors who started as number theorists use plant-based medicine?

Primitive roots are both a concept in number theory and a characterisation of pharmacognosy.

*Devised 2022-314*

Why did the linear algebraist bury the dead letter-pair?

Self-explanatory. Look up the terms.

*Devised 2022-305*

You thought the famous Italian Tartaglia was a mathematician, but really, he was a psychiatrist. (Why?)

"Depressed cubic" refers to `t`³ + `p``t` + `q`, which was solved by (among others) the actual mathematician Nicolo Tartaglia.

*Devised 2022-305*

Teachers can't compute determinants by cofactor expansion. (Why?)

Self-explanatory. Look up the terms.

*Devised 2022-303*

What do we call the study of surjective functions?

Ontology is an actual branch of philosophy, and surjective functions are also called "onto".

*Devised 2022-302*

What kind of function do you need to represent the nations of the world?

For rational functions (polynomial divided by polynomial), complex-analytic poles perfectly coincide with zeroes in the denominator, and degree `n` implies `n` zeroes.

*Devised 2022-302*

Why do mathematicians imbibe concentrated alcoholic drinks?

"Proof" is both a unit of alcohol concentration and a common task in mathematics.

*Devised 2022-302*

The factorial of complex numbers produces red blood cells. (Why?)

The gamma function, which generalises factorials to complex numbers, is actually meromorphic, and bone marrow is mainly known for producing red blood cells.

*Devised 2022-302*

Mathematicians call natural gas "domain". (Why?)

"Range" refers both to a type of stove (often fueled by natural gas) and a set of a function's outputs, contrasted with the "domain", a set of a function's inputs.

*Devised 2022-302*

What kind of shoes do Native American circles wear?

A mix of "moccasins", the type of shoe Native Americans actually wore, and "cosine", a function closely associated with circles.

*Devised 2022-301*

What did the lattice say to the poset?

The presence of a meet for every pair of elements is what distinguishes lattices from posets.

*Devised I don't know when*

We can prove that there's only one intramuscular drug to cure any particular disease. (How?)

Injective functions are those such that each output (in this case, a bodily state) has at most a single input leading to it (in this case, a drug).

*Devised 2022-301*

What do you call a proof made using a result which bounds a function between two others, which approach the same value?

That bounding procedure would be followed by the squeeze theorem. "Lemma", the term for part of a proof, is close to "lemon", and if you squeeze a lemon, you get lemon juice.

*Devised 2022-301*

What differential equation does hell satisfy?

Sine, often abbreviated "sin", is one prominent solution to `y''` = -`y`.

*Devised I don't know when*

Why is exponentiation inherently consumerist?

exp(`a` + `b`) = exp(`a`) exp(`b`)

*Devised I don't know when*

Diseases from bad medical practice make the radius component of spherical coordinates imaginary. (Why?)

Diseases from bad medical practice are iatrogenic. `i` is the imaginary unit. `ρ` (Greek letter rho) is the radius component of spherical coordinates.

*Devised 2022-300*

An Integration Bee should use single-variable integrals only, not multivariable. (Why?)

Integration is (basically) the inverse of differentiation, so differentiation is how one would judge in an Integration Bee. When there are multiple variables, the derivatives are partial.

*Devised 2022-298*

How many bounded entire functions does it take to change a lightbulb?

Liouville's theorem: an entire function (i.e. complex differentiable everywhere), if bounded (i.e. magnitude less than a given value everywhere), must be constant (i.e. never change).

*Devised I don't know when*

Why are matrices good at basketball?

"Pivot" is a term both for a type of matrix component and (if I recall correctly; I'm no athlete) a useful move in basketball.

*Devised 2022-257*

Why can't you totally order a set with more than 10 elements?

"Toset" is an established abbreviation for "totally ordered set".

*Devised 2022-257*

A fan, in geometry, is a set of planes (around the same line). A bivector is mostly equivalent to a plane (it contains more information). However, a multivector (vector, bivector, trivector, etc) is known as a blade. Thus ...

Self-explanatory. Look up the terms if you don't believe me.

*Devised 2022-213*

If you have a tape measure, you can evaluate a Lebesgue integral over it.

A Lebesgue integral is defined with reference to a "measure", often the Lebesgue measure.