# Maths joke collection

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.

## § Hyperbolic geometry and pickup lines

Devised 2023-293

"Are you a large hyperbolic triangle?"

Explanation

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.

## § Computational complexity and Undertale

Devised 2023-233

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

Explanation

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.

## § Trigonometry

Devised 2023-223

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

Explanation

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

## § Abstract algebra and psychology

Devised 2023-163

Suppose M = Sn, i.e. the nth symmetric group. Then the set with n elements is neurodivergent. (Why?)

Explanation

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.

## § Integral transforms

Devised 2023-155

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

Explanation

The Laplace transform is an integral transform.

## § Linear algebra and swimming

Devised 2023-086

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

Explanation

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.

## § Vector calculus and fuel

Devised 2023-060

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

Explanation

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).

## § Number theory

Devised 2023-060

There is only one subprime mortgage.

Explanation

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

## § Vector calculus

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?)

Explanation

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

## § Physics and idioms

Devised 2023-046

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

Explanation

Work is the path integral of force.

## § Differential calculus and physics

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 ...

Explanation

Self-explanatory. Look up the terms.

## § Vector calculus and American politics

Devised 2023-033

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

Explanation

"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".

## § Statistics and philosophy

Devised 2023-031

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

Explanation

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.

## § Complex analysis and alcohol

Devised 2023-025

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

Explanation

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

## § Topology and video games

Devised 2023-024

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

Explanation

"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.

## § Category theory and anatomy

Devised 2023-023

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

Explanation

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.

## § Linear algebra and philosophy

Devised 2023-019

Singular matrices have free will. (Why?)

Explanation

Singular matrices actually have a determinant of zero.

## § Category theory

Devised 2023-012

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

Explanation

Self-explanatory. Look up the terms.

## § Game theory and marketing

Devised 2023-012

How do you convince people to study game theory?

Explanation

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

## § Linear algebra and computing history

Devised 2023-010

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

Explanation

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 PDP⁻¹.

## § Analytic geometry and anatomy

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 ...

Explanation

The bone in the thigh happens to be the femur.

## § Exterior algebra

Devised 2022-364

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

Explanation

Self-explanatory. Look up the terms.

## § Topology and astronomy

Devised 2022-358

What topological relation connects dwarf planets in the Kuiper belt?

Explanation

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

## § Statistics and alcohol

Devised 2022-358

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

Explanation

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

## § Linear algebra and psychology

Devised 2022-354

What colour do matrices see?

Explanation

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

## § Category theory and philosophy

Devised 2022-354

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

Explanation

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

## § Abstract algebra

Devised 2022-354

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

Explanation

"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.

## § Linear algebra and military

Devised 2022-350

Why is the military led by invertible matrices?

Explanation

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

## § Order theory

Devised 2022-349

How do posets prepare their coffee?

Explanation

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

## § Linear algebra and sports

Devised 2022-348

Why do we have to pay basketball players so much?

Explanation

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

## § Multivariable integral calculus

Devised 2022-343

The result of any double integral is x² + C.

Explanation

"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) = 2x.

## § Abstract algebra and love

Devised 2022-341

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

Explanation

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

## § Geometry and dialects

Devised 2022-340

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

Explanation

"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).

## § Differential geometry

Devised 2022-338

Why shouldn't you trust groups on differentiable manifolds?

Explanation

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

## § Differential geometry and history

Devised 2022-334

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

Explanation

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

## § Proofs and automobiles

Devised 2022-333

What kind of automobile can mathematicians get cheaply?

Explanation

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

## § Category theory

Devised 2022-332

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

Explanation

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".

## § Complex analysis and botany

Devised I don't know when

Why can't you grow trees on hyperbolic cosines?

Explanation

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

## § Abstract algebra and agriculture

Devised I don't know when

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

Explanation

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

## § Linear algebra and drugs

Devised 2022-323

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

Explanation

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.

## § Complex analysis

Devised 2022-323

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

Explanation

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

## § Vector calculus and theory of computation

Devised 2022-320

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

Explanation

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.

## § Number theory

Devised 2022-316

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

Explanation

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

## § Linear algebra

Devised 2022-314

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

Explanation

Self-explanatory. Look up the terms.

## § Algebra history

Devised 2022-305

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

Explanation

"Depressed cubic" refers to t³ + pt + q, which was solved by (among others) the actual mathematician Nicolo Tartaglia.

## § Determinants

Devised 2022-305

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

Explanation

Self-explanatory. Look up the terms.

## § Functions and philosophy

Devised 2022-303

What do we call the study of surjective functions?

Explanation

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

## § Complex analysis and nations

Devised 2022-302

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

Explanation

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

## § Alcohol

Devised 2022-302

Why do mathematicians imbibe concentrated alcoholic drinks?

Explanation

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

## § Complex analysis and biology

Devised 2022-302

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

Explanation

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

## § Functions and fuel

Devised 2022-302

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

Explanation

"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.

## § Trigonometry and Native Americans

Devised 2022-302

What kind of shoes do Native American circles wear?

Explanation

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

## § Order theory

Devised 2022-301

What did the lattice say to the poset?

Explanation

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

## § Functions and medicine

Devised I don't know when

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

Explanation

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).

## § Proofs and limits

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?

Explanation

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.

## § Differential equations and religion

Devised 2022-301

What differential equation does hell satisfy?

Explanation

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

## § Homomorphisms and capitalism

Devised I don't know when

Why is exponentiation inherently consumerist?

Explanation

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

## § 3D analytic geometry and medicine

Devised I don't know when

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

Explanation

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

## § Multivariable calculus, derivatives, and integrals

Devised 2022-300

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

Explanation

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.

## § Complex analysis and lightbulbs

Devised 2022-298

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

Explanation

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).

## § Linear algebra and sports

Devised I don't know when

Why are matrices good at basketball?

Explanation

"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.

## § Set theory and order theory

Devised 2022-257

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

Explanation

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

## § Geometry and exterior algebra

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 ...

Explanation

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

## § Measure theory

Devised 2022-213

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

Explanation

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