Absolute value – the distance of a number from 0, always a positive number, represented by |□|

Abstract – applying ideas of one domain across to other domains

Acute – an angle that’s less than 90 degrees

Acute triangle – a triangle with less than 90 degrees on all 3 sides

Addition – aka putting together, combining grouped values together, is commutative

Affine geometry – the only Euclidean geometry left after forgetting distance and angle

Algebraic – applying algebra to other domains (e.g., algebraic geometry)

Analysis or Analytic – logically comparing and contrasting values with more logic or math, often by factoring and composing/decomposing to find patterns, contrast to synthetic

Angle – a part-circle relationship between geometric elements, represented in degrees

Applied mathematics – a branch of mathematics that makes math useful

Area – the measured interior of a 2-dimensional shape or the exterior of a 3-dimensional shape, contrast to perimeter

Arithmetic – the combined domains of addition, subtraction, division, and multiplication operations

Arithmetical – applying arithmetic to other domains (e.g., arithmetic geometry)

Asymptotic or Asymptote – describing something that limits something else

Base – the counting basis before the increment increases, with our standard numbers being base-10 and computer math being base-2 (e.g., a base-3 number system would count as 1, 2, 3, 11, 12, 13, 21, etc.)

Cardinality – the number of elements in a set

Cartesian coordinates – a system that precisely represents 2-dimensional information with two fixed perpendicular lines and signed distances at even intervals, named after its inventory René Descartes (who also developed Enlightenment-era philosophy)

Circle – a 1-sided 2-dimensional shape where the distance is the same from the center

Circumference – the perimeter of a circle

Classical – a math discipline that uses Euclidean space and conventional perspectives of number theory, tends to be the most useful for practical tasks

Combinatorial or Combinatorics – the study of various ways to count permutations and combinations of objects beyond addition or multiplication

Commutative property – an operation that can rearrange the operands and come to the same answer (e.g., 4 + 3 = 3 + 4), contrast to non-commutative

Complex – deals with imaginary numbers as well as real numbers

Composing – combining multiple smaller elements to make larger math elements, opposite of decomposing

Computable or Computational – applies to computer-based math

Connected sum – in topology, the sum of two manifolds

Constructive – based on the philosophy of constructivism, where a thing has to be assembled from logic instead of being proven simply by observation

Convergent series – a sum of an infinite series of numbers

Correlant – two values that are correlated

Cube – a 6-sided 3-dimensional shape composed of 6 squares

Curve – a line that moves in at least 1 additional dimension

Data – information, plural of datum

Decompose – splitting a larger element into smaller elements, opposite of composing

Decrement – a fixed amount that gets reduced, opposite of increment

Degree – the rotated part-circle distance between two points or lines, with 360 being a full circle, represented as °

Denominator – the bottom part of a fraction that denominates the numerator

Diameter – the length of a line segment with ends on the circumference that passes through the center of a circle or sphere

Differential – tracks quantities of things changing

Dimension – aka space, a measurable range that can be geometrically defined, can be Euclidean or non-Euclidean

Discrete – counting-based, instead of continuous (measuring-based)

Distributive property – the qualities of being able to distribute values [e.g., a (b + c) = ab + ac]

Dividend – the number that’s getting divided in a division problem

Division – separating out values from a dividend into a divisor’s number of equally-sized components (e.g., 15 / 3 is 3 values of 5 each, or 5), results in a quotient

Divisor – the number of equal components to split a dividend in a division problem

Edge – a line that represents part of a shape

Element – something in math that’s clearly defined (e.g., 2, *i*, f(x))

Elementary – basic or simple

Equal – aka equality or equivalent, the state of two things being the same in some mathematical way

Equilateral – a shape where all the edges have the same lateral angle

Equation – a mathematical formula that shows whether two expressions are equal

Euclidean space – the realm of space that inhabits our 3 dimensions, and we call “reality”, named after Euclid’s proofs, contrasts with non-Euclidean space

Evaluate – to parse out the math problem into something else (e.g., 3 + 3 = x becomes x = 6)

Exponent – a number multiplied by itself, represented by superscript (e.g., 3^{2}), contrast to square root

Exterior – where the surface area is the same between multiple things

Expression – a logical mathematical statement with at least 2 numbers or variables and at least one operation

Extremal – how big or small things can be

Face – the side of a shape

Factor – aka factorize, to break apart the components that make a larger value or formula [e.g., 2x + 6y = 2 (x + 3y)]

Fermi problem – aka from-the-hip guess, a math problem that requires intuitively estimating real-world math

Field theory – performing arithmetic on rational and real numbers

Finite – only as a limited number of possible things, instead of infinite

Forget – to ignore for the sake of finding an answer

Formula – a group of operations

Fraction – a representation of unresolved division that indicates a part of another value, has a numerator and denominator

Function – a clear pattern that can be represented by a formula

Game theory – mathematical models of strategic interactions, most notably decisions based on understood and imagined circumstances

Galois theory – a connection between field theory and group theory

Geometry – a branch of mathematics dealing with shapes

Geometric – applying geometry to other domains (e.g., geometric algebra)

Graph theory – the study of networks of lines and vertices

Group or Group Theory – a domain of mathematics that involves conceptually putting things together

Higher or Derived – a middle-point on the way to “abstract”

Increment – a fixed amount that gets increased, opposite of decrement

Infinitesimals – numbers so tiny that they’re closer to 0 than to any real number

Integer – a natural number, 0, or a negative natural number

Integral – the collective sum of something

Intersection – a place where two or more geometric elements are in the same location

Interval – a patterned difference in states, which often represents as a number (e.g., 3 to 5 to 7 is an interval increase of 2).

Inversion – reversing a shape

Knot – a circle tangled in Euclidean space

Line – an imaginary direction that extends forever both ways, represents a dimension

Line segment – aka segment, a portion of a line, typically indicates some type of shape in more than one dimension

Manifold – a topological space where each point represents something like Euclidean space (e.g., a science fiction wormhole)

Matrix – a rectangular array of things

Multiplication – aka times, adding a second value multiple times to a first value, is commutative

Natural number – a clear-cut number that represents itself in nature as we perceive it (e.g., the numbers 2 or 15)

Net – a two-dimensional cross-section of a three-dimensional object

Non-commutative – where changing the order of things changes the results (e.g., 5-2 is *not* the same as 2-5)

Non-Euclidean space – theoretical realms of space that don’t abide by our 3-dimensional reality

Nonlinear – where the outputs of something aren’t proportional to the inputs

Number – a clear, precise representation of quantity

Numerator – the top part of a fraction that is denominated by the denominator

Operation – a mathematical action guided by defined rules, uses an operator, can be commutative

Operand – the object of an operation

Operator – a formal language symbol that indicates what logical rules should be followed, works on an operand

Oval – a 1-sided 2-dimensional shape that’s not a circle

p-adic numbers – rational prime numbers that show a continuous pattern of decimals that aren’t 0

Parallel – a condition where two lines, segments or rays will never touch intersect, opposite of perpendicular

Parallelogram – a 4-sided 2-dimensional shape that’s not a square and has sides that are parallel to each other

Percent – aka per cent, a x/100 comparison to another number

Per mille – aka per mil or per mill, a x/1000 comparison to another number

Perfect square – an integer where a square root of itself is also an integer

Perimeter – the line segments that make the outside of a 2-dimensional shape or the edges of a 3-dimensional shape

Perpendicular – a condition where two lines, segments or rays are at right angles to each other, opposite of parallel

Place value – the specific left or right placement of a number and its relative significance to other numbers (e.g., 1,000 is 10 times more than 100)

Polyhedron – a 3-dimensional shape with flat polygon faces, straight edges, and sharp vertices, plural is polyhedra

Prime number – a real number that can’t be divided by anything but itself and 1

Primitive – a base component of a concept

Primorial – the sum of all prime numbers up to a given number

Prism – a polyhedron with two polygon faces parallel to each other and the other faces as parallelograms

Probability – the chance of a thing happening, represented as a percent

Probabilistic – applying statistical probability to other domains

Proof – a means to indicate with absolute deductive certainty that a mathematical concept is true

Quadrilateral – a 4-sided 2-dimensional shape

Quotient – the number coming from the result of division, where the divisor divides the dividend

Radius – a line segment with ends on a circle’s center and its circumference

Ratio – a comparative and scalable relationship between two numbers (e.g., 1:2)

Rational – a number that can be expressed as a fraction

Ray – an imaginary direction that extends forever in one direction, contrast to a line

Real – using integers to represent something, contrast to complex numbers

Reality – an incidental and somewhat tenuous connection to math in general

Rhombus – aka, equilateral quadrilateral, a 4-sided 2-dimensional shape where each side has the same length

Rectangle – a 4-sided 2-dimensional shape that isn’t a square and all the sides are at a right angle to each other

Right angle – aka perpendicular angle, an angle at 90 degrees, happens to be *very* useful for many calculations

Right triangle – a triangle with one of its corners at a 90 degree right angle

Round – an approximated estimation relative to a number (e.g., 413 rounded to the nearest 100 is 400)

Set theory – the logical study of sets, which are collections of things

Shape – an object with a defined form, exists in at least one dimension on a plane

Sphere – a 1-sided 3-dimensional shape where the distance is the same from the center

Square – a 4-sided 2-dimensional shape where each side has the same length and all the sides are at a right angle to each other

Square root – A result number that, if squared, would be the original number (e.g., √9 = 3), represented by the radical symbol, contrast to exponent

Subtraction – aka taking away, demarcating and separating grouped values, is *not* commutative

Surface area – the measured exterior surface of a 3-dimensional shape, similar to area for 2-dimensional objects

Symmetry or Equivariance – a condition where a shape is the same on both sides, can be reflectional (mirrored), rotational (can be rotated to match), translational (can be moved without changing shape), helical (translational + rotational), scale (can change size while keeping shape), glide (reflectional + translational), and rotoreflection (reflectional + rotational)

Synthetic or Axiomatic – Using subjective language instead of discrete reference points, contrast to analytic

Topological – where geometry isn’t easy to accurately measure with numbers

Triangle – a 3-sided 2-dimensional shape

Variable – a clearly specified number that’s undefined for the purposes of the math problem (e.g., x represents any possible number, but we don’t know yet)

Vertex or Vertices – a point where two or more curves, lines, or edges meet, plural is vertices