Math puzzles aren't for everyone, but they can be played by anyone! However, for a newcomer or someone who's already forgotten mathematical terms they learned in school so long ago, it can be confusing to see some of them appear in games like Mathler and Nerdle.

Not to worry, as here's a glossary that can help everyone understand the most common terms they need to know!

Quick Links:

Arithmetic & Expression Basics
Core Puzzle Vocabulary
Game Modes & UI
FAQ

Arithmetic & mathematical expression-game basics

Absolute value

The absolute value of a number is its non-negative distance from zero on a number line. It doesn't matter in which direction the number is; the absolute value will always be non-negative.

Addend

These are the numbers being added to one another to create a sum. They can also be referred to as the digits involved with a plus (+) operator.

Addition

The mathematical process of combining two or more numbers. Its operator symbol is +.

Additive identity

A property that basically makes the sum of any mathematical expression result in itself, regardless of whether there are two or more variables in the equation. In addition, the answer to any additive identity is always going to be zero (0), as adding 0 to any addition expression will land on itself.

Algorithm

A process or set of rules to be followed in a calculation, multiple calculations or a problem-solving operation. These are mostly used by computers, and are used in the generation of most digital math puzzles on websites and apps.

Bounds

This refers to a number's minimum and maximum values after being rounded down or up. The lower bound is the smallest value the number can be, and the upper bound is the highest value.

Constant

A fixed value that can't be changed. It can be a number, symbol, variable, etc. For example, zero is a natural constant.

Common multiple

This refers to a number that is a multiple of two or more numbers. To give an idea, 30 is a multiple of 4 and 5, and 3 and 10.

Commutative

This refers to the mathematical property that states that the order of numbers doesn't affect the outcome of an expression for either addition or multiplication.

Constraints

In math, these are conditions that limit the possible solutions to a problem. In a math puzzle setting, these are usually the rules of the game that a player needs to follow to solve it.

Dependent variable

A variable that changes its value depending on the independent variable. These are usually used in algebraic expressions and are useful in more complex math puzzles.

Digit

A single symbol used to form numbers. There are ten individual digits, from 0-9.

Dividend

The number that is to be divided by another number (divisor).

Divisibility

This refers to the capability of a number to be divided by another number and have no remainder afterward. For example, 6 is divisible by 3, as there's no remainder. 5 is not divisible by 2, as there is a remainder of 1.

Division

A mathematical process of splitting a number into equal parts or groups with another number. Its operational symbol is /.

Divisor

The number that divides another number without leaving a remainder, or is the number used to divide the main number (dividend).

Duplicate

In a math and math puzzle setting, this is to double a number. Basically, it's multiplying a number by 2.

Equation

A mathematical statement that shows the equality of two mathematical expressions. These are several of the common types of equations:

• Linear equations - most commonly used in problems and are usually used in math puzzle games
• Quadratic equations - an equation where the highest power of a variable is 2
• Cubic equations - an equation where the highest power of a variable is 3

Exponent

A number written in superscript over another number that dictates how many times a should be multiplied by itself. The difference between this and duplication is that duplication just multiplies a number by 2.

Expression

This refers to the combination of numbers, variables and operators that represent a value but does not contain an equal sign at the end.

Exponential form

The method of writing a base number to be raised to an exponent. The base number is the number that is to be multiplied by itself x number of times indicated by the exponent.

Expression slots

In a math puzzle setting, this refers to the input boxes or slots a puzzle provides to write or insert digits and operators.

Factor pair

A set of two numbers that, if multiplied together, result in a specific product. Factor pairs are always whole numbers.

Formula

A written rule, fact or principle that uses symbols to express relationships between two or more variables.

Fundamental theorem

In math, a fundamental theorem refers to the central, foundational theorem that makes up the core of a specific mathematical field. There's a Fundamental Theorem of Calculus, Fundamental Theorem of Arithmetic, and so on and so forth.

Imaginary number

An imaginary number is the product of a real number and an imaginary unit. While not commonly used in most math puzzles, the more complex ones use imaginary numbers in their calculations (mainly grid-based games).

Independent variable

A variable that stands alone, can't be altered and influences changes upon dependent variables.

Integer

A whole number that can be positive, negative or zero, but never includes decimals and fractions.

Invalid expression

In both math and math puzzles, this is an expression that is, at its core, incorrect. In math puzzles like Mathler, players get prompts that their input is wrong and it won't go through the system.

Linear equation

An algebraic expression that, when graphed, forms a straight line. While uncommon with most web games, there are dot (or point)-based puzzles that become easier to solve with math.

Minuend

The main number that is to be lessened by another number (subtrahend).

Multiplication

A mathematical operation that represents a repeated addition of a number to itself.

Numeral

This refers to a symbol or name used to represent a number.

Operators

This refers to the symbols that indicate a mathematical operation. Here are the most common types:

• Arithmetic operators - for calculations (+,-,* and /)
• Comparison operators - for value comparison (=,>,<, etc.)
• Logic operators - for programming or status combinations (AND and OR)

Parentheses

These symbols are used to group expressions, with operations inside being performed first. They can also be used to multiply numbers when they are placed next to them. Most of the more advanced difficulties of math puzzles incorporate the use of parentheses.

PEMDAS

An acronym that refers to the fundamental order of operations in arithmetic. It is as follows:

• Parentheses
• Exponents
• Multiplication/Division (from left to right)
• Addition/Subtraction (from left to right)

Subtraction

The mathematical process of taking away a number or quantity from a main number to find a difference.

Subtrahend

This is the number being subtracted from the main number (minuend).

Syntax

This refers to the rules for correctly arranging symbols and expressions in statements and mathematical equations.

Valid expression

In both math and math puzzles, this is an expression that is considered correct, syntax-wise. In math puzzles, this is an input expression that is acceptable by the game's system and constraints.

Variable

A written symbol (usually a letter) that represents an unknown value. This is commonly found in an algebraic expression or problem, but is present in most other fields of math and science, like calculus and physics, respectively.

Whole number

A non-negative integer that includes zero and all positive numbers, but doesn't count decimals and fractions.

Core math vocabulary for puzzlers

Color-feedback system

A color response scheme that changes depending on input. In modern puzzles, this is more commonly referred to as the Wordle® color system.

Composite number

A number that is greater than 1 and has more than two factors. A good example is 6; its factors are 1, 2, 3 and 6 itself.

Cube

There are two common meanings to this term:

• Cube, the shape - this is the three-dimensional shape made up of six identical squares put together
• Cube, in algebra - this is when a number is multiplied by itself three times

Estimation

This refers to the process of finding an approximate answer or the closest guess possible using available numbers or data.

Even number

An integer that is exactly divisible by 2 and leaves no remainder.

Factor

A number that divides another number evenly with no remainder. A good example is that 4 and 5 or 2 and 10 are factors of 20 because they result in each other.

Grid

A system of intersecting lines that creates a series of squares or other geometric shapes. One of the most common formats for math puzzles.

Greatest common factor

This refers to the largest positive integer that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD).

Multiple

The product of a given number and any integer. For example, multiples of 2 are 2, 4, 6, 8, 10 and so on.

Odd number

A whole number that can't be divided by 2 and leaves a remainder.

Parity

This refers to whether an integer is even or odd. This is especially useful to know in math puzzles that focus on expression-building.

Prime number

A positive integer that has only two factors, with one of them being always 1. A great example is the number 13; it can only be divided by itself and the number 1.

Rounding

This is the process of simplifying a number to its nearest estimated value. For example, if one were round 28 to the nearest multiple of ten, then 30 is the nearest, and it's called a "round up" because it increased. If one were to round 23 to the nearest multiple of ten, then it would be 20, and it's called a "round down" because it decreased.

Starter guess

This refers to the first and opening guess a player makes in a math puzzle or game. Starter guesses are usually done for information gathering, and isn't meant to solve the puzzle on the first attempt (but it can and does happen!)

Target number (sometimes called the given)

The number you are trying to reach with a valid expression. In games like Mathler, the target number is displayed up front, and your job is to build an expression that equals it using the allowed digits and operators.

Game modes & user interface/experience

Archive

A feature in most web games and apps where all previous puzzles or games are stored for player access.

Classic mode

The game mode that is the core of any math puzzle. It has all the primary features and functions of the game and is always middling in difficulty.

Daily mode

A game mode that refreshes daily on a set time. This mode is usually paired with streaks and other in-game features.

Difficulty

This refers to the level setting of challenge a puzzle or game offers to a player. Here are the most common difficulty settings in most math web games or apps:

• Easy
• Normal/Classic
• Hard
• Killer/Expert
• Master

Hint

A feature that, if used, will provide information or an answer that will help progress a puzzle or game if the player is stuck.

Practice mode

A game mode specifically made for practicing mechanics, tactics and more. This feature usually doesn't count towards streaks or scores.

Reset

There are two definitions for these terms in a math puzzle:

• Puzzle reset time - this is when a daily puzzle resets after a set time
• Reset puzzle - clears all inputs made on the puzzle or game and restarts from the beginning

Share

A feature in most modern math puzzles or games that allow a player to share their results on social media.

Spoiler

This refers to something that will show the result or process of something you are probably going to play or experience.

Streak

A number that indicates successive wins. This is usually implemented along with other game modes, such as Daily and Classic.

FAQ

What are the differences between numbers, digits and numerals?

• Numbers are a concept or idea that represents a quality or value (e.g. 2, -2, π).
• Numerals are symbols or names used to represent a number (e.g. 4, IV, four).
• Digits are a single character within 0 to 9 that are used to build numerals and numbers.

To summarize, numbers are more of an umbrella term that refers to something that has a value or quality, numerals are specifically for counting and digits are every single character that makes up numerals and numbers.

For example, 500 is both a number and a numeral, and its digits are 5, 0 and 0.

What are the differences between an expression, equation and formula?

• Expressions are a combination of numbers, variables and operators without an equal sign.
• Equations are made up of expressions and have an equal sign at the end.
• Formulas are used specifically for calculating something, like the area of a circle or the speed of sound.

To summarize, here's a table showing you their primary differences:

Expression	5x − 3	No equal sign
Equation	5x − 3 = 2	Has equal sign
Formula	F=ma	Reusable for different calculations