# Wikidata:WikiProject Mathematics

## GoalsEdit

### Long term goalsEdit

- Organize data about mathematics

### Short term goalsEdit

- Use the property has facet polytope (P1312) on all applicable items (7/??), and create missing items
- Gather information from infoboxes
- Create more properties that semantically describe items
- Create featured items that show how properties should be used
- Create "has part" property entries for formula components / identifiers -> discussion

## InfoboxesEdit

- Category:Mathematics infobox templates (Q8612039)
- Infobox Méthode scientifique (Infobox scientific method) for French Wikipedia (Q8447)
- Infobox Discipline for French Wikipedia (Q8447)

## Useful lists and queriesEdit

- List of integers in Wikidata
- Subclass tree for number (Q11563): http://tools.wmflabs.org/wikidata-todo/tree.html?q=11563&rp=279&lang=en
- Table of all theorems
- Table of notable numbers
- Uses of OEIS ID

Error detection: please make sure the query below returns zero results, and fix any item that appears.

## PropertiesEdit

*See also:* Wikidata:List of properties/mathematics (bot-generated list)

### Properties used in WikipediaEdit

The following properties are available in Wikipedia, Wikiversity, and other Wikimedia wikis and are displayed when clicking on the annotated formulae. See w:Help:Displaying_a_formula#Semantics_and_links for a more detailed documentation. The assumption when implementing the semantics feature in mw:Extension Math was that relations or formulae like the Mass-Energy-Equivalence are annotated on Wikidata.

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

defining formula | P2534 | Mathematical expression | formula: mathematical formula representing a theorem or law. Maximum length: 400 characters | ideal gas law <defining formula> | - |

has part or parts | P527 | Item | has part, consist of and meronymy: part of this subject; inverse property of "part of" (P361). See also "has parts of the class" (P2670). | ideal gas law <has part or parts> pressure | part of |

quantity symbol (string) | P416 | String | quantity symbol: symbol for a mathematical or physical quantity | electric charge <quantity symbol (string)> Q and q | - |

### General PropertiesEdit

As opposed to the properties above that are used for semantic annotations in Wikipedia the following properties are used under the assumption that the corresponding wikidata item defines a mathematical/physical concept which has a definiendum that can be derived (calculated from) other symbols.

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

defining formula | P2534 | Mathematical expression | formula: mathematical formula representing a theorem or law. Maximum length: 400 characters | Pythagorean theorem <defining formula> | - |

in defining formula | P7235 | Mathematical expression | variable, identifier and pronumeral: any symbol used in the defining formula (P2534) | f-number <in defining formula> | - |

quantity symbol (LaTeX) | P7973 | Mathematical expression | quantity symbol: symbol for a mathematical or physical quantity in LaTeX | electric charge <quantity symbol (LaTeX)> | - |

calculated from | P4934 | Item | calculation: value of the subject item cannot be measured directly or can be calculated from the following measurands or attributes | body mass index <calculated from> human body weight and human height | - |

relative to | P2210 | Item | reference point: qualifier: what a statement value is relative to | FTCS scheme <has part or parts> Euler method<relative to> time | - |

studied by | P2579 | Item | academic discipline: subject is studied by this science or domain | numerical method <studied by> numerical analysis | studies |

has quality | P1552 | Item | quality: the entity has an inherent or distinguishing non-material characteristic | mathematical proof <has quality> validity | - |

notation | P913 | Item | notation: mathematical notation or another symbol | equality <notation> equals sign | - |

statement describes | P2384 | Item | formalization of the statement contains a bound variable in this class | Pythagorean theorem <statement describes> right triangle | - |

admissible rule in | P2577 | Item | admissible rule: this logic inference rule is admissible in that logical system | modus ponens <admissible rule in> classical logic | - |

generalization of | P7719 | Item | logical implication: the subject statement is a particular case of this object statement, or the truth of this object statement is implied by the truth of the subject statement | law of cosines <generalization of> Pythagorean theorem | - |

### NumbersEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

numeric value | P1181 | Quantity | numeric value and quantity value: numerical value of a number, a mathematical constant, or a physical constant | golden ratio <numeric value> 1,6180339887±0,0000000001 | - |

prime factor | P5236 | Item | prime factor: one of the prime numbers that can be multiplied to give this number | 2334 <prime factor> 2, 389 and 3 | - |

greater than | P5135 | Item | greater than: instances of the item have a greater value than corresponding instances of the object, for the given measure | 100 <greater than> 99 | less than |

less than | P5136 | Item | less than: instances of the item have a lesser value than corresponding instances of the object, for the given measure | −1 <less than> zero | greater than |

number of decimal digits | P7316 | Quantity | numerical digit: number of decimal digits of a natural number | 10^90 <number of decimal digits> 91 | - |

radix | P3264 | Item | radix: number of distinct digits in a positional numeral system | hexadecimal <radix> 16 | - |

### Mathematicans and Mathematical HistoryEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

discoverer or inventor | P61 | Item | inventor, innovator, discoverer, discovery and invention: subject who discovered, first described, invented, or developed this discovery or invention | Poincaré conjecture <discoverer or inventor> Henri Poincaré | - |

time of discovery or invention | P575 | Point in time | invention, discovery and archaeological find: date or point in time when the item was discovered or invented | Euler method <time of discovery or invention> 1768 | - |

named after | P138 | Item | eponym, memorial society and namesakes: entity or event that inspired the subject's name, or namesake (in at least one language). Qualifier "applies to name" (P5168) can be used to indicate which one | Euler method <named after> Leonhard Euler | - |

proved by | P1318 | Item | person who proved something | Poincaré conjecture <proved by> Grigori Perelman | - |

solved by | P1136 | Item | person that solved a scientific question | Fermat's Last Theorem <solved by> Andrew Wiles | - |

based on | P144 | Item | based on: the work(s) used as the basis for subject item | Pythagorean trigonometric identity <based on> Pythagorean theorem | derivative work |

Erdős number | P2021 | Quantity | Erdős number: the "collaborative distance" between mathematician Paul Erdős and another person. Use point in time (P585) as qualifier and should be used with a source. | Paul Erdős <Erdős number> 0 | - |

title in LaTeX | P6835 | Mathematical expression | LaTeX: (qualifier) for title property (P1476), to write title in LaTeX/math notation, if the string can't render it normally. Enclose normal text with "\text{" and "}" | On the Integers of the Form xk +yk <title in LaTeX> | - |

### Sets, Algebras, and TopologyEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

cardinality of this set | P2820 | Item | cardinality: measure of number of elements of a set | rational number <cardinality of this set> aleph null | - |

group cardinality | P1164 | Quantity | group order: number of elements in a finite group | dihedral group of order 6 <group cardinality> 6 | - |

identity element | P8864 | Item | identity element: value of the identity element of the mathematical operation | addition <identity element> zero | - |

has operator | P8866 | Item | operator: mathematical operator associated with this algebraic structure | additive group <has operator> addition | - |

mathematical inverse | P8865 | Item | mathematical inverse: inverse element with respect to binary operation given as a qualifier | 2 <mathematical inverse> ½ | mathematical inverse |

contains | P4330 | Item | insertion: item or substance located within this item but not part of it | sphere <contains> open ball | - |

has part(s) of the class | P2670 | Item | has part of class: the subject instance (the subject is not a class) has one or more parts of the object class | set of real numbers <has part(s) of the class> real number | - |

Alexander polynomial | P5350 | Mathematical expression | Alexander polynomial: invariant of a knot or link. Use 't' as variable and list monomials in decreasing order. | unknot <Alexander polynomial> | - |

Conway polynomial | P5351 | Mathematical expression | Conway–Alexander polynomial: invariant of a knot. Use z as variable and list monomials in decreasing order. | unknot <Conway polynomial> | - |

Jones polynomial | P5352 | Mathematical expression | Jones polynomial: invariant of a knot or link. Use q as variable and list monomials in decreasing order. | unknot <Jones polynomial> | - |

Alexander–Briggs notation | P6432 | Mathematical expression | Alexander-Briggs notation: common notation of abstract knots and links | unknot <Alexander–Briggs notation> | - |

Dowker-Thistlethwaite notation | P8378 | Mathematical expression | Dowker–Thistlethwaite notation: descriptive property of mathematical knots, also known as Dowker notation | trefoil knot <Dowker-Thistlethwaite notation> | - |

Dowker-Thistlethwaite name | P8416 | Mathematical expression | Dowker–Thistlethwaite name: unambiguous systematic identifier scheme for mathematical knots | unknot <Dowker-Thistlethwaite name> | - |

graph radius | P7391 | Quantity | graph radius: the minimum eccentricity of any vertex of a graph | claw graph <graph radius> 1 | - |

To model whether a set is open or closed, use

For a class item that is a union of other items, use

**real number (Q12916)**union of (P2737) list values as qualifiers (Q23766486)**/**of (P642) irrational number (Q607728), rational number (Q1244890), integer (Q12503),**real number (Q12916)**disjoint union of (P2738) list values as qualifiers (Q23766486)**/**of (P642) irrational number (Q607728), rational number (Q1244890).

### Methods and AlgorithmsEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

computes solution to | P2159 | Item | problem that this algorithm or method solves | DPLL algorithm <computes solution to> boolean satisfiability problem | - |

solution to | P9030 | Item | a mathematical object that satisfies the criteria for a mathematical problem | eigenvalue <solution to> characteristic equation | - |

uses | P2283 | Item | use: item or concept used by the subject or in the operation (see also instrument [P1303] and armament [P520]) | method of lines <uses> discretization | used by |

approximation algorithm | P1171 | Item | approximation algorithm: method used to approximate a number | pi <approximation algorithm> Gauss–Legendre algorithm | - |

computational complexity | P10374 | Item | computational complexity: the most specific complexity class this computational problem has been proved to belong to; if available, provide the tight complexity, otherwise both hardness and membership can be specified | st-connectivity <computational complexity> NL-complete | - |

best-case time complexity | P3753 | Mathematical expression | time complexity: time complexity of an algorithm at least | quicksort <best-case time complexity> | - |

average time complexity | P3754 | Mathematical expression | time complexity: time complexity of an algorithm on average | quicksort <average time complexity> | - |

worst-case time complexity | P3752 | Mathematical expression | time complexity: time complexity of an algorithm at most | quicksort <worst-case time complexity> | - |

best-case space complexity | P3756 | Mathematical expression | space complexity: space complexity of an algorithm at least | merge sort <best-case space complexity> | - |

average space complexity | P3757 | Mathematical expression | space complexity: space complexity of an algorithm on average | quicksort <average space complexity> | - |

worst-case space complexity | P3755 | Mathematical expression | space complexity: space complexity of an algorithm at most | quicksort <worst-case space complexity> | - |

Butcher tableau | P8558 | Mathematical expression | Butcher tableau: table containing the coefficients of a Runge-Kutta method | backward Euler method <Butcher tableau> | - |

The following are also useful for iterative numerical methods

**Euler method (Q868454)**has quality (P1552) order of convergence (Q97940482)**/**numeric value (P1181) "1"**Euler method (Q868454)**has quality (P1552) number of steps (Q98293869)**/**quantity (P1114) "1" (number of steps (Q98293869): number of previous steps used in an iterative numerical method to calculate the next iteration)**Euler method (Q868454)**has quality (P1552) number of stages (Q97672364)**/**quantity (P1114) "1" (number of stages (Q97672364): the number of stages in a Runge-Kutta method)**backward Euler method (Q2736820)**has quality (P1552) L-stability (Q277932)**Euler method (Q868454)**does not have quality (P6477) A-stability (Q65926322)

### FunctionsEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

definition domain | P1568 | Item | domain of a function: set of "input" or argument values for which a mathematical function is defined | square function <definition domain> real number | - |

codomain | P1571 | Item | codomain: codomain of a function | square function <codomain> real number | - |

image of function | P2396 | Item | image: set of values that a mathematical function actually takes | square function <image of function> set of non-negative real numbers | - |

input set | P1851 | Item | input set: a superset of the domain of a function or relation that may include some inputs for which the function is not defined; to specify the set of only those inputs for which the function is defined use domain (P1568) | tangent <input set> set of real numbers | - |

support of a function | P10731 | Mathematical expression | support: subset of the domain containing those elements which are not mapped to zero | normal distribution <support of a function> | - |

Several properties of functions are modeled in Wikdata using the has quality (P1552) and does not have quality (P6477) properties.

**cosine (Q1256164)**has quality (P1552) boundedness (Q60644809)**exponential function (Q168698)**has quality (P1552) monotonicity (Q78056921)**cosine (Q1256164)**does not have quality (P6477) monotonicity (Q78056921)**square function (Q3075175)**has quality (P1552) arity (Q1315869)**/**numeric value (P1181) "1"

To specify symmetry, use

**cosine (Q1256164)**instance of (P31) even function (Q12138960)**sine (Q152415)**instance of (P31) odd function (Q18088516)

### GeometryEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

has facet polytope | P1312 | Item | facet: facet of a polytope, in the next-lower dimension | dodecahedron <has facet polytope> pentagon | - |

has vertex figure | P1678 | Item | vertex figure: the figure exposed when a corner of a polytope is sliced off | cuboctahedron <has vertex figure> rectangle | - |

base | P3263 | Item | base and base face: configuration of a polytop vertices around the symmetry axis | pentagonal prism <base> pentagon | - |

Euler characteristic | P6438 | Quantity | Euler characteristic: topological invariant of a space; the alternating sum of the dimensions of the (co)homology of a space | sphere <Euler characteristic> 2 | - |

dual to | P1322 | Item | duality, dual polytope and dual graph: dual of a polytope, graph or curve | cube <dual to> octahedron | - |

Schläfli symbol | P3228 | String | Schläfli symbol: notation that defines regular polytopes and tessellations | regular polygon <Schläfli symbol> {n} | - |

### ProbabilityEdit

invalid 'id' parameter should be a number or 'new', none provided

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

probability mass function | P10732 | Mathematical expression | probability mass function: function that gives the probability that a discrete random variable is exactly equal to some value | Poisson distribution <probability mass function> | - |

cumulative distribution function | P10736 | Mathematical expression | cumulative distribution function: probability that X will take a value less than or equal to x | normal distribution <cumulative distribution function> | - |

quantile function | P10737 | Mathematical expression | quantile function: value at which the probability of the random variable is less than or equal to the given probability | normal distribution <quantile function> | - |

mean of a probability distribution | P10738 | Mathematical expression | expected value: long-run average value of repetitions of the experiment it represents | normal distribution <mean of a probability distribution> | - |

median of a probability distribution | P10739 | Mathematical expression | median: value separating the higher half of a data sample, a population, or a probability distribution, from the lower half | normal distribution <median of a probability distribution> | - |

mode of a probability distribution | P10740 | Mathematical expression | mode: value that appears most often in a set of data | normal distribution <mode of a probability distribution> | - |

variance of a probability distribution | P10743 | Mathematical expression | variance: expectation of the squared deviation of a random variable from its mean | normal distribution <variance of a probability distribution> | - |

skewness | P10744 | Mathematical expression | skewness: measure of the asymmetry of the probability distribution of a real-valued random variable about its mean | normal distribution <skewness> | - |

excess kurtosis | P10745 | Mathematical expression | kurtosis: measure of the "tailedness" of the probability distribution of a real-valued random variable | normal distribution <excess kurtosis> | - |

information entropy | P10746 | Mathematical expression | information entropy: expected value (average) of the information contained in each message | normal distribution <information entropy> | - |

moment-generating function | P10747 | Mathematical expression | moment-generating function: alternative specification of its probability distribution | normal distribution <moment-generating function> | - |

characteristic function | P10735 | Mathematical expression | characteristic function: Fourier transform of the probability density function | normal distribution <characteristic function> | - |

Fisher information | P10734 | Mathematical expression | Fisher information: way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X | normal distribution <Fisher information> | - |

probability generating function | P10733 | Mathematical expression | probability-generating function: power series representation (the generating function) of the probability mass function of the random variable | Poisson distribution <probability generating function> | - |

support of a function | P10731 | Mathematical expression | support: subset of the domain containing those elements which are not mapped to zero | normal distribution <support of a function> | - |

### External IdentifiersEdit

Title | ID | Data type | Description | Examples | Inverse |
---|---|---|---|---|---|

OEIS ID | P829 | External identifier | On-Line Encyclopedia of Integer Sequences: identifer on the On-Line Encyclopedia of Integer Sequences | Fermat number <OEIS ID> A000215 | - |

Mathematics Genealogy Project ID | P549 | External identifier | Mathematics Genealogy Project: identifier for mathematicians and computer scientists at the Mathematics Genealogy Project | Patrick Ion <Mathematics Genealogy Project ID> 8691 | - |

zbMATH author ID | P1556 | External identifier | zbMATH database: identifier of a person in the Zentralblatt MATH database | Patrick Ion <zbMATH author ID> ion.patrick-d-f | - |

zbMATH work ID | P894 | External identifier | zbMATH database: identifier in the zbMath database | Game Theory: A Multi-Leveled Approach <zbMATH work ID> 1147.91001 | - |

MathWorld identifier | P2812 | External identifier | MathWorld: identifier for entries in MathWorld, online mathematics reference work | aleph null <MathWorld identifier> Aleph-0 | - |

ProofWiki ID | P6781 | External identifier | ProofWiki: identifier for a ProofWiki article | Euclid's theorem <ProofWiki ID> Euclid's Theorem | - |

## PolytopesEdit

Root item | Query | Query description | Count date | Count quantity | Count link |
---|---|---|---|---|---|

polytope (Q747980) | tree[747980][][279] | subclasses | 2014-10-07 | 813 | autolist2 |

vertex (Q26401) | web[26401][1312] | polytopes with property "has facet polytope" (direct, not inherited) | 2014-10-07 | 534 | autolist2 |

## ParticipantsEdit

The participants listed below can be notified using the following template in discussions:

`{{Ping project|Mathematics}}`

## UserboxEdit

- See: Wikidata:Userboxes

This user is a member ofWikiProject Mathematics |

## Related WikiProjectsEdit

### WikidataEdit

- Shared symmetry properties (crystallography):