Shortcut: WD:MATH

Wikidata:WikiProject Mathematics

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Long term goals[edit]

  • Organize data about mathematics

Short term goals[edit]

  • 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


Useful lists and queries[edit]

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


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

Properties used in Wikipedia[edit]

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 formulaP2534Mathematical expressionformula: mathematical formula representing a theorem or law. Maximum length: 400 charactersideal gas law <defining formula> -
has partP527Itemhas 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> pressurepart of
quantity symbol (string)P416Stringquantity symbol: symbol for a mathematical or physical quantityelectric charge <quantity symbol (string)> Q and q-

General Properties[edit]

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 formulaP2534Mathematical expressionformula: mathematical formula representing a theorem or law. Maximum length: 400 charactersPythagorean theorem <defining formula> -
in defining formulaP7235Mathematical expressionvariable, identifier and pronumeral: any symbol used in the defining formula (P2534)f-number <in defining formula> -
quantity symbol (LaTeX)P7973Mathematical expressionquantity symbol: symbol for a mathematical or physical quantity in LaTeXelectric charge <quantity symbol (LaTeX)> -
calculated fromP4934Itemcalculation: value of the subject item cannot be measured directly or can be calculated from the following measurands or attributesbody mass index <calculated from> human body weight and human height-
relative toP2210Itemreference point: qualifier: what a statement value is relative toFTCS scheme <has part> Euler method
<relative to> time
studied byP2579Itemacademic discipline and branch of engineering: subject is studied by this science or domain or by this type of studentnumerical method <studied by> numerical analysisstudies
has qualityP1552Itemquality: the entity has an inherent or distinguishing non-material characteristicmathematical proof <has quality> validity-
notationP913Itemnotation: mathematical notation or another symbolequality <notation> equals sign-
statement describesP2384Itemformalization of the statement contains a bound variable in this classPythagorean theorem <statement describes> right triangle-
admissible rule inP2577Itemadmissible rule: this logic inference rule is admissible in that logical systemmodus ponens <admissible rule in> classical logic-
generalization ofP7719Itemlogical implication: statement that is a particular case of this statement or whose truth is implied by this statementlaw of cosines <generalization of> Pythagorean theorem-


Title ID Data type Description Examples Inverse
numeric valueP1181Quantitynumber: numerical value of a number, a mathematical constant, or a physical constantgolden ratio <numeric value> 1,6180339887±0,0000000001-
prime factorP5236Itemprime factor: one of the prime numbers that can be multiplied to give this number2334 <prime factor> 2, 389 and 3-
greater thanP5135Itemgreater than: instances of the item have a greater value than corresponding instances of the object, for the given measure100 <greater than> 99less than
less thanP5136Itemless than: instances of the item have a lesser value than corresponding instances of the object, for the given measure−1 <less than> zerogreater than
number of decimal digitsP7316Quantitynumerical digit: number of decimal digits of a natural number10^90 <number of decimal digits> 91-
radixP3264Itemradix: number of distinct digits in a positional numeral systemhexadecimal <radix> 16-

Mathematicans and Mathematical History[edit]

Title ID Data type Description Examples Inverse
discoverer or inventorP61Iteminventor, innovator, discoverer, discovery and invention: subject who discovered, first described, invented, or developed this discovery or inventionPoincaré conjecture <discoverer or inventor> Henri Poincaré-
time of discovery or inventionP575Point in timeinvention and discovery: date or point in time when the item was discovered or inventedEuler method <time of discovery or invention> 1768-
named afterP138Itemeponym and memorial society: 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 oneEuler method <named after> Leonhard Euler-
proved byP1318Itemperson who proved somethingPoincaré conjecture <proved by> Grigori Perelman-
solved byP1136Itemperson that solved a scientific questionFermat's Last Theorem <solved by> Andrew Wiles-
based onP144Itembased on: the work(s) used as the basis for subject itemPythagorean trigonometric identity <based on> Pythagorean theoremderivative work
Erdős numberP2021QuantityErdős 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 LaTeXP6835Mathematical expressionLaTeX: (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 Topology[edit]

Title ID Data type Description Examples Inverse
cardinality of this setP2820Itemcardinality: measure of number of elements of a setrational number <cardinality of this set> aleph null-
group cardinalityP1164Quantitygroup order: number of elements in a finite groupdihedral group of order 6 <group cardinality> 6-
identity elementP8864Itemidentity element: value of the identity element of the mathematical operationaddition <identity element> zero-
has operatorP8866Itemoperator: mathematical operator associated with this algebraic structureadditive group <has operator> addition-
mathematical inverseP8865Itemmathematical inverse: inverse element with respect to binary operation given as a qualifier2 <mathematical inverse> ½mathematical inverse
containsP4330Iteminsertion: item or substance located within this item but not part of itsphere <contains> open ball-
has parts of the classP2670Itemhas part of class: the subject instance has parts of the object class (the subject is usually not a class)set of real numbers <has parts of the class> real number-
Alexander polynomialP5350Mathematical expressionAlexander polynomial: invariant of a knot or link. Use 't' as variable and list monomials in decreasing order.unknot <Alexander polynomial> -
Conway polynomialP5351Mathematical expressionConway–Alexander polynomial: invariant of a knot. Use z as variable and list monomials in decreasing order.unknot <Conway polynomial> -
Jones polynomialP5352Mathematical expressionJones polynomial: invariant of a knot or link. Use q as variable and list monomials in decreasing order.unknot <Jones polynomial> -
Alexander–Briggs notationP6432Mathematical expressionAlexander-Briggs notation: common notation of abstract knots and linksunknot <Alexander–Briggs notation> -
Dowker-Thistlethwaite notationP8378Mathematical expressionDowker–Thistlethwaite notation: descriptive property of mathematical knots, also known as Dowker notationtrefoil knot <Dowker-Thistlethwaite notation> -
Dowker-Thistlethwaite nameP8416Mathematical expressionDowker–Thistlethwaite name: unambiguous systematic identifier scheme for mathematical knotsunknot <Dowker-Thistlethwaite name> -
graph radiusP7391Quantitygraph radius: the minimum eccentricity of any vertex of a graphclaw 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

Methods and Algorithms[edit]

Title ID Data type Description Examples Inverse
computes solution toP2159Itemproblem that this algorithm or method solvesDPLL algorithm <computes solution to> boolean satisfiability problem-
solution toP9030Itema mathematical object that satisfies the criteria for a mathematical problemeigenvalue <solution to> characteristic equation-
usesP2283Itemuse: item or concept used by the subject or in the operation (see also instrument [P1303] and armament [P520])method of lines <uses> discretizationused by
approximation algorithmP1171Itemapproximation algorithm: method used to approximate a numberpi <approximation algorithm> Gauss–Legendre algorithm-
best-case time complexityP3753Mathematical expressiontime complexity: time complexity of an algorithm at leastquicksort <best-case time complexity> -
average time complexityP3754Mathematical expressiontime complexity: time complexity of an algorithm on averagequicksort <average time complexity> -
worst-case time complexityP3752Mathematical expressiontime complexity: time complexity of an algorithm at mostquicksort <worst-case time complexity> -
best-case space complexityP3756Mathematical expressionspace complexity: space complexity of an algorithm at leastmerge sort <best-case space complexity> -
average space complexityP3757Mathematical expressionspace complexity: space complexity of an algorithm on averagequicksort <average space complexity> -
worst-case space complexityP3755Mathematical expressionspace complexity: space complexity of an algorithm at mostquicksort <worst-case space complexity> -
Butcher tableauP8558Mathematical expressionButcher tableau: table containing the coefficients of a Runge-Kutta methodbackward Euler method <Butcher tableau> -

The following are also useful for iterative numerical methods


Title ID Data type Description Examples Inverse
definition domainP1568Itemdomain of a function: set of "input" or argument values for which a mathematical function is definedsquare function <definition domain> real number-
codomainP1571Itemcodomain: codomain of a functionsquare function <codomain> real number-
image of functionP2396Itemimage of a function: set of values that a mathematical function actually takescosine <image of function> closed interval from −1 to 1-
input setP1851Iteminput 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-

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

To specify symmetry, use


Title ID Data type Description Examples Inverse
has facet polytopeP1312Itemfacet: facet of a polytope, in the next-lower dimensiondodecahedron <has facet polytope> pentagon-
has vertex figureP1678Itemvertex figure: the figure exposed when a corner of a polytope is sliced offcuboctahedron <has vertex figure> rectangle-
baseP3263Itembase and base face: configuration of a polytop vertices around the symmetry axispentagonal prism <base> pentagon-
Euler characteristicP6438QuantityEuler characteristic: topological invariant of a space; the alternating sum of the dimensions of the (co)homology of a spacesphere <Euler characteristic> 2-
dual toP1322Itemduality, dual polytope and dual graph: dual of a polytope, graph or curvecube <dual to> octahedron-
Schläfli symbolP3228StringSchläfli symbol: notation that defines regular polytopes and tessellationsregular polygon <Schläfli symbol> {n}-

External Identifiers[edit]

Title ID Data type Description Examples Inverse
OEIS IDP829External identifierOn-Line Encyclopedia of Integer Sequences: identifer on the On-Line Encyclopedia of Integer SequencesFermat number <OEIS ID> A000215-
Mathematics Genealogy Project IDP549External identifierMathematics Genealogy Project: identifier for mathematicians and computer scientists at the Mathematics Genealogy ProjectPatrick Ion <Mathematics Genealogy Project ID> 8691-
zbMATH author IDP1556External identifierzbMATH database: identifier of a person in the Zentralblatt MATH databasePatrick Ion <zbMATH author ID> ion.patrick-d-f-
zbMATH work IDP894External identifierzbMATH database: identifier in the zbMath databaseGame Theory: A Multi-Leveled Approach <zbMATH work ID> 1147.91001-
MathWorld identifierP2812External identifierMathWorld: identifier for entries in MathWorld, online mathematics reference workaleph null <MathWorld identifier> Aleph-0-
ProofWiki IDP6781External identifierProofWiki: identifier for a ProofWiki articleEuclid's theorem <ProofWiki ID> Euclid's Theorem-


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



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Related WikiProjects[edit]


  • Shared symmetry properties (crystallography):