Wikidata:WikiProject Mathematics

Goals edit

Long term goals edit

  • Organize data about mathematics

Short term goals edit

Scope edit

Infoboxes edit

Useful lists and queries edit

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

Properties edit

See also: List of properties related to mathematics (SPARQL query), Template:Mathematics properties (manually curated), List of mathematics-related Wikidata properties by usage count (SPARQL query) and 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 part(s)P527Itemhas 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(s)> 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(s)> Euler method
<relative to> time
studied byP2579Itemacademic discipline: subject is studied by this science or domainnumerical method <studied by> numerical analysisis the study of
has characteristicP1552Itemquality: inherent or distinguishing quality or feature of the entity. Use a more specific property when possible.mathematical proof <has characteristic> 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: the subject statement in particular gives this object statement, or the truth of this object statement is implied by the truth of the subject statementlaw of cosines <generalization of> Pythagorean theorem-

Numbers edit

Title ID Data type Description Examples Inverse
numeric valueP1181Quantitynumeric value and quantity value: 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 measureem dash <greater than> en dashless than
less thanP5136Itemless than: instances of the item have a lesser value than corresponding instances of the object, for the given measureaerostat <less than> airgreater 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, invention and discoveries and inventions: subject who discovered, first described, invented, or developed this discovery or invention or scientific hypothesis or theoryPoincaré conjecture <discoverer or inventor> Henri Poincaré-
time of discovery or inventionP575Point in timeinvention, discovery and archaeological find: date or point in time when the item was discovered or inventedEuler method <time of discovery or invention> 1768-
named afterP138Itemeponym, 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 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 group in mathematicsdihedral 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 inverseP8865Iteminverse: inverse element with respect to binary operation given as a qualifier using P22102 <mathematical inverse> ½mathematical inverse
containsP4330Iteminsertion: item or substance located within this item but not part of itsphere <contains> open balllocation
has part(s) of the classP2670Itemhas part of class: the subject instance (the subject is not a class) has one or more parts of the object classset of real numbers <has part(s) of the class> real number-
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

  • set of real numbers (Q26851380)has characteristic (P1552)openness (Q60644734)

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

Knots and Links edit

Title ID Data type Description Examples Inverse
crossing numberP11035Quantitycrossing number: crossing number for mathematical knots; the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant.unknot <crossing number> 0-
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>  -
Gauss notationP11034Mathematical expressionGauss notation: Gauss notation for knots and linksunknot <Gauss notation> not applicable-

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-
computational complexityP10374Itemcomputational 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 specifiedst-connectivity <computational complexity> NL-complete-
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

Functions edit

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: set of values that a mathematical function actually takessquare function <image of function> set of non-negative real numbers-
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-
support of a functionP10731Mathematical expressionsupport: subset of the domain containing those elements which are not mapped to zeronormal distribution <support of a function>  -
power series expansionP10969Mathematical expressionpower series expansion: power series expansion of the subjectexponential function <power series expansion>  -

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

To specify symmetry, use

Geometry edit

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> octahedrondual to
Schläfli symbolP3228StringSchläfli symbol: notation that defines regular polytopes and tessellationsregular polygon <Schläfli symbol> {n}-

Probability edit

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Title ID Data type Description Examples Inverse
probability mass functionP10732Mathematical expressionprobability mass function: function that gives the probability that a discrete random variable is exactly equal to some valuePoisson distribution <probability mass function>  -
cumulative distribution functionP10736Mathematical expressiondistribution function: probability that X will take a value less than or equal to xnormal distribution <cumulative distribution function>  -
quantile functionP10737Mathematical expressionquantile function: value at which the probability of the random variable is less than or equal to the given probabilitynormal distribution <quantile function>  -
mean of a probability distributionP10738Mathematical expressionmean: long-run average value of repetitions of the experiment it representsnormal distribution <mean of a probability distribution>  -
median of a probability distributionP10739Mathematical expressionmedian: value separating the higher half of a data sample, a population, or a probability distribution, from the lower halfnormal distribution <median of a probability distribution>  -
mode of a probability distributionP10740Mathematical expressionmode: value that appears most often in a set of datanormal distribution <mode of a probability distribution>  -
variance of a probability distributionP10743Mathematical expressionvariance: expectation of the squared deviation of a random variable from its meannormal distribution <variance of a probability distribution>  -
skewnessP10744Mathematical expressioncoefficient of skewness: measure of the asymmetry of the probability distribution of a real-valued random variable about its meannormal distribution <skewness>  -
excess kurtosisP10745Mathematical expressionexcess kurtosis: measure of the "tailedness" of the probability distribution of a real-valued random variablenormal distribution <excess kurtosis>  -
information entropyP10746Mathematical expressioninformation entropy: expected value (average) of the information contained in each messagenormal distribution <information entropy>  -
moment-generating functionP10747Mathematical expressionmoment-generating function: alternative specification of its probability distributionnormal distribution <moment-generating function>  -
characteristic functionP10735Mathematical expressioncharacteristic function: Fourier transform of the probability density functionnormal distribution <characteristic function>  -
Fisher informationP10734Mathematical expressionFisher 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 Xnormal distribution <Fisher information>  -
probability generating functionP10733Mathematical expressionprobability-generating function: power series representation (the generating function) of the probability mass function of the random variablePoisson distribution <probability generating function>  -
support of a functionP10731Mathematical expressionsupport: subset of the domain containing those elements which are not mapped to zeronormal distribution <support of a function>  -

External Identifiers edit

Title ID Data type Description Examples Inverse
OEIS IDP829External identifierOn-Line Encyclopedia of Integer Sequences: identifier 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 Open: identifier of a person in the Zentralblatt MATH databasePatrick Ion <zbMATH author ID> ion.patrick-d-f-
zbMATH Open document IDP894External identifierzbMATH Open: identifier in the zbMATH Open databaseGame Theory: A Multi-Leveled Approach <zbMATH Open document ID> 1147.91001-
MathWorld IDP2812External identifierMathWorld: identifier for entries in MathWorld, online mathematics reference workaleph null <MathWorld ID> Aleph-0-
nLab IDP4215External identifiernLab: name of a page in nLab wikitotal order <nLab ID> total order-
ProofWiki IDP6781External identifierProofWiki: identifier for a ProofWiki articleEuclid's theorem <ProofWiki ID> Euclid's Theorem-
Encyclopedia of Mathematics wiki IDP7554External identifierEncyclopedia of Mathematics: identifier for an article on the Encyclopedia of Mathematics wikiCauchy–Schwarz inequality <Encyclopedia of Mathematics wiki ID> Cauchy_Schwarz_inequality-

Polytopes edit

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


Participants edit

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Subpages edit

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Related WikiProjects edit

Wikidata edit

  • Shared symmetry properties (crystallography):