Wikidata:WikiProject Mathematics

Goals

Long term goals

Organize data about mathematics

Short term goals

Review the #Scope
Use maintained by WikiProject (P6104) on all items and properties within #Scope
- Use field of usage (P9488) on senses of lexemes within #Scope (uses)
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

Scope

All Wikidata properties for which instance of (P31) has the value Wikidata property related to mathematics (Q22988631)   (see list).
All Wikidata entities with a statement that involves any of these properties.
Auxiliary wiki pages that assist with the above.

Infoboxes

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

Useful lists and queries

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
- pairs of equivalent theorems / axioms / principles (using loops of generalization of (P7719) )
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.

Properties

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

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	ideal gas law <defining formula> $PV=nRT$	-
has part(s)	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(s)> 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 Properties

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	Pythagorean theorem <defining formula> $a^{2}+b^{2}=c^{2}$	-
in defining formula	P7235	Mathematical expression	variable: any symbol used in the defining formula (P2534)	f-number <in defining formula> $N$	-
quantity symbol (LaTeX)	P7973	Mathematical expression	quantity symbol: symbol for a mathematical or physical quantity in LaTeX	electric charge <quantity symbol (LaTeX)> $Q$	-
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(s)> Euler method <relative to> time	-
studied in	P2579	Item	academic discipline: subject is studied by this science or domain	numerical method <studied in> numerical analysis	is the study of
has characteristic	P1552	Item	quality: inherent or distinguishing quality or feature of the entity. Use a more specific property when possible	mathematical proof <has characteristic> validity	characteristic of
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 and extension: statement logically implied by the subject or a similar algorithm/function whose domain is a subset of the subject's domain	law of cosines <generalization of> Pythagorean theorem	-
is invariant under	P12457	Item	invariant: subject is unchanged by this process / function / group of transformation	graph property <is invariant under> graph isomorphism	-

Numbers

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	em dash <greater than> en dash	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	aerostat <less than> air	greater than
number of decimal digits	P7316	Quantity	numerical digit and decimal 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 History

Title	ID	Data type	Description	Examples	Inverse
discoverer or inventor	P61	Item	inventor, innovator, discoverer, discovery, invention and discoveries and inventions: subject who discovered, first described, invented, or developed this discovery or invention or scientific hypothesis or theory	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) or inputs used as the basis for subject item; for fictional analog use P1074	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> ${\text{On the Integers of the Form }}x^{k}+y^{k}$	-

Sets, Algebras, and Topology

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 in mathematics	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	inverse: inverse element with respect to binary operation given as a qualifier using P2210	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	location
has part(s) of the class	P2670	Item	has parts of class: the subject has one or more parts of the object class	set of real numbers <has part(s) of the class> real number	-
graph radius	P7391	Quantity	graph radius: the minimum eccentricity of any vertex of a graph	claw graph <graph radius> 1	-
underlying structure(s)	P12322	Item	underlying structure: mathematical structure(s) obtained by deleting some data of the subject	metric space <underlying structure(s)> metrizable space	-

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

Title	ID	Data type	Description	Examples	Inverse
crossing number	P11035	Quantity	crossing 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 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> $1$	-
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> $1$	-
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> $1$	-
Alexander–Briggs notation	P6432	Mathematical expression	Alexander-Briggs notation: common notation of abstract knots and links	unknot <Alexander–Briggs notation> $0_{1}$	-
Dowker-Thistlethwaite notation	P8378	Mathematical expression	Dowker–Thistlethwaite notation: descriptive property of mathematical knots, also known as Dowker notation	trefoil knot <Dowker-Thistlethwaite notation> $4,6,2$	-
Dowker-Thistlethwaite name	P8416	Mathematical expression	Dowker–Thistlethwaite name: unambiguous systematic identifier scheme for mathematical knots	unknot <Dowker-Thistlethwaite name> $0_{1}$	-
Gauss notation	P11034	Mathematical expression	Gauss notation: Gauss notation for knots and links	unknot <Gauss notation> not applicable	-

Methods and Algorithms

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> $O(n\log n)$	-
average time complexity	P3754	Mathematical expression	time complexity: time complexity of an algorithm on average	quicksort <average time complexity> $O(n\log n)$	-
worst-case time complexity	P3752	Mathematical expression	time complexity: time complexity of an algorithm at most	quicksort <worst-case time complexity> $O(n^{2})$	-
best-case space complexity	P3756	Mathematical expression	space complexity: space complexity of an algorithm at least	merge sort <best-case space complexity> $O(1)$	-
average space complexity	P3757	Mathematical expression	space complexity: space complexity of an algorithm on average	quicksort <average space complexity> $O(\log n)$	-
worst-case space complexity	P3755	Mathematical expression	space complexity: space complexity of an algorithm at most	quicksort <worst-case space complexity> $O(n)$	-
Butcher tableau	P8558	Mathematical expression	Butcher tableau: table containing the coefficients of a Runge-Kutta method	backward Euler method <Butcher tableau> ${\begin{array}{l\|l}1&1\\\hline &1\end{array}}$	-

The following are also useful for iterative numerical methods

Euler method (Q868454)has characteristic (P1552)order of convergence (Q97940482)numeric value (P1181)"1"
Euler method (Q868454)has characteristic (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 characteristic (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 characteristic (P1552)L-stability (Q277932)
Euler method (Q868454)does not have characteristic (P6477)A-stability (Q65926322)

Functions

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; subset of input set	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> $\displaystyle \mathbb {R}$	-
power series expansion	P10969	Mathematical expression	power series expansion: power series expansion of the subject	exponential function <power series expansion> $e^{x}=\sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}=1+x+{\frac {x^{2}}{2!}}+{\frac {x^{3}}{3!}}+\cdots +{\frac {x^{n}}{n!}}+\cdots$	-

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

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	dual to
Schläfli symbol	P3228	String	Schläfli symbol: notation that defines regular polytopes and tessellations	regular polygon <Schläfli symbol> {n}	-
Schläfli symbol	P3228	String	Schläfli symbol: notation that defines regular polytopes and tessellations	regular polygon <Schläfli symbol> {n}	-
is invariant under	P12457	Item	invariant: subject is unchanged by this process / function / group of transformation	regular icosahedron <is invariant under> icosahedral symmetry	-

Probability

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> ${\frac {\lambda ^{k}e^{-\lambda }}{k!}}$	-
cumulative distribution function	P10736	Mathematical expression	distribution function: probability that X will take a value less than or equal to x	normal distribution <cumulative distribution function> ${\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sigma {\sqrt {2}}}}\right)\right]$	-
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> $\mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2F-1)$	-
mean of a probability distribution	P10738	Mathematical expression	mean: long-run average value of repetitions of the experiment it represents	normal distribution <mean of a probability distribution> $\mu$	-
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> $\mu$	-
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> $\mu$	-
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> $\sigma ^{2}$	-
skewness	P10744	Mathematical expression	coefficient of skewness: measure of the asymmetry of the probability distribution of a real-valued random variable about its mean	normal distribution <skewness> $0$	-
excess kurtosis	P10745	Mathematical expression	excess kurtosis: measure of the "tailedness" of the probability distribution of a real-valued random variable	normal distribution <excess kurtosis> $0$	-
information entropy	P10746	Mathematical expression	information entropy: expected value (average) of the information contained in each message	normal distribution <information entropy> ${\tfrac {1}{2}}\ln(2\sigma ^{2}\pi \,e\,)$	-
moment-generating function	P10747	Mathematical expression	moment-generating function: alternative specification of its probability distribution	normal distribution <moment-generating function> $\exp\{\mu t+{\frac {1}{2}}\sigma ^{2}t^{2}\}$	-
characteristic function	P10735	Mathematical expression	characteristic function: Fourier transform of the probability density function	normal distribution <characteristic function> $\mathrm {e} ^{\mathrm {i} \mu t-{\frac {\sigma ^{2}t^{2}}{2}}}$	-
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> ${\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}$	-
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> $\exp(\lambda (z-1))$	-
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> $\displaystyle \mathbb {R}$	-

Graph theory

Title	ID	Data type	Description	Examples	Inverse
graph diameter	P7462	Quantity	graph diameter: maximum eccentricity of any vertex in the graph	claw graph <graph diameter> 2	-
graph girth	P8986	Quantity	girth: length of a shortest cycle contained in the graph	double-star snark <graph girth> 6	-
graph radius	P7391	Quantity	graph radius: the minimum eccentricity of any vertex of a graph	claw graph <graph radius> 1	-
The House of Graphs ID	P12934	External identifier	House of Graphs: ID for an undirected graph on houseofgraphs.org	triangle graph <The House of Graphs ID> 1374	-

External Identifiers

Title	ID	Data type	Description	Examples	Inverse
OEIS ID	P829	External identifier	On-Line Encyclopedia of Integer Sequences: identifier on the On-Line Encyclopedia of Integer Sequences	Fermat number <OEIS ID> A000215	-
Mathematics Genealogy Project ID	P549	External identifier	identifier for mathematicians and computer scientists at the Mathematics Genealogy Project	Patrick Ion <Mathematics Genealogy Project ID> 8691	-
zbMATH author ID	P1556	External identifier	identifier of a person in the Zentralblatt MATH database	Patrick Ion <zbMATH author ID> ion.patrick-d-f	-
zbMATH Open document ID	P894	External identifier	identifier in the zbMATH Open database	Game Theory: A Multi-Leveled Approach <zbMATH Open document ID> 1147.91001	-
MathWorld ID	P2812	External identifier	MathWorld: identifier for entries in MathWorld, online mathematics reference work	aleph null <MathWorld ID> Aleph-0	-
nLab ID	P4215	External identifier	name of a page in nLab wiki	total order <nLab ID> total order	-
ProofWiki ID	P6781	External identifier	identifier for a ProofWiki article	Euclid's theorem <ProofWiki ID> Euclid's Theorem	-
Encyclopedia of Mathematics article ID	P7554	External identifier	identifier for an article on the Encyclopedia of Mathematics wiki (encyclopediaofmath.org)	Cauchy–Schwarz inequality <Encyclopedia of Mathematics article ID> Cauchy_Schwarz_inequality	-
Mathematical Reviews ID	P889	External identifier	identifier in Mathematical Reviews, a journal and online database	Introduction to the Theory of Games <Mathematical Reviews ID> 50248	-

Polytopes

Root item	Query	Query description	Count date	Count quantity	Count link
polytope (Q747980)	tree[747980][][279]	subclasses	2014-10-07	813	autolist2 tree
vertex (Q26401)	web[26401][1312]	polytopes with property "has facet polytope" (direct, not inherited)	2014-10-07	534	autolist2 tree

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