Erdős number concept
E554296
The Erdős number concept is a measure of collaborative distance in mathematical research, indicating how many coauthorship links separate a given author from the prolific Hungarian mathematician Pál Erdős.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Erdős number | 3 |
| Erdős number concept canonical | 1 |
| Erdős–Bacon number concept | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5896701 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Erdős number concept Context triple: [Pál Erdős, knownFor, Erdős number concept]
-
A.
Pál Erdős
Pál Erdős was a highly prolific 20th-century Hungarian mathematician renowned for his extensive contributions to number theory, combinatorics, and discrete mathematics, as well as his famously collaborative working style.
-
B.
Eddington number
The Eddington number is a dimensionless quantity in astrophysics that represents the maximum luminosity a star can have before radiation pressure overcomes gravitational attraction, leading to mass loss.
-
C.
Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
-
D.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
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E.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Erdős number concept Target entity description: The Erdős number concept is a measure of collaborative distance in mathematical research, indicating how many coauthorship links separate a given author from the prolific Hungarian mathematician Pál Erdős.
-
A.
Pál Erdős
Pál Erdős was a highly prolific 20th-century Hungarian mathematician renowned for his extensive contributions to number theory, combinatorics, and discrete mathematics, as well as his famously collaborative working style.
-
B.
Eddington number
The Eddington number is a dimensionless quantity in astrophysics that represents the maximum luminosity a star can have before radiation pressure overcomes gravitational attraction, leading to mass loss.
-
C.
Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
-
D.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
E.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
bibliometric indicator
ⓘ
collaboration distance measure ⓘ mathematical concept ⓘ |
| appliesTo | authors of mathematical research papers ⓘ |
| assumes |
coauthored works are documented in bibliographic databases
ⓘ
coauthorship as a symmetric relation ⓘ |
| baseCaseDescription | Pál Erdős himself has Erdős number 0 ⓘ |
| basedOn | graph theory ⓘ |
| defines |
Erdős number 0
ⓘ
Erdős number 1 ⓘ Erdős number 2 ⓘ Erdős number n ⓘ |
| describes | collaborative distance in mathematical authorship ⓘ |
| domain |
mathematics
ⓘ
network science ⓘ scientometrics ⓘ |
| formalizedAs | distance metric on the induced subgraph of authors connected to Pál Erdős ⓘ |
| hasAlternativeName |
Erdős number
ⓘ
linked to:
Erdős number concept
|
| hasBaseCase | Erdős number 0 ⓘ |
| hasConstraint | only joint authorship on scholarly works counts as an edge ⓘ |
| hasCulturalImpact | popular among mathematicians and scientists as a measure of collaborative closeness to Erdős ⓘ |
| hasDefinition | the length of the shortest coauthorship path between a given author and Pál Erdős ⓘ |
| hasHistoricalContext | developed in the late 20th century as Erdős’s collaboration network became widely studied ⓘ |
| hasNotation |
Erdős number
ⓘ
linked to:
Erdős number concept
|
| hasProperty |
depends on the underlying publication database used
ⓘ
non‑authors or authors not connected by coauthorship to Erdős have undefined or infinite Erdős number ⓘ values can change as new coauthored papers are published or discovered ⓘ |
| hasValueType | non‑negative integer ⓘ |
| inspired | similar collaboration distance measures for other scientists and artists ⓘ |
| isSubconceptOf |
academic collaboration metrics
ⓘ
collaboration distance ⓘ |
| measurementUnit | steps in a coauthorship graph ⓘ |
| namedAfter | Pál Erdős ⓘ |
| number1Description | authors who coauthored a paper directly with Pál Erdős have Erdős number 1 ⓘ |
| number2Description | authors who coauthored with an Erdős‑1 author but not with Erdős directly have Erdős number 2 ⓘ |
| originatedFrom | study of Pál Erdős’s extensive coauthorships ⓘ |
| recursiveDefinition | an author has Erdős number n+1 if they coauthored with at least one author of Erdős number n and have no smaller Erdős number ⓘ |
| relatedTo |
Bacon number concept
ⓘ
Erdős–Bacon number concept ⓘ
linked to:
Erdős number concept
academic genealogy ⓘ coauthorship network ⓘ |
| representedAs | shortest‑path length in a coauthorship network graph ⓘ |
| usedFor |
illustrating small‑world phenomena in scientific collaboration
ⓘ
informal prestige or novelty in mathematical culture ⓘ studying collaboration networks in mathematics ⓘ |
| usesRelation | coauthorship of research papers ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Erdős number concept Description of subject: The Erdős number concept is a measure of collaborative distance in mathematical research, indicating how many coauthorship links separate a given author from the prolific Hungarian mathematician Pál Erdős.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Erdős number concept
linked to: Erdős number concept
linked to: Erdős number concept
linked to: Erdős number concept