On Numbers and Games
E30395
On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
All labels observed (2)
| Label | Occurrences |
|---|---|
| On Numbers and Games canonical | 11 |
| On Numbers and Games second edition | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T231159 — 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: On Numbers and Games Context triple: [John H. Conway, notableWork, On Numbers and Games]
-
A.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
B.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
C.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
D.
von Neumann paradox in set theory
The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
-
E.
De ratiociniis in ludo aleae
De ratiociniis in ludo aleae is a pioneering 17th-century treatise on probability theory, particularly as applied to games of chance.
- 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: On Numbers and Games Target entity description: On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
-
A.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
B.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
C.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
D.
von Neumann paradox in set theory
The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
-
E.
De ratiociniis in ludo aleae
De ratiociniis in ludo aleae is a pioneering 17th-century treatise on probability theory, particularly as applied to games of chance.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics book ⓘ |
| author |
John H. Conway
ⓘ
John H. Conway ⓘ
surface form:
John Horton Conway
|
| countryOfOrigin | United Kingdom ⓘ |
| field |
combinatorial game theory
ⓘ
number theory ⓘ |
| firstPublicationYear | 1976 ⓘ |
| genre | mathematics ⓘ |
| hasConcept |
Conway numbers
ⓘ
canonical forms of games ⓘ equivalence of games ⓘ game values ⓘ long games ⓘ short games ⓘ surreal number construction by transfinite recursion ⓘ temperature of a game ⓘ |
| hasPart |
Part One
ⓘ
Part One: Numbers ⓘ Part Two ⓘ Part Two: Games ⓘ Part Zero ⓘ Part Zero: Preliminaries ⓘ |
| influenced |
The Book of Numbers
ⓘ
Winning Ways for your Mathematical Plays ⓘ later research in combinatorial game theory ⓘ |
| language | English ⓘ |
| notableFor |
foundational work in combinatorial game theory
ⓘ
introducing surreal numbers in book form ⓘ |
| publisher |
A K Peters
ⓘ
Academic Press ⓘ |
| style |
informal exposition with formal proofs
ⓘ
playful ⓘ rigorous ⓘ |
| targetAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ mathematicians ⓘ |
| topic |
Go endgames
ⓘ
Hackenbush ⓘ cold games ⓘ combinatorial games ⓘ game theory ⓘ hot games ⓘ impartial games ⓘ nim ⓘ normal play convention ⓘ ordinal numbers ⓘ partizan games ⓘ Surreal numbers ⓘ
surface form:
surreal numbers
|
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: On Numbers and Games Description of subject: On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
Referenced by (12)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Part Two (On Numbers and Games)
this entity surface form:
On Numbers and Games second edition