An Elementary Investigation of the Theory of Numbers
E695718
An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| An Elementary Investigation of the Theory of Numbers canonical | 2 |
| An Elementary Investigation of the Theory of Numbers (1811) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7854056 — 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: An Elementary Investigation of the Theory of Numbers Context triple: [Peter Barlow, notableWork, An Elementary Investigation of the Theory of Numbers]
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A.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
B.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
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C.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
-
D.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
-
E.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
- 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: An Elementary Investigation of the Theory of Numbers Target entity description: An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
-
A.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
B.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
-
C.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
-
D.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
-
E.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
mathematician
ⓘ
mathematics book ⓘ non-fiction book ⓘ number theory treatise ⓘ |
| author | Peter Barlow ⓘ |
| contributedTo | development of elementary number theory ⓘ |
| countryOfOrigin | United Kingdom ⓘ |
| describedAs | foundational treatise on number theory ⓘ |
| field |
mathematics
ⓘ
mathematics ⓘ number theory ⓘ |
| genre | mathematical treatise ⓘ |
| hasAuthor | Peter Barlow ⓘ |
| hasPart |
chapters on Diophantine analysis
ⓘ
chapters on divisors and multiples ⓘ chapters on modular arithmetic ⓘ chapters on prime numbers ⓘ |
| intendedAudience |
professional mathematicians
ⓘ
students of mathematics ⓘ |
| knownFor | An Elementary Investigation of the Theory of Numbers ⓘ |
| language | English ⓘ |
| mainSubject |
Diophantine equations
ⓘ
arithmetic functions ⓘ congruences ⓘ divisibility ⓘ integers ⓘ prime numbers ⓘ properties of integers ⓘ |
| notableFor |
early comprehensive English-language exposition of number theory
ⓘ
systematic treatment of properties of integers ⓘ |
| publicationCentury | 19th century ⓘ |
| timePeriod | 19th-century mathematics ⓘ |
| usedIn | historical studies of number theory ⓘ |
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: An Elementary Investigation of the Theory of Numbers Description of subject: An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: An Elementary Investigation of the Theory of Numbers
subject linked to:
An Elementary Investigation of the Theory of Numbers