An Introduction to the Theory of Numbers
E120387
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| An Introduction to the Theory of Numbers canonical | 4 |
| Hardy and Wright, An Introduction to the Theory of Numbers | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1060235 — 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 Introduction to the Theory of Numbers Context triple: [G. H. Hardy, notableWork, An Introduction to the Theory of Numbers]
-
A.
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.
-
B.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
-
C.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
-
D.
Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
-
E.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
- 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 Introduction to the Theory of Numbers Target entity description: 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.
-
A.
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.
-
B.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
-
C.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
-
D.
Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
-
E.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ number theory textbook ⓘ textbook ⓘ |
| author |
Edward M. Wright
ⓘ
G. H. Hardy ⓘ |
| coAuthor |
Edward M. Wright
ⓘ
G. H. Hardy ⓘ |
| coversConcept |
Pell equations
ⓘ
binary quadratic forms ⓘ congruence classes ⓘ fundamental theorem of arithmetic ⓘ greatest common divisor ⓘ least common multiple ⓘ quadratic residues ⓘ |
| describedAs | classic textbook in number theory ⓘ |
| educationalLevel |
beginning graduate
ⓘ
undergraduate ⓘ |
| field | mathematics ⓘ |
| focus | elementary number theory ⓘ |
| genre |
mathematics textbook
ⓘ
non-fiction ⓘ |
| hasCoauthorRelationship |
G. H. Hardy
ⓘ
surface form:
G. H. Hardy and Edward M. Wright
|
| hasReputation | standard reference in elementary number theory ⓘ |
| intendedAudience |
mathematicians
ⓘ
students of mathematics ⓘ |
| language | English ⓘ |
| mainSubject | number theory ⓘ |
| structure | systematic development of fundamental concepts in number theory ⓘ |
| teaches |
methods of proof in number theory
ⓘ
problem-solving in number theory ⓘ |
| topic |
Diophantine approximation
ⓘ
Diophantine equations ⓘ arithmetic functions ⓘ congruences ⓘ continued fractions ⓘ distribution of primes ⓘ divisibility ⓘ prime numbers ⓘ quadratic forms ⓘ |
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 Introduction to the Theory of Numbers Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hardy and Wright, An Introduction to the Theory of Numbers