Disquisitiones Arithmeticae
E29358
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
All labels observed (12)
How this entity was disambiguated
This entity first appeared as the object of triple T228917 — 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: Disquisitiones Arithmeticae Context triple: [Carl Friedrich Gauss, notableWork, Disquisitiones Arithmeticae]
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A.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
B.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
-
C.
The Mathematical Analysis of Logic
The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
-
D.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
-
E.
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
- 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: Disquisitiones Arithmeticae Target entity description: Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
A.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
B.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
-
C.
The Mathematical Analysis of Logic
The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
-
D.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
-
E.
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical treatise ⓘ non-fiction book ⓘ number theory work ⓘ |
| author | Carl Friedrich Gauss ⓘ |
| countryOfOrigin | Holy Roman Empire ⓘ |
| describedAs | foundational treatise on number theory ⓘ |
| discusses |
Diophantine equations
ⓘ
composition of forms ⓘ cyclotomic equations ⓘ prime numbers ⓘ quadratic non-residues ⓘ quadratic residues ⓘ representation of numbers by quadratic forms ⓘ |
| field | mathematics ⓘ |
| genre | scientific literature ⓘ |
| hasInfluencedPerson |
André Weil
ⓘ
David Hilbert ⓘ Ernst Eduard Kummer ⓘ
surface form:
Ernst Kummer
Leopold Kronecker ⓘ Richard Dedekind ⓘ |
| hasLatinTitle | Disquisitiones Arithmeticae self-link ⓘ |
| hasPart |
Book I
ⓘ
Book II ⓘ Book III ⓘ Book IV ⓘ Book V ⓘ Book VI ⓘ |
| influenced |
19th-century mathematics
ⓘ
algebraic number theory ⓘ modern number theory ⓘ |
| introducedConcept |
Legendre symbol notation refinement
ⓘ
congruence modulo n ⓘ |
| mainSubject | number theory ⓘ |
| notableFor |
classification of quadratic forms
ⓘ
development of quadratic reciprocity ⓘ introduction of congruence notation ⓘ systematic development of number theory ⓘ theory of binary quadratic forms ⓘ work on cyclotomic fields ⓘ |
| originalLanguage | Latin ⓘ |
| publicationCentury | 19th century ⓘ |
| publicationYear | 1801 ⓘ |
| titleLanguage | Latin ⓘ |
| translatedInto |
English
ⓘ
French ⓘ German ⓘ |
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: Disquisitiones Arithmeticae Description of subject: Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
Referenced by (27)
Full triples — surface form annotated when it differs from this entity's canonical label.
construction of the regular 17-gon with straightedge and compass
→
isDescribedIn
→
Disquisitiones Arithmeticae
ⓘ
this entity surface form:
Gauss's Disquisitiones Arithmeticae
subject surface form:
Gauss’s lemma (number theory)
this entity surface form:
Gauss’s Disquisitiones Arithmeticae
subject surface form:
Book I (Disquisitiones Arithmeticae)
subject surface form:
Book I (Disquisitiones Arithmeticae)
this entity surface form:
Book II (Disquisitiones Arithmeticae)
subject surface form:
Book I (Disquisitiones Arithmeticae)
this entity surface form:
Book III (Disquisitiones Arithmeticae)
subject surface form:
Book I (Disquisitiones Arithmeticae)
this entity surface form:
Book IV (Disquisitiones Arithmeticae)
subject surface form:
Book I (Disquisitiones Arithmeticae)
this entity surface form:
Book V (Disquisitiones Arithmeticae)
subject surface form:
Book I (Disquisitiones Arithmeticae)
this entity surface form:
Book VI (Disquisitiones Arithmeticae)
subject surface form:
Book I (Disquisitiones Arithmeticae)
this entity surface form:
Book VII (Disquisitiones Arithmeticae)
subject surface form:
Book III (Disquisitiones Arithmeticae)
subject surface form:
Book III (Disquisitiones Arithmeticae)
this entity surface form:
Gauss’s Disquisitiones Arithmeticae
subject surface form:
Book IV (Disquisitiones Arithmeticae)
subject surface form:
Book IV (Disquisitiones Arithmeticae)
this entity surface form:
Book III (Disquisitiones Arithmeticae)
subject surface form:
Book IV (Disquisitiones Arithmeticae)
this entity surface form:
Book V (Disquisitiones Arithmeticae)
subject surface form:
Book IV (Disquisitiones Arithmeticae)
this entity surface form:
Disquisitiones Arithmeticae, Liber Quartus
subject surface form:
Book V (Disquisitiones Arithmeticae)
subject surface form:
Book V (Disquisitiones Arithmeticae)
this entity surface form:
Book VI (Disquisitiones Arithmeticae)
subject surface form:
Book V (Disquisitiones Arithmeticae)
this entity surface form:
Book IV (Disquisitiones Arithmeticae)
subject surface form:
Book VI (Disquisitiones Arithmeticae)
subject surface form:
Book VI (Disquisitiones Arithmeticae)
this entity surface form:
Disquisitiones Arithmeticae Book I–VI
subject surface form:
Book VI (Disquisitiones Arithmeticae)
this entity surface form:
Book V (Disquisitiones Arithmeticae)
subject surface form:
Book VI (Disquisitiones Arithmeticae)
subject surface form:
Book VI (Disquisitiones Arithmeticae)
this entity surface form:
Disquisitiones Arithmeticae (English translation)