Elementary Mathematics from an Advanced Standpoint
E50329
"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.
All labels observed (3)
How this entity was disambiguated
This entity first appeared as the object of triple T397948 — 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: Elementary Mathematics from an Advanced Standpoint Context triple: [Felix Klein, notableWork, Elementary Mathematics from an Advanced Standpoint]
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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.
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.
-
C.
Principles of Mathematics
Principles of Mathematics is Bertrand Russell’s foundational work in mathematical logic and the philosophy of mathematics, arguing that mathematics can be derived from purely logical principles.
-
D.
Prince of Mathematicians
Prince of Mathematicians is the honorific title given to Carl Friedrich Gauss, reflecting his status as one of the greatest and most influential mathematicians in history.
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E.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
- 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: Elementary Mathematics from an Advanced Standpoint Target entity description: "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.
-
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.
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.
-
C.
Principles of Mathematics
Principles of Mathematics is Bertrand Russell’s foundational work in mathematical logic and the philosophy of mathematics, arguing that mathematics can be derived from purely logical principles.
-
D.
Prince of Mathematicians
Prince of Mathematicians is the honorific title given to Carl Friedrich Gauss, reflecting his status as one of the greatest and most influential mathematicians in history.
-
E.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
nonfiction book ⓘ three-volume work ⓘ |
| aimsTo |
bridge gap between school mathematics and university mathematics
ⓘ
improve teacher understanding of mathematics ⓘ |
| approach |
advanced theoretical treatment of elementary topics
ⓘ
integration of history, pedagogy, and rigorous mathematics ⓘ |
| author | Felix Klein ⓘ |
| countryOfOrigin | Germany ⓘ |
| covers |
algebra
ⓘ
analysis ⓘ approximation methods ⓘ arithmetic ⓘ foundations of calculus ⓘ geometry ⓘ historical development of mathematical concepts ⓘ projective geometry aspects of school geometry ⓘ |
| emphasizes |
conceptual understanding over rote computation
ⓘ
historical and genetic method in teaching ⓘ structural viewpoint on elementary topics ⓘ |
| firstPublicationCentury | 20th century ⓘ |
| focusesOn |
connection between school mathematics and higher mathematics
ⓘ
reexamination of school mathematics ⓘ rigorous foundations of elementary topics ⓘ |
| genre |
mathematics textbook
ⓘ
pedagogical treatise ⓘ |
| hasInfluenced |
20th-century mathematics education
ⓘ
teacher training curricula ⓘ |
| hasTranslation | English ⓘ |
| intendedAudience |
mathematicians interested in education
ⓘ
mathematics teachers ⓘ prospective mathematics teachers ⓘ |
| language | German ⓘ |
| notableFor |
influence on modern views of mathematical rigor in schools
ⓘ
systematic analysis of school mathematics from higher standpoint ⓘ |
| numberOfVolumes | 3 ⓘ |
| originalTitle |
Elementary Mathematics from an Advanced Standpoint
self-linksurface differs
ⓘ
surface form:
Elementarmathematik vom höheren Standpunkte aus
|
| publisher | Springer ⓘ |
| relatedTo |
Felix Klein’s program for mathematics teacher education
ⓘ
Faculty of Mathematics and Computer Science of the University of Göttingen ⓘ
surface form:
Göttingen school of mathematics
|
| subject |
elementary mathematics
ⓘ
mathematics education ⓘ pedagogy of mathematics ⓘ |
| translatedTitle | Elementary Mathematics from an Advanced Standpoint self-link ⓘ |
| volume |
Arithmetic, Algebra, Analysis
ⓘ
Geometry ⓘ Precision and Approximation ⓘ |
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: Elementary Mathematics from an Advanced Standpoint Description of subject: "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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
Elementary Mathematics from an Advanced Standpoint
→
originalTitle
→
Elementary Mathematics from an Advanced Standpoint
self-linksurface differs
ⓘ
this entity surface form:
Elementarmathematik vom höheren Standpunkte aus
Elementary Mathematics from an Advanced Standpoint
→
translatedTitle
→
Elementary Mathematics from an Advanced Standpoint
self-link
ⓘ
this entity surface form:
Felix Klein’s Elementary Mathematics from an Advanced Standpoint series