Elementary Mathematics from an Advanced Standpoint

E50329

mathematics book nonfiction book three-volume work

"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.

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All labels observed (3)

Label	Occurrences
Elementary Mathematics from an Advanced Standpoint canonical	3
Elementarmathematik vom höheren Standpunkte aus	1
Felix Klein’s Elementary Mathematics from an Advanced Standpoint series	1

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]

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
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	Elementarmathematik vom höheren Standpunkte aus ⓘ linked to: Elementary Mathematics from an Advanced Standpoint
publisher	Springer ⓘ
relatedTo	Felix Klein’s program for mathematics teacher education ⓘ Göttingen school of mathematics ⓘ linked to: Faculty of Mathematics and Computer Science of the University of Göttingen
subject	elementary mathematics ⓘ mathematics education ⓘ pedagogy of mathematics ⓘ
translatedTitle	Elementary Mathematics from an Advanced Standpoint ⓘ
volume	Arithmetic, Algebra, Analysis ⓘ Geometry ⓘ Precision and Approximation ⓘ

How these facts were elicited

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Felix Klein → notableWork → Elementary Mathematics from an Advanced Standpoint ⓘ

Elementary Mathematics from an Advanced Standpoint → originalTitle → Elementarmathematik vom höheren Standpunkte aus ⓘ

linked to: Elementary Mathematics from an Advanced Standpoint

Elementary Mathematics from an Advanced Standpoint → translatedTitle → Elementary Mathematics from an Advanced Standpoint ⓘ

Precision and Approximation → partOfSeries → Elementary Mathematics from an Advanced Standpoint ⓘ

Precision and Approximation → isVolumeOf → Felix Klein’s Elementary Mathematics from an Advanced Standpoint series ⓘ