Hermann Amandus Schwarz
E827207
Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Hermann Amandus Schwarz canonical | 1 |
| Hermann Schwarz | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9843842 — 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: Hermann Amandus Schwarz Context triple: [Cauchy–Schwarz inequality, namedAfter, Hermann Amandus Schwarz]
-
A.
Rudolf Lipschitz
Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
-
B.
Alfred Clebsch
Alfred Clebsch was a 19th-century German mathematician known for his influential work in algebraic geometry and invariant theory.
-
C.
Karl Weierstrass
Karl Weierstrass was a 19th-century German mathematician renowned as a founder of modern analysis, particularly for his rigorous formulation of calculus and the theory of functions.
-
D.
Adolf Hurwitz
Adolf Hurwitz was a German mathematician known for his influential work in complex analysis, algebra, and number theory, including foundational contributions to the theory of Riemann surfaces and algebraic functions.
-
E.
Bernhard Riemann
Bernhard Riemann was a 19th-century German mathematician whose groundbreaking work in analysis, number theory, and differential geometry laid the foundations for modern mathematics and general relativity.
- 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: Hermann Amandus Schwarz Target entity description: Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
-
A.
Rudolf Lipschitz
Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
-
B.
Alfred Clebsch
Alfred Clebsch was a 19th-century German mathematician known for his influential work in algebraic geometry and invariant theory.
-
C.
Karl Weierstrass
Karl Weierstrass was a 19th-century German mathematician renowned as a founder of modern analysis, particularly for his rigorous formulation of calculus and the theory of functions.
-
D.
Adolf Hurwitz
Adolf Hurwitz was a German mathematician known for his influential work in complex analysis, algebra, and number theory, including foundational contributions to the theory of Riemann surfaces and algebraic functions.
-
E.
Bernhard Riemann
Bernhard Riemann was a 19th-century German mathematician whose groundbreaking work in analysis, number theory, and differential geometry laid the foundations for modern mathematics and general relativity.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
human
ⓘ
mathematician ⓘ |
| academicAdvisor | Karl Weierstrass NERFINISHED ⓘ |
| countryOfCitizenship |
Germany
ⓘ
Prussia ⓘ
surface form:
Kingdom of Prussia
|
| dateOfBirth | 1843-01-25 ⓘ |
| dateOfDeath | 1921-11-30 ⓘ |
| educatedAt |
Humboldt University of Berlin
ⓘ
surface form:
University of Berlin
University of Halle NERFINISHED ⓘ |
| employer |
ETH Zurich
NERFINISHED
ⓘ
University of Berlin NERFINISHED ⓘ University of Göttingen NERFINISHED ⓘ |
| familyName | Schwarz NERFINISHED ⓘ |
| fieldOfWork |
complex analysis
ⓘ
geometry ⓘ mathematical analysis ⓘ mathematics ⓘ |
| givenName |
Amandus
NERFINISHED
ⓘ
Hermann NERFINISHED ⓘ |
| hasAcademicDiscipline |
potential theory
ⓘ
theory of minimal surfaces ⓘ |
| hasNotableConcept |
Schwarz lantern
NERFINISHED
ⓘ
Schwarz minimal surface NERFINISHED ⓘ Schwarz triangle NERFINISHED ⓘ Schwarzian derivative NERFINISHED ⓘ |
| influenced |
David Hilbert
NERFINISHED
ⓘ
Felix Klein NERFINISHED ⓘ |
| influencedBy |
Augustin-Louis Cauchy
NERFINISHED
ⓘ
Karl Weierstrass NERFINISHED ⓘ |
| knownFor |
Schwarz lemma
NERFINISHED
ⓘ
Schwarz reflection principle NERFINISHED ⓘ Schwarz–Christoffel mapping NERFINISHED ⓘ co-formulation of the Cauchy–Schwarz inequality ⓘ fundamental contributions to complex analysis ⓘ |
| languageOfWorkOrName | German ⓘ |
| memberOf | Prussian Academy of Sciences ⓘ |
| nativeLanguage | German ⓘ |
| notableWork | Cauchy–Schwarz inequality NERFINISHED ⓘ |
| partOf |
19th-century German mathematicians
ⓘ
20th-century German mathematicians ⓘ |
| placeOfBirth |
Hermsdorf, Silesia
NERFINISHED
ⓘ
Prussia NERFINISHED ⓘ |
| placeOfDeath | Berlin ⓘ |
| positionHeld | professor of mathematics ⓘ |
| sexOrGender | male ⓘ |
| studentOf | Karl Weierstrass NERFINISHED ⓘ |
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: Hermann Amandus Schwarz Description of subject: Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hermann Schwarz