Hermann Amandus Schwarz

E827207

human mathematician

Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.

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All labels observed (2)

Label	Occurrences
Hermann Amandus Schwarz canonical	1
Hermann Schwarz	1

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.

Cauchy–Schwarz inequality → namedAfter → Hermann Amandus Schwarz ⓘ

Schwarz lemma → namedAfter → Hermann Amandus Schwarz ⓘ

this entity surface form: Hermann Schwarz