Lindemann–Weierstrass theorem precursor
E113531
The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Lindemann–Weierstrass theorem | 2 |
| Lindemann–Weierstrass theorem precursor canonical | 1 |
| Sur la fonction exponentielle (proof of transcendence of e) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T964267 — 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: Lindemann–Weierstrass theorem precursor Context triple: [Ferdinand von Lindemann, knownFor, Lindemann–Weierstrass theorem precursor]
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A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
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B.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
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C.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
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D.
Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
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E.
Weierstrass factorization theorem
The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
- 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: Lindemann–Weierstrass theorem precursor Target entity description: The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
-
C.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
-
D.
Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
-
E.
Weierstrass factorization theorem
The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
- F. None of above. chosen
Statements (11)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in transcendental number theory ⓘ |
| areaOfApplication | theory of transcendental numbers ⓘ |
| author | Ferdinand von Lindemann ⓘ |
| consequence | development of the full Lindemann–Weierstrass theorem ⓘ |
| field | transcendental number theory ⓘ |
| influenced | later work of Karl Weierstrass on exponentials of algebraic numbers ⓘ |
| namedAfter | Ferdinand von Lindemann ⓘ |
| precedes |
Lindemann–Weierstrass theorem
ⓘ
linked to:
Lindemann–Weierstrass theorem precursor
|
| relatedTo |
Lindemann–Weierstrass theorem
ⓘ
linked to:
Lindemann–Weierstrass theorem precursor
|
| topic | algebraic independence of exponentials of algebraic numbers ⓘ |
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: Lindemann–Weierstrass theorem precursor Description of subject: The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Lindemann–Weierstrass theorem precursor
linked to: Lindemann–Weierstrass theorem precursor
linked to: Lindemann–Weierstrass theorem precursor