Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Abel–Ruffini theorem | Statement: [Niels Henrik Abel, knownFor, Abel–Ruffini theorem]

Target entity: Abel–Ruffini theorem
Context triple: [Niels Henrik Abel, knownFor, Abel–Ruffini theorem]

• A. 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.
• B. Noether's problem
  Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
• C. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• D. 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.
• E. Évariste Galois
  Évariste Galois was a pioneering 19th-century French mathematician whose foundational work in group theory and the theory of equations gave rise to modern Galois theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Abel–Ruffini theorem
Triple: [Niels Henrik Abel, knownFor, Abel–Ruffini theorem]

The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.

Target entity: Abel–Ruffini theorem
Target entity description: The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.

• A. 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.
• B. Noether's problem
  Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
• C. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• D. 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.
• E. Évariste Galois
  Évariste Galois was a pioneering 19th-century French mathematician whose foundational work in group theory and the theory of equations gave rise to modern Galois theory.
• F. None of above. chosen