Triple

T1281480
Position Surface form Disambiguated ID Type / Status
Subject Pierre de Fermat E27335 entity
Predicate notableWork P4 FINISHED
Object Fermat's Last Theorem
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
E146188 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
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).
Input
Phrase: Fermat's Last Theorem | Statement: [Pierre de Fermat, notableWork, Fermat's Last Theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fermat's Last Theorem
Context triple: [Pierre de Fermat, notableWork, Fermat's Last Theorem]
  • A. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • B. Millennium Prize Problem
    The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
  • C. 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.
  • D. 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.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
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]"
Input
Entity: Fermat's Last Theorem
Triple: [Pierre de Fermat, notableWork, Fermat's Last Theorem]
Generated description
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fermat's Last Theorem
Target entity description: Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • A. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • B. Millennium Prize Problem
    The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
  • C. 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.
  • D. 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.
  • E. 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.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69a496d3710c8190955dee8bc0dacb50 completed March 1, 2026, 7:43 p.m.
NER Named-entity recognition batch_69a4c0b317788190a1672b5ee422a049 completed March 1, 2026, 10:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69aca2fb746881909ac7a8dd672fc939 completed March 7, 2026, 10:13 p.m.
NEDg Description generation batch_69aca3752a3c81908bd6d9744ad5f5a2 completed March 7, 2026, 10:15 p.m.
NED2 Entity disambiguation (via description) batch_69aca3e44bf481908c5726adddc4b428 completed March 7, 2026, 10:17 p.m.
Created at: March 1, 2026, 7:50 p.m.