Fermat's Last Theorem
E146188
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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Fermat’s Last Theorem | 14 |
| Fermat's Last Theorem canonical | 11 |
| Fermat equation x^n + y^n = z^n | 1 |
| Fermat problem | 1 |
| Fermat's conjecture | 1 |
| Fermat's marginal note on Arithmetica | 1 |
| Pierre de Fermat’s last theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1281480 — 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: 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.
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
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf | mathematical theorem ⓘ |
| allowsSolutionsFor |
n = 1
ⓘ
n = 2 ⓘ |
| alsoKnownAs |
Fermat's conjecture
ⓘ
linked to:
Fermat's Last Theorem
|
| assertsNonexistenceOf | nontrivial integer solutions for x^n + y^n = z^n with n > 2 ⓘ |
| classification | Diophantine equation problem ⓘ |
| conditionOnExponent | n is an integer greater than 2 ⓘ |
| conjectureDateApproximate | circa 1637 ⓘ |
| conjecturedBy | Pierre de Fermat ⓘ |
| correctedProofPublicationYear | 1995 ⓘ |
| culturalImpact | one of the most famous problems in mathematics ⓘ |
| difficulty | famously difficult problem in mathematics ⓘ |
| domainOfVariables |
integers
ⓘ
whole numbers ⓘ |
| equationForm | x^n + y^n = z^n ⓘ |
| equivalentTo | nonexistence of certain semistable elliptic curves over the rationals ⓘ |
| exponent | n ⓘ |
| field | number theory ⓘ |
| historicalStatus | last of Fermat's conjectures to be proved ⓘ |
| influencedField |
algebraic number theory
ⓘ
arithmetic geometry ⓘ modular forms theory ⓘ |
| languageOfOriginalNote | Latin ⓘ |
| namedAfter | Pierre de Fermat ⓘ |
| openProblemDuration | over 350 years ⓘ |
| originalClaim | Fermat claimed to have a marvelous proof too large to fit in the margin ⓘ |
| originalSource | margin note in Fermat's copy of Diophantus's Arithmetica ⓘ |
| proofAnnouncementYear | 1993 ⓘ |
| proofCompletedWith | Richard Taylor ⓘ |
| proofPublishedIn | Annals of Mathematics ⓘ |
| proofRecognition | contributed to Andrew Wiles receiving the Abel Prize in 2016 ⓘ |
| proofStrategy | proof of a special case of the Taniyama–Shimura–Weil conjecture ⓘ |
| proofUses |
Galois representations
ⓘ
elliptic curves ⓘ modular forms ⓘ |
| provedBy | Andrew Wiles ⓘ |
| relatedConjecture |
Taniyama–Shimura–Weil conjecture
ⓘ
modularity theorem ⓘ |
| relatedProblem |
Beal conjecture
ⓘ
abc conjecture ⓘ |
| solutionTypeExcluded | nonzero integer solutions for n > 2 ⓘ |
| specialCaseFor | Pythagorean triples when n = 2 ⓘ |
| statement | There are no three positive integers x, y, z that satisfy x^n + y^n = z^n for any integer n > 2 ⓘ |
| statusAfter1990s | proved theorem ⓘ |
| statusBefore1990s | unproved conjecture ⓘ |
| variable |
x
ⓘ
y ⓘ z ⓘ |
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: Fermat's Last Theorem Description of subject: 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.
Referenced by (30)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem
linked to: Fermat's Last Theorem