fermat's last theorem
C2 (Very Low Frequency)Formal, Academic, Technical
Definition
Meaning
A famous unsolved conjecture in number theory, proposed by Pierre de Fermat in 1637, stating that no three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.
A historical problem in mathematics that became one of the most famous and long-standing unsolved problems, acting as a symbol of mathematical mystery and intellectual challenge until it was proven by Andrew Wiles in 1994. It also represents the concept of a simple conjecture with an extraordinarily difficult proof.
Linguistics
Semantic Notes
It is a proper noun referring to a specific historical mathematical statement. It is often cited as a paradigm case of a mathematical conjecture that is simple to state but immensely difficult to prove.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling of 'theorem' is consistent. Potential minor variation in pronunciation of 'Fermat' (/ˈfɜː.mɑː/ vs /fɜːrˈmɑː/).
Connotations
Identical connotations in both varieties: intellectual achievement, historical mystery, mathematical rigour.
Frequency
Equally low frequency in both dialects, confined to academic, historical, and popular science contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
[Subject] proves/disproves Fermat's Last Theorem.The proof of Fermat's Last Theorem [verb]...Fermat's Last Theorem states/asserts that...They worked on Fermat's Last Theorem for years.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “A Fermat-like problem (a deceptively simple but intractable challenge)”
- “The Last Theorem's shadow (an imposing, unresolved intellectual obstacle)”
Usage
Context Usage
Business
Extremely rare. Could be used metaphorically: 'Solving this supply chain issue is our Fermat's Last Theorem.'
Academic
Primary context. Used in history of mathematics, number theory, and popular science writing to discuss the problem, its proof, and its historical significance.
Everyday
Very rare. Might appear in quizzes, documentaries, or general knowledge discussions about famous puzzles.
Technical
Specific context in mathematics. Refers precisely to the conjecture and the methods (e.g., modularity theorem) used in its proof by Andrew Wiles.
Examples
By Part of Speech
verb
British English
- Mathematicians have sought to Fermat's-Last-Theorem the problem for centuries. (non-standard, metaphorical)
American English
- He's trying to Fermat this puzzle, but it's too complex. (non-standard, metaphorical)
adverb
British English
- The problem remained unsolved, Fermat's-Last-Theorem-like, for decades.
American English
- The code was Fermat's-Last-Theorem difficult to crack.
adjective
British English
- It was a Fermat's-Last-Theorem-level challenge for the research team.
American English
- The negotiations took on a Fermat's Last Theorem complexity.
Examples
By CEFR Level
- Fermat's Last Theorem is a famous maths problem.
- The story of Fermat's Last Theorem is very interesting because it took 357 years to solve.
- Andrew Wiles finally proved Fermat's Last Theorem in 1994, a monumental achievement in mathematics.
- Wiles's proof of Fermat's Last Theorem, which leveraged the modularity theorem for elliptic curves, resolved one of history's most enduring enigmas in number theory.
Learning
Memory Aids
Mnemonic
Fermat Left a Tricky Theorem: For n>2, aⁿ+bⁿ=cⁿ has No answer.
Conceptual Metaphor
A MOUNTAIN PEAK (an ultimate challenge to be conquered), A HOLY GRAIL (a long-sought, almost mythical object of intellectual pursuit), A LOCKED DOOR (something simple in appearance but requiring a unique key to open).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid literal translation of 'Last' as 'последний' in a temporal sense ('final one he made'). It means 'final' in the sense of 'ultimate, remaining unproven'.
- It is a 'теорема' (theorem) in English, but was a 'гипотеза' (conjecture/hypothesis) until 1994. This historical shift can cause confusion.
Common Mistakes
- Incorrect: 'Fermat Last Theorem' (missing possessive 's).
- Incorrect: 'Fermat's Last Theory' (confusing 'theorem' with 'theory').
- Incorrect: Using it as a common noun, e.g., 'a fermat's last theorem' (it is a unique proper noun).
Practice
Quiz
What does Fermat's Last Theorem state?
FAQ
Frequently Asked Questions
British mathematician Andrew Wiles, with assistance from his former student Richard Taylor, finally proved the theorem in 1994 after seven years of secret work.
It was the last of Fermat's asserted theorems (noted in the margin of his copy of Diophantus' Arithmetica) to remain without proof, thus the 'last' one to be resolved.
Most scholars believe Fermat did not have a valid general proof for all n>2. His marginal note claimed a 'truly marvelous proof' but the space was too small to contain it. He likely only had a proof for a specific case (e.g., n=4).
It required the development of entirely new mathematical fields and connections, particularly between elliptic curves and modular forms (the Taniyama–Shimura–Weil conjecture). The tools from Fermat's time were insufficient for a general proof.