Cubes Quote by Pierre de Fermat s
““It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain. [Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.]””
About This Quote
Source Letter: Correspondence with a friend, 1637
Fermat claimed a proof exists for the impossibility of expressing higher powers as sums of two like powers, but he never wrote it down.
In simple terms: No proof shown for higher power sums.
Key Takeaway
Recognize limits of known proofs.
Themes
mathematics
number theory
impossibility
Mood
curious
analytical
Type
historical
philosophical
When to use this quote
- academic research
- teaching
- problem solving
- historical analysis
Key Concepts
Fermat's Last Theorem
proof gaps
Questions to Reflect On
- What does the missing proof suggest about mathematical discovery?
- How do we handle claims without evidence?
A Different Perspective
Proof may not exist; proof could be lost.
