A 358-year journey from conjecture to computer-verified proof
Anthropic Research
2025
In 1637, Pierre de Fermat scribbled a note in the margin of his copy of Arithmetica, claiming to have a "truly marvelous proof" — but never wrote it down. For over three centuries, this became mathematics' most famous unsolved problem.
No three positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for n > 2
Fermat's Last Theorem
For n > 2:
aⁿ + bⁿ ≠ cⁿ
for any positive integers a, b, cMarginal claim of proof, never published
Key connection to elliptic curves discovered
Andrew Wiles completes the first correct proof
Complete formal proof verified by proof assistants
From human understanding to machine-verified certainty
Every step checked by proof assistants like Lean, ensuring no gaps or errors
Every assumption explicitly stated, every inference formally validated
Creates an enduring, checkable proof that transcends human limitations
Formalized results become reusable components for future mathematics
Convert Wiles' proof into the Lean proof assistant language
Formalize underlying theories: elliptic curves, modular forms, Galois theory
Computer checks every logical inference automatically
Create comprehensive formalized mathematics for future research
Irrefutable certainty for one of history's most complex proofs
Demonstrates that modern tools can handle the most sophisticated mathematics
Formalized foundations enable faster progress in number theory
Marks a new era where computers and mathematicians collaborate
From Fermat's marginal note to computer-verified certainty — mathematics evolves