Fermat's Last Theorem

The most famous unsolved problem in mathematics — for 358 years.

The claim

In 1637, Pierre de Fermat scribbled a note in the margin of his copy of Diophantus’s Arithmetica: no three positive integers a, b, c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. (For n=2, this is just the Pythagorean theorem, with infinitely many solutions like 3² + 4² = 5².) Fermat added: “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.”

He almost certainly didn’t have a valid proof. But the claim launched 358 years of effort by the world’s best mathematicians.

Fermat’s death and the novel

Fermat died in 1665 — the year the plague hits London and Newton retreats to Woolsthorpe. The novel notes (page 124) the arrival of word that Fermat has died, leaving behind a collection of unproven claims scrawled in margins. For the mathematicians of the Royal Society, this is simultaneously a legacy and a provocation: Fermat claimed to have proofs for dozens of theorems but published almost none of them. His heirs published the margin notes posthumously, setting off a mathematical treasure hunt that lasted centuries.

Why it mattered

Fermat’s Last Theorem became the most famous unsolved problem in mathematics not because it was the most important but because it was the most tantalizing. The statement is simple enough for a child to understand. The proof eluded everyone — Euler, Gauss, Kummer, and hundreds of others made partial progress but couldn’t crack it. The problem drove the development of entire branches of mathematics (algebraic number theory, modular forms) as mathematicians built increasingly powerful tools to attack it.

The solution

Andrew Wiles proved Fermat’s Last Theorem in 1995, using techniques (elliptic curves, modular forms, Galois representations) that didn’t exist in Fermat’s time — confirming that whatever Fermat thought he’d found in 1637 was almost certainly wrong or incomplete.

In the novel

Fermat’s death fits the novel’s pattern of marking time through intellectual events rather than political ones. The Royal Society cares more about what Fermat left behind than about who sits on the throne. The unsolved theorem also echoes the novel’s recurring theme of problems that seem simple but resist solution — like longitude, like the relationship between mind and matter, like the question of what money actually is.