Pierre de Fermat was a full-time lawyer and part-time mathematician who scribbled one of history’s most tantalizing notes in the margin of a book: “I have discovered a truly marvelous proof of this theorem, which this margin is too narrow to contain.” That marginal note — Fermat’s Last Theorem — took 358 years and the full machinery of modern mathematics to prove. The amateur who posed the problem could not have imagined the revolution required to solve it.

This episode traces Fermat from his legal career in Toulouse through his correspondence that co-founded probability theory, the number theory that made him immortal, and the marginal note that obsessed mathematicians for over three centuries.

• Fermat’s career as a magistrate in Toulouse and his treatment of mathematics as a gentleman’s hobby
• The correspondence with Pascal that founded probability theory
• Fermat’s Last Theorem — the marginal note and the 358-year quest to prove it
• Andrew Wiles’s 1995 proof and why Fermat almost certainly did not have the proof he claimed