Narrator: In 1963, a ten-year-old boy named Andrew Wiles was browsing his local library in Cambridge, England. He stumbled upon a book about a single mathematical problem. The problem itself was astonishingly simple, an equation he could understand with his limited schoolboy math: xⁿ + yⁿ = zⁿ. A 17th-century French mathematician named Pierre de Fermat had claimed that for any whole number 'n' greater than 2, this equation had no whole number solutions. Fermat had scribbled a note in the margin of a book, claiming he had a "marvelous proof" but that the margin was too small to contain it. For over 300 years, the world's greatest minds had tried and failed to find this proof. The boy was captivated. He knew from that moment that he would never let it go; he had to solve it. This childhood dream would set in motion one of the most remarkable intellectual journeys of the 20th century. Simon Singh's book, Fermat's Last Theorem, chronicles this epic 358-year quest, revealing a story not just of numbers, but of human obsession, brilliant creativity, and profound discovery.

Narrator: The story begins with Pierre de Fermat, a 17th-century French civil servant and judge. Mathematics was not his profession but his passion, earning him the title "the prince of amateurs." He was a reclusive genius who rarely published his work, preferring to taunt his contemporaries by sending them theorems without their proofs, challenging them to match his intellect. His greatest challenge came from a note he scribbled around 1637 in his copy of the ancient Greek text Arithmetica. Next to a problem about splitting a square number into two other squares—the basis of Pythagoras's theorem—Fermat wrote his famous assertion. He claimed that while squares could be split (3² + 4² = 5²), the same was impossible for cubes, fourth powers, or any higher power. He then added the tantalizing line: "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain." He never wrote it down anywhere else. After his death, his son published his notes, and this marginal comment became Fermat's Last Theorem. It was a riddle that was both infuriatingly simple to state and, as it turned out, impossibly difficult to prove, launching a mathematical odyssey that would span centuries.

Narrator: For the next two centuries, the theorem resisted the efforts of the world's most brilliant mathematicians. The first significant breakthrough came from the Swiss prodigy Leonhard Euler in the 18th century. A man of almost superhuman calculating ability, Euler managed to prove the theorem was true for n=3 (cubes). To do so, he had to invent a new type of number—imaginary numbers—demonstrating that solving Fermat's riddle required creating entirely new fields of mathematics.

Perhaps the most remarkable early contributor was Sophie Germain, a French woman living in the early 19th century when women were barred from formal education. Undeterred, she assumed the identity of a male student, "Monsieur Le Blanc," to obtain lecture notes from the École Polytechnique in Paris and correspond with the legendary mathematician Carl Friedrich Gauss. Fearing she wouldn't be taken seriously as a woman, she worked in secret, developing a grand strategy that provided a proof for a whole class of prime numbers, a major leap forward. Her story highlights the immense human dedication the problem inspired, proving that the quest for its solution was a powerful force that transcended societal barriers.

Narrator: By the early 20th century, professional mathematicians had largely abandoned Fermat's Last Theorem, viewing it as an isolated and likely unsolvable puzzle. Interest was unexpectedly reignited by a German industrialist and amateur mathematician named Paul Wolfskehl. The story goes that Wolfskehl, despondent over a failed romance, had decided to end his life. He meticulously planned his suicide, setting the time for midnight. With a few hours to spare, he went to the library and began reading about the latest failure to prove Fermat's Last Theorem. He became so engrossed in checking the logic that he lost all track of time. By the time he found and fixed a small flaw in the reasoning, dawn had broken, and his appointed time for death had passed. Mathematics had saved his life. In his will, Wolfskehl left a fortune of 100,000 marks—a huge sum in 1908—to whoever could finally prove the theorem. The Wolfskehl Prize transformed the problem, attracting thousands of amateur proofs and ensuring that Fermat's riddle would never again be forgotten.

Narrator: The ultimate key to solving Fermat's Last Theorem came from a completely unexpected direction. In the 1950s, two young Japanese mathematicians, Yutaka Taniyama and Goro Shimura, proposed a radical idea. They were studying two seemingly unrelated areas of mathematics: elliptic curves (a type of equation) and modular forms (a strange, highly symmetric type of function). They conjectured that every elliptic curve was secretly a modular form in disguise. This idea, which became known as the Taniyama-Shimura conjecture, was so outlandish that it was initially ignored. It was like suggesting a fundamental link between bridges and oranges.

Tragically, Taniyama, a brilliant but troubled mind, took his own life in 1958, never seeing the impact of his work. Decades later, in 1984, a German mathematician named Gerhard Frey made a stunning connection. He showed that if Fermat's Last Theorem were false, it would create a bizarre, hypothetical elliptic curve—one so strange it could never be a modular form. This meant that if the Taniyama-Shimura conjecture were true (that all elliptic curves are modular), then Fermat's Last Theorem must also be true. A mathematician named Ken Ribet later proved Frey's link was solid. Suddenly, the 350-year-old riddle was no longer an isolated problem. It was now part of a grand, unified theory of mathematics. Proving the Taniyama-Shimura conjecture would automatically prove Fermat's Last Theorem.

Narrator: When Andrew Wiles—the boy from the library, now a professor at Princeton—heard that the link was proven, he was electrified. His childhood dream was no longer a fringe pursuit; it was now connected to one of the most important conjectures in modern mathematics. In 1986, he made a momentous decision. He would dedicate himself entirely to proving the Taniyama-Shimura conjecture, and he would do it in complete secrecy. For the next seven years, he worked in the attic of his home, telling no one but his wife what he was truly doing. He knew that any hint of his work would attract immense scrutiny and competition. He described the process of mathematical research as entering a dark, unfurnished mansion. You stumble around, bumping into furniture, and only after months of mapping it out in the dark do you find the light switch. Then, you move into the next dark room. For seven years, Wiles moved from room to room, slowly illuminating a path through this vast, uncharted mansion of mathematics.

Narrator: In June 1993, at a conference in Cambridge, Andrew Wiles announced to a stunned audience that he had completed his proof. The news made global headlines. After 358 years, the riddle was solved. But the story wasn't over. As experts began to referee his 200-page manuscript, a tiny but critical flaw was discovered in one part of his argument. The entire proof was in jeopardy. Wiles was devastated. He once again retreated into isolation, this time joined by his former student Richard Taylor, to try and fix the gap. For over a year, they struggled. Every attempt to patch the hole seemed to fail. Wiles was on the verge of admitting defeat.

Then, on the morning of September 19, 1994, as he was staring at the problem one last time, he had a moment of incredible revelation. He realized that the very method that had failed could be combined with a different technique he had abandoned years earlier. The two approaches, one failed and one incomplete, fit together perfectly to solve the problem. It was, he said, "so indescribably beautiful; it was so simple and so elegant." The corrected proof was published in 1995, and the quest was finally, truly over.

Narrator: The story of Fermat's Last Theorem is far more than a tale of a mathematical puzzle. As Simon Singh masterfully shows, it is a testament to the power of a single, elegant idea to drive progress across centuries. The pursuit of this seemingly abstract problem led to the creation of entire new branches of mathematics, ultimately helping to build a grand, unified theory that connected disparate worlds of thought. It reveals that the journey of discovery, with all its failures, rivalries, and moments of brilliant insight, is as important as the destination itself.

In the end, this is a profoundly human story. It reminds us that even in the purest realms of logic and reason, the driving forces are passion, curiosity, and the unwavering dedication to a childhood dream. It leaves us to wonder: what other simple, beautiful riddles are still out there, waiting in the margins for the next Andrew Wiles to stumble upon them?