The Lawyer Who Loved Numbers

In the small French town of Beaumont-de-Lomagne, nestled in the rolling hills of southern France, a child was born on August 17, 1601, who would unknowingly set in motion one of mathematics’ greatest challenges. Pierre de Fermat entered the world as the privileged son of a wealthy leather merchant and local government official – what we might today call a “silver spoon” child of 17th century France.

Unlike most children of his era, young Fermat received private tutoring at home, displaying equal aptitude for both humanities and sciences. When university called, he dutifully followed his father’s advice to study law – the most respectable profession for French gentlemen at the time. The family’s influence and wealth secured him positions as both a lawyer and councillor in the Toulouse parliament, where he would eventually rise to become the king’s advocate in the local court.

Fermat’s official biography would end here as just another successful civil servant, were it not for his extraordinary after-hours passion. Mathematics became his secret love, a private intellectual playground where this government official would make discoveries that professional mathematicians would spend centuries trying to unravel.

The Infamous Margin Note

The year 1637 marked the birth of mathematical legend. While reading an ancient Greek text – Diophantus’s Arithmetica – in his Toulouse study, Fermat encountered a problem about Pythagorean triples. These are sets of three positive integers (like 3, 4, 5) that satisfy the equation x² + y² = z².

In a moment of either brilliance or mischief, Fermat scribbled in the book’s margin that no such solutions exist when the exponent is greater than 2. His notorious note claimed: “I have discovered a truly marvelous proof of this proposition, which this margin is too narrow to contain.”

This casual annotation would become mathematics’ most tantalizing unsolved problem. The proposition, later known as Fermat’s Last Theorem, states simply: For all integers n > 2, the equation xⁿ + yⁿ = zⁿ has no positive integer solutions.

Fermat never published his supposed proof. When his son later collected and published his father’s notes, mathematicians across Europe found themselves staring at this provocative claim – a mathematical gauntlet thrown down for generations to come.

Centuries of Frustration

The first serious attempt to prove Fermat’s claim came 133 years later from Leonhard Euler, the prolific Swiss mathematician. In 1770, Euler successfully proved the case for n=3, but his method couldn’t be generalized. The mathematical community soon realized Fermat’s Last Theorem wasn’t just another problem – it was a mountain that resisted all known climbing techniques.

The 19th century saw incremental progress amid bitter competition. French mathematician Sophie Germain, facing gender discrimination, made significant contributions by proving special cases where n and 2n+1 are both prime numbers. In 1825, Dirichlet and Legendre independently proved the n=5 case. Then in 1847, a dramatic episode unfolded when two prominent mathematicians, Lamé and Cauchy, both announced they had complete proofs – only to have their work demolished by German mathematician Ernst Kummer, who showed their approaches were fundamentally flawed.

Kummer delivered an even more devastating blow: contemporary mathematical tools were insufficient to prove the theorem. This verdict plunged Fermat’s Last Theorem into mathematical exile for nearly 50 years.

The Prize That Changed Everything

In 1908, German industrialist Paul Wolfskehl injected new life into the quest. His motivation was extraordinary: Fermat’s theorem had literally saved his life. After a romantic rejection, the despondent Wolfskehl planned suicide at midnight. While waiting for the appointed hour, he idly read about Fermat’s Last Theorem – and became so engrossed that dawn arrived before he could pull the trigger.

Grateful for this unexpected reprieve, Wolfskehl established a 100,000-mark prize (worth over £1 million today) for whoever could prove the theorem. The reward attracted both serious mathematicians and amateur enthusiasts, though the problem remained stubbornly resistant.

The 20th century brought new tools – computers could now verify the theorem for specific exponents up to the millions – but no general proof emerged. By the 1960s, many mathematicians considered Fermat’s Last Theorem fundamentally unprovable with current mathematics. The Wolfskehl Prize’s 2007 deadline loomed with no solution in sight.

The Boy Who Would Conquer Fermat

In 1963, a pivotal moment occurred in a Cambridge library. Ten-year-old Andrew Wiles stumbled upon a book about Fermat’s Last Theorem and became mesmerized. “It looked so simple, and yet all the great mathematicians in history couldn’t solve it,” Wiles later recalled. “I knew from that moment I would never let it go.”

True to his childhood vow, Wiles dedicated his career to number theory. By 1986, as a Princeton professor, he made a radical decision: to work secretly on Fermat’s Last Theorem, abandoning all other projects. He estimated needing a decade of solitary focus.

Seven painstaking years later, in June 1993, Wiles delivered a series of lectures at Cambridge’s Isaac Newton Institute. On the final day, after filling multiple blackboards with equations, he casually concluded: “I think I’ll stop here.” The audience erupted – they recognized they’d just witnessed history. Newspapers worldwide heralded the 300-year-old problem’s solution.

But mathematical rigor demanded verification. During peer review, a subtle flaw emerged in Wiles’s proof. For nine agonizing months, he struggled to repair it. Just as he prepared to concede defeat, on September 19, 1994, inspiration struck: combining two previously unrelated approaches could patch the gap. The completed proof, submitted that October, withstood all scrutiny.

The Legacy of a Mathematical Grail

Wiles’s 1997 acceptance of the Wolfskehl Prize (just before the German mark’s retirement) marked the formal end of a 358-year quest. His proof, running over 100 pages and employing cutting-edge 20th century mathematics, demonstrated that Fermat’s original claim was correct – though almost certainly beyond 17th century techniques.

The theorem’s impact transcends its elegant statement. The quest to solve it spurred development of entirely new mathematical fields, including algebraic number theory and modular forms. Wiles’s proof itself bridged two seemingly unrelated mathematical worlds – the Taniyama-Shimura conjecture and Fermat’s equation – opening new research avenues.

Culturally, Fermat’s Last Theorem became mathematics’ most famous problem, appearing in everything from Star Trek episodes to literary works. It symbolizes both mathematics’ deceptive simplicity and its profound depth – how a schoolchild can understand a problem that resisted centuries of genius.

As for Fermat himself? Historians doubt he actually possessed a valid proof. More likely, the clever lawyer recognized his margin note would ensure immortality – making Pierre de Fermat, the “amateur mathematician,” one of history’s most influential number theorists through a single provocative sentence. His legacy reminds us that great discoveries often begin not with answers, but with questions that refuse to let go of the human imagination.