Fermat’s Last Theorem: The Essential Science Book Revealing 350 Years of Mathematical Secrets

Did you know that the number 26 is unique? It’s the sole integer nestled between the square number 25 (⁵) and the cube number 27 (³). This intriguing detail highlights that no other examples exist between zero and infinity.

Simon Singh’s 1997 book Fermat’s Last Theorem is an insightful exploration of mathematical proof. It delves into what proof means, how it can be achieved, and what drives mathematicians in their passionate pursuits. This book narrates a captivating quest for evidence, making it a compelling read. Given that it took 350 years for the proof to surface, it also offers an impressive historical lens on mathematics. For many, the essence of mathematics feels like abstract reasoning beyond reach. Yet, Singh’s work transports readers into this captivating realm, remaining a treasure even nearly 30 years after its publication.

Singh begins with Pythagoras, renowned for his contributions to triangle theory. Most people are familiar with the Pythagorean theorem, stating that the sum of the squares of a right triangle’s two shorter sides equals the square of the longest side (² + ^y2 = ^z2). While others used this methodology before, Singh highlights how Pythagoras distinguished himself by proving it true for all right triangles—not through trial and error, but via inarguable logic. “The quest for mathematical proof is a pursuit for absolute knowledge,” Singh asserts.

My favorite segment involves the tale of Pythagoras, as I learned he was the founder of the Secret Brotherhood of Proofs, and was fascinated by the story of Cyclone, a man denied admission, who conspired against Pythagoras.

Next, Pierre de Fermat enters the narrative. Living in 17th-century France, this judge revealed remarkable mathematical prowess. He famously proved the uniqueness of the number 26. Fermat became renowned for his “last theorem,” an elegant extension of the Pythagorean theorem. While an infinite number of integers can satisfy the Pythagorean equation, Fermat proposed that tweaking it to ⁿ + ^yn = ^zn with any integer n results in no integer solutions. In 1637, he audaciously claimed to possess “really excellent” proof, though he never documented it.

For 350 years, mathematicians chased its secrets. Singh adeptly navigates this journey, introducing a colorful cast of characters. One standout is Sophie Germain, a pioneering French mathematician who operated under a male alias. Evariste Galois, a fervent revolutionary, made significant contributions but fell in a duel. Yutaka Taniyama, a brilliant Japanese mathematician, played a key role in the eventual proof but tragically took his life.

Yet, our narrative’s hero is mathematician Andrew Wiles, who ultimately proved Fermat’s theorem true in 1994. Singh skillfully portrays Wiles, illuminating his notable achievements, even as he shunned the limelight. Through Wiles’ work—constructing a logical bridge between elliptic curves and modular forms—readers gain insight into complex mathematical realms.

However, the journey contains a tense twist: Wiles’ original proof revealed an error—a nightmare scenario. Yet, he rose from these ashes, ultimately correcting the flaws. My only critique is that this part of the narrative could have been more concise.

Although Singh’s book dates back to the 90s, its themes remain pertinent in modern mathematics. One concept tying both the book and Wiles’ proof is the Langlands program, proposed by mathematician Robert Langlands in 1967. It suggests that various mathematical areas are interconnected, and uncovering these ties could lead to breakthroughs in previously unsolvable problems. Wiles’ research provided early confirmation of the Langlands conjecture, with recent discoveries shedding further light on this vibrant area of mathematics.

Upon finishing the book, I felt as if I was wandering through a gallery of abstract art. Mathematics proofs, like art, invite quiet observation, arousing curiosity about the minds behind them, and providing glimpses beyond everyday experience. This book deserves the highest praise for evoking such profound emotions.