Fermat's Last Theorem
To read it is to realize that there is a world of beauty and intellectual challenge that is denied to 99.99 per cent of us who are not high-level mathematicians. - The Times
The Enigma of Numbers
Fermat's Last Theorem. A deceptively simple statement that has consumed the minds of mathematicians for centuries.
It whispers of cubes that can't be cubed, of fourth powers defying addition, and stands as a testament to the captivating allure of numbers.
But the story behind the theorem is as rich as the mathematics itself, a tale of a brilliant mind, a posthumous challenge, and an intellectual quest that spanned generations.
Pierre de Fermat, the man who ignited this mathematical firestorm, was a 17th-century French lawyer with a hidden passion.
By day, he argued cases in courtrooms, but by night, he delved into the enchanting world of numbers. A true amateur mathematician, Fermat made significant contributions to number theory, probability, and analytic geometry.
Yet, his most famous work wasn't a published treatise, but a marginal note scribbled in a book.
What was this firestorm?
In 1637, Fermat supposedly jotted down his theorem in the margins of Diophantus' Arithmetica, an ancient Greek text on number theory.
Pythagoras’s famous theorem stated in schools says, “Sum of squares of sides of every right angled triangle is equal to square of the hypotenuse.” Otherwise recognized as -
Fermat was contemplating a variant of Pythagoras’s creation -
Soon he said that such equation is not possible for any value greater than two, and this small statement lit up a firestorm, which I’ll explain briefly below!
The note, famously translated as, "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers," laid down a gauntlet for mathematicians to come.
Fermat claimed to have a "truly remarkable proof," but the margin, as he lamented, was simply "too small to contain it."
It was as if a challenge posed by Ferma,t whether anyone has capabilities of matching his intellectual brilliance.
This was the spark that ignited a mathematical wildfire. For centuries, the theorem remained unproven, a taunting challenge from beyond the grave.
Mathematicians chipped away, proving the theorem true for specific values of n, but the general case remained elusive. Leonhard Euler, the mathematical giant, devoted years to the problem, ultimately falling short.
The quest for a complete proof became an obsession for some, a lifelong pursuit.
…and the Mathematician Who’d Haunt Them
Then, in 1994, the mathematical world held its breath. Andrew Wiles, a brilliant British mathematician, announced a proof of Fermat's Last Theorem - After 358 years!
The journey, however, was far from straightforward. Wiles had spent seven years in seclusion, working on a revolutionary approach that drew upon advanced concepts from number theory and elliptic curves.
The initial announcement was met with euphoria, but scrutiny revealed errors. After a year of intense work, Wiles plugged the holes, and the mathematical community finally had its long-sought prize.
Fermat's Last Theorem, though beautiful in its simplicity, became a cornerstone of modern mathematics. Wiles' proof, a testament to human ingenuity, opened new avenues of research.
But beyond the technicalities, the story is a reminder of the enduring power of mathematics, its ability to challenge, frustrate, and ultimately, lead us to a deeper understanding of the universe and the language of numbers.
The theorem, once a solitary note in a margin, has become a legend, a testament to the human spirit's relentless pursuit of the unknown.
Amazing story right? If you want to know more, read the book “Fermat’s Last Theorem,” written by Simon Singh:
I’ve written this article in respect of the beauty of mathematics and mathematicians, and the amazing world around us.
The way mathematics, creation of human being is able to describe universe so aptly; the fact that it works is simply jaw-dropping for me.
Thanks for reading all the way dear folks. Subscribe if you’d love to have these types of articles every day!