Pierre de Fermat blessed the world with a problem that took 358 years to be solved. Often called the founder of the modern theory of numbers, Pierre de Fermat was born in Beaumont-de-Lomagne, France. Although he was a lawyer by profession and just an amateur mathematician, Fermat was one of the two leading mathematicians of the first half of the 17th century. In this article, we will learn about Fermat’s last theorem, which troubled the mathematical community for 358 years.
What is Fermat’s last theorem?
Fermat’s last theorem states that no three positive integers p, q, and r satisfy the equation:
pª + qª = rª
For any integer value of a greater than 2. Since ancient times, the cases a = 1 and a = 2 have been known to have infinite solutions. a = 2 becomes the Pythagoras theorem of geometry.
Story behind Fermat’s last theorem
Fermat always refused to publish his work. So, his friends and loved ones always feared that his work would soon be forgotten unless they did something about it. Finally, his son Samuel thought of an idea. He started collecting Fermat’s letters and other mathematical papers. He also found his comments written in books with the object of publishing his father’s mathematical ideas.
In this way, the famous ‘Last Theorem’ was published. Samuel found it written as a marginal note in his father’s copy of Diophantus’s Arithmetica. This also included a note by Fermat which says:
“I have discovered a truly remarkable proof which this margin is too small to contain.” Hence, only the theorem was found by Samuel. The proof of the theorem was never discovered by anyone back then.
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Attempts to find the proof
Many attempts were made time and again to prove Fermat’s last theorem. But, things were not as simple as they seemed to be. Mathematicians toiled hard for more than three centuries to have a satisfying proof of this famous theorem. No doubt, there were many speculations about the authenticity of this theorem as the publication was done by Fermat’s son without his consent after his death.
After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles. This proof was formally published in 1995. However, even before Wiles’s proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence.
Wiles’ proof of the theorem
In his much-awaited proof, Andrew Wiles has used many techniques from algebraic geometry and number theory. It has many outcomes in these branches of mathematics. This proof is also based on the standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th-century techniques that were not available to Fermat.
Wiles’ proof was compiled in two papers. Together, these papers were 129 pages long. This consumed over seven years of Wiles’ research time. Nevertheless, John Coates described the proof as one of the highest achievements of number theory, and John Conway called it the proof of the century.
Editor at ‘The Secrets Of The Universe’, I have completed my Master’s in Physics from India and I am soon going to join Institute of Space Sciences, Barcelona for my doctoral studies on Exoplanets. I love to write about a plethora of topics concerned with planetary sciences, observational astrophysics, quantum mechanics and atomic physics, along with the advancements taking place in the space industry.