Rodrigo Gonsalves

History’s hardest math problem ever: Fermat's Last Theorem (FLT) is one of the most legendary problems in the history of mathematics, attributed to Pierre de Fermat, a 17th-century French lawyer and mathematician. aⁿ + bⁿ = cⁿ Fermat's Last Theorem states that there are no three positive integers a, b, and c such that the equation shown above holds for any integer value of “n” greater than 2. This is an extension of the Pythagorean theorem, which holds for n=2. In the margin of his copy of Diophantus' "Arithmetica," Fermat wrote that he had discovered a "truly marvelous proof" of this proposition, which the narrow margin could not contain. This note was discovered after his death by his son, Samuel, who published it. Despite Fermat's assertion, no proof was ever found among his papers or correspondences. This has led to much speculation about whether he actually had a valid proof or if he might have been mistaken. Over 350 Years of Attempts: From Euler to Sophie Germain, many mathematicians made progress by proving special cases of the theorem, but the general case remained elusive. In 1906, Paul Wolfskehl left a bequest for a prize to be awarded for the first correct proof of FLT, spurring further interest. By the late 20th century, advanced techniques in number theory, particularly those involving elliptic curves and modular forms, began to intersect with FLT. In 1993, Andrew Wiles, a British mathematician, unveiled a proof at a series of lectures at the Isaac Newton Institute. His work was based on proving a special case of the Taniyama-Shimura-Weil conjecture (now called the Modularity Theorem), which linked elliptic curves with modular forms. In 1994, Wiles and Taylor submitted a revised proof, which was published in 1995. This proof not only settled FLT but also significantly advanced the field of number theory. While Fermat's claim of a "marvelous proof" remains unverified, his theorem's journey through mathematics history showcases the evolution of mathematical thought. Andrew Wiles' proof, using techniques far more sophisticated than those available in Fermat's time, resolved one of mathematics' longest-standing puzzles, proving that sometimes, the path to truth in mathematics requires centuries of collective human endeavor. If you want to learn more I strongly recommend to read the book “Fermat’s Enigma” by Simon Singh, with out a doubt, one of my favourite books ever. What do you think @SLSingh , do you think Fermat actually solved it? #Math #Curiosidades