Pierre De Fermat Essay Example

he earned his civil law degree and became a councilor at the High Court of Judicature in Toulouse (JOC/EFR, 1996). Fluent in Latin, Greek, Italian, and Spanish, Mr. de Fermat dedicated his life to mathematics. Although he never married, he did have a son. Furthermore, de Fermat resided near Toulouse in southwest France during the seventeenth century while working as a lawyer and magistrate. He dealt with several gruesome cases and was involved in the condemnation of a burning priest at the stake.

To avoid conflicts of interests, judges were typically instructed not to socialize within the community. Consequently, Fermat would isolate himself in his study during the evenings, focusing on his mathematical endeavors. He is credited for successfully resolving four important math problems that greatly influenced the advancement of calculus. Additionally, before Sir Isaac Newton was born, he developed a method for finding the tangent of a curve. It is evident that he consistently strived to improve and perfect his mathematical system. Nevertheless, he is only acknowledged for publishing one paper.

It appears that he lacked belief in people's willingness to accept the theories he developed, thus he refrained from publishing them. Following de Fermat's passing in 1665, his son took on the responsibility of gathering his letters and other papers. Among these were numerous mathematical publications, accompanied by his notes and explanations in the margins. This is how the renowned "Last Theorem" came to see the light of day. What truly astonishes is that unlike other theorists, his published works underwent very few revisions or alterations, leading theorists to speculate that he would consistently revise his work and only publish it

once fully satisfied.

Fermat's published work was considered by him as the ultimate version of his research, none of which had any dates before his death. Only one significant manuscript, identified by the initials M. P. E. A. S., was released while he was still alive. When Roberval proposed to edit and publish some of Fermat's works, Fermat refused, expressing his desire not to have his name associated with them. Nevertheless, he continued to engage in extensive correspondence with mathematicians, often sharing his findings bit by bit or presenting them as challenges.

Fermat, a pioneer in analytic geometry who collaborated with Pascal to establish probability theory and contribute to the development of calculus, is honored in Paris with two streets named after him - "Passage Fermat" and "Rue Fermat." He also has a moon crater named after him called "Crater Fermat." These details were discovered in the margins of a copy of Diophantus's Arithmetica, an ancient Greek text written around AD 250. Arithmetica functioned as a guide for number theory, focusing on the study of whole numbers and their various relationships and patterns they form. (JOC/EFR, 1996; Lattes, 2006)

In the book, it was discovered that Mr. e Fermat had made numerous mathematical discoveries throughout his life. This book served as his inspiration to develop the Last Theorem by exploring various aspects of Pythagoras' Theorem. Mr. de Fermat concluded that there existed a new equation, derived from Pythagorean Theory. He further believed that, according to the Last Theorem, the power of the equation would increase without any solution. This is represented by the math statement xn + yn = zn, where n

is a number greater than 2. Additionally, he hypothesized that the only possible integral factors of n were unity, leading to equations x+y=n and x-y=1.

According to O'Connor & Robertson (1996), evidence was provided to support Diophantus' statement that the sum of the squares of two numbers cannot be in the form of 4n-1. A constraint was also introduced, indicating that it is unlikely for the multiplication of a square and a prime number to yield 4n-1. It is possible that there was doubt about the validity of this proof, as only one proof was presented and this statement was rare within his manual.

According to O'Connor & Robertson (1996), there exists a remarkable example of this concept that is too long to fit within the confines of this margin. The individual in question would express his writing difficulties repeatedly before sending them off to fellow mathematicians. Following his passing, his son came across and provided the missing proof, sparking the interest of numerous mathematicians throughout Europe who sought to rediscover it. This pursuit could have either been fruitless or yielded an extraordinary treasure. Throughout history, mathematicians were unable to resist the allure of this treasure. Nevertheless, during the 18th and 19th centuries, no set of numbers fulfilling his equation could be found. Consequently, while it seemed that this theorem was true, uncertainty persisted without tangible proof.

Despite many attempts by individuals to prove specific equations, none were able to match the comprehensive proof achieved by one person. As problems like the Musgrave Ritual remained unsolvable for longer periods of time, they gained more significance and gave rise to tales involving wealth,

mystery, and even suicide. One particular story revolves around Paul Wolfskehl, a German industrialist and amateur mathematician. According to O'Connor & Robertson (1996), Mr. Wolfskehl had reached the point where he contemplated ending his own life, even going as far as setting a date and time to shoot himself in the head. However, before this tragic event took place, he decided to visit his library and delve into the latest research on the theorem.

Despite becoming obsessed with a new approach to prove the theorem, he eventually realized it was a dead-end after dedicating hours to it. However, this setback reignited his enthusiasm for life as he appreciated the beauty of number theory once again. He attributed the theorem for saving his life and generously left 100,000 Marks as a reward for anyone who could prove it. In the first year after his death, over 621 flawed proofs were submitted. By 1980, the University of Illinois utilized computers to successfully demonstrate the theorem's validity up to four million.

Nevertheless, complete proof has not been achieved, as it requires absolute confidence. However, my theorem should be sufficient evidence. If it holds true for numbers up to four million, it should also be applicable to 4,000,001 and beyond. However, the proof cannot be established until there is a way to test an equation for infinite numbers. Since infinity is unobtainable, the proof will remain unproven. Euler demonstrated a theorem in 1753, where he informed Goldbach that he had a proof for the theorem when n=3 (O'Connor ; Robertson, 1996).

For over two hundred years, it was believed that there are no whole number solutions

according to Euler's conjecture and Fermat's equation. However, in 1988, Noam Elkies, a Harvard mathematician, proved Euler's conjecture false and demonstrated the existence of multiple solutions to the equation. In his extensive proof consisting of more than two-hundred pages, Andrew Wiles claimed to have solved Fermat's Last Theorem equation. Wiles and Richard Taylor presented this proof during a ten-day conference at Boston University in August of 1995. The conference drew an audience of over three-hundred people.

The conference led by Professor Jeremy Teitelbaum of the University of Illinois resulted in a poem appearing on the cover. This event gained significant publicity, including an appearance on Oprah. A team of referees meticulously reviewed the evidence and gradually discovered critical flaws in one aspect of the argument. Regrettably, as Professor Teitelbaum attempted to address one flaw, another would arise, transforming his childhood dream into an endless nightmare.

He achieved a significant breakthrough, discarding an earlier alternative approach that had led to recent failures. Wiles believes that the battle to prove Fermat's theorem is concluded, stating, "There is no other problem that holds the same significance for me. It was my passion during childhood, and there is nothing to fill that void. I had the exceptional opportunity to pursue in my adult life what had been my childhood dream. I understand it is a rare privilege, but if you can engage in something during adulthood that holds such profound meaning, it is more gratifying than anything imaginable." (O'Connor ; Robertson, 1996)

During his life, Ludolph Van Ceulen, a renowned mathematician who approximated Pi to thirty-five places, and Sir Isaac Newton, known for his theory about

sitting under an apple tree and the force that governs the movements of the Moon, passed away. These individuals, as well as others who followed, made significant contributions to the field of mathematics. Not only did Mr. de Fermat compile interesting formulas in his lifetime, but other mathematicians continue to build upon his work. Perhaps one day, his theorems will be proven true.