Fermat's Last Theorem Research Paper

The creations of Pythagoras were very powerful during the era in which he lived in. He created a community of followers (known as the Pythagoreans) who believed that mathematics was fundamental and ‘at the heart of reality’ (source 1). The people in the society were all proficient mathematicians took mathematics very seriously, to the extent that it was similar to a religion (source 1).

The statement “The greatest happiness for the greatest number is the measure of right and wrong” was coined by the English philosopher Jeremy Bentham as the fundamental axiom of his philosophy. Bentham is respected as the father of Modern Utilitarianism; this strand of ethical thinking has not only been adopted by followers of Bentham, for example John Stuart Mill or Peter Singer, but also by economists and lawyers as a means of creating a fair society, with the highest potential for co-operation. However, although utilitarianism is widely followed and supported, there are many issues that arise due to its subjectivity

We use mathematics to our great advantage to explain many things. Although Pythagoras, applied A^2+B^2=C^2, he did not create the substance of the equation, this theorem is timeless, he only brought it to our attention.

Two scientists decided to take Godel’s theorem and see if it actually worked. Christoph Benzmüller and Bruno Paleo were able to mathematically prove correct Godel’s theorem using an ordinary Mac book. Their formulas appear in the same order as the above arguments.

In Famous scientist’s (2015) article Pythagoras it states that five 3D solids were brought into existence by Pythagoras and the Pythagoreans, these items are identical on all of the sides and today they are called dice. The ranged from four sides all the way up to twenty and later Plato believed they belonged to the five Greek elements including aether (n.pag). They said “Pythagoras believed that, like everything else, music was based on whole number ratios. He also believed in its healing properties.”(n.pag) He later would learn that music was controlled by rations, like if a sting is shortened by half it raises an octave or if it’s shortened two-thirds then it moved the pit up one-fifth discovering that octaves are split into fifths not halves (n.pag). Those are the biggest discoveries of Pythagoras and the Pythagoreans, but they still has many more different discoveries. He has been accredited with a lot for being an enigma, and having written no books in his life. Even so the thoughts from learning of this brilliant mathematician tickles the mind and creates great and wonderful thoughts and ideas for many people. Learning about all of this should inspire anyone to travel and learn the ways of other countries and customs and even grasp their mathematical

All throughout history mathematical accomplishments have shaped the world for the better, from Pi to the Pythagorean Theorem. With new technology being invented, the more mathematical accomplishments are being made, and in the 19th century it was getting bigger.

As you can tell by the name of the book, Michael Guillen writes about 5 equations that he felt changed the world. In about 50 pages per equation Guillen gives a backstory and explanation of why and how each scientist discovered their equation of how the world works. The five equations were:

The definition of a logarithm is “the exponent of the power to which a base number must be raised to equal a given number.” A question that has been around for ages presents the question of whether a logarithm is an invention or a discovery. Logarithms are essentially the same as mathematics, so likewise, the question also queries whether mathematics is an invention or a discovery. The primary difference between an invention or discovery is the existence of the thing being discussed. If the thing did not exist before someone brought it into existence, then the thing was invented; however, if the thing did exist before its existence was known, then it was discovered. In part, logarithms and mathematics are both invented and discovered. Someone invented their existence and discovered the facts to support their ideas, as all experiments go.

     The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote

4) Srinivasa Aaiyangar Ramanujan is undoubtedly the most celebrated Indian Mathematical genius. He was born at Erode in Tamil Nadu on December 22, 1887. During an illness in England, Hardy visited Ramanujan in the hospital. When Hardy remarked that he had taken taxi number 1729, a singularly unexceptional number, Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=1³+12³=9³+10³.

Fermat's proof is as follows. Let n be prime, and suppose it is equal to x2 -y2 that is, to (x+y)(x-y). Now, by hypothesis, the only basic, integral factors of n and n and unity, hence x+y=n and x-y=1. Solving these equations we get x=1 /2 (n+1) and y=1 /2(n-1). -He gave a proof of the statement made by Diophantus that the sum of the squares of two numbers cannot be the form of 4n-1. He added a corollary which I take to mean that it is impossible that the product of a square and a prime form 4n-1[even if multiplied by a number that is prime to the latter], can be either a square or the sum of two squares. For example, 44 is a multiple of 11(which is of the form 4 x 3 - 1) by 4, therefore it cannot be expressed as the sum of two squares. He also stated that a number of the form a2 +b2, where a is prime b, cannot be divided by a prime of the form 4n-1. -Every prime of the form 4n+1 is accurate as the sum of two squares. This problem was first solved by Euler, who showed that a number of the form 2(4n+1) can be always showen as the sum of two squares, of course it was Mr. Pierre de Fermat. -If a, b, c, are integers, a2 + b2= c2, then ab cannot be a square. Lagrange solved this. - The determination of a number x such that x2n+1 may be squared, where n is a given integer which is not squared. Lagrange gave a solution of this also. -There is only one integral solution of the equation x2 +4=y3. The required

Have you heard of Fermat’s Last Theorem? It was the world’s most notorious (which means famous in a bad kind of way) mathematical problem because it kept the world’s greatest minds dumbfounded for more than three centuries!

In the Fourth Objections, Arnauld proposes a case to suggest that Descartes’ reasoning is problematic. Imagine someone knows that a triangle is right-angled, but doubts, or has not grasped for certain, that the square of the hypotenuse is equal to the sum

In the documentary “Einstein’s Big Idea”, viewers enter the world of E=mc² and the people and discoveries behind that important equation. Albert Einstein came to the conclusion of E=mc² but not without the help of many important figures who came before him. Scientists like Michael Faraday, who rose from being a person of basic education to one of the greatest scientists of time and started the revolution of energy; Emilie du Chatelet, a female physicist who used Leibnitz’s idea of squaring and believed that light was squared, and many other prominent figures helped Einstein discover each piece of the equation. Before watching the film, I didn’t think much of the equations that we use in daily life, but after watching it, I was exposed to all the people who dedicated their lives to discovering something so important. While watching the film, I was impressed by how the discoveries of many different people had helped create one thing that was so powerful and important. The world’s renown equation E=mc² was created by the greatest scientific discoveries made by important scientists, brought together by Albert Einstein and made an

I am most famous for discovering the Pythagorean Theorem, which solves the length of the hypotenuse of a right triangle. Use the equation a² + b² = c², where "a" and "b" are the two sides forming the right angle to solve "c" which is the hypotenuse (Bruce E. Meserve 46).