What Makes Fermat's Last Theorem

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).

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

Finally, during the European enlightenment, men like Fermat, Pascal, and Isaac Barrow further pursued the emerging new field developing the concept of the derivative. Barrow even offered the first proof of the fundamental theorem of calculus linking the concepts of differentiation and integration; however, it was one of Barrow’s young students, Isaac Newton who would make the next big splash in the creation of the art of calculus.

In Europe, the second half of the 17th century was a time of major innovation. Calculus provided a new opportunity in mathematical physics to solve long-standing problems. Several mathematicians contributed to these breakthroughs, notably John Wallis and Isaac Barrow. James Gregory proved a special case of the second fundamental theorem of calculus in AD 1668.

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

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.

The mathematic that not only facilitated in the renaissance but provide the key a new science of nature from Galileo.

She published philosophical works clarifying facts and generalizing the into laws to form a system of sociology and psychology. Years later, Germain was the first person to provide proof of Fermat’s Last Theorem, that has been a struggle for mathematicians for the past 200 years. “That if xn + yn = zn, then neither x, y, nor z can be a natural number if n is greater than 2, stated from Fermat's Last Theorem" (Barrow-Green). Germain used her proficiency on prime numbers to help to prove this theorem. Successful from her work, she published her deeds in a supplement to her acquaintance Adrien-Marie Legendre's work Théorie des nombres.” (The Remarkable Life of Sophie Germain)

His interests ranged across many mathematical and scientific fields, including geometry, trigonometry, calculus, optics, astronomy, cartography, mechanics, and even music theory (Euler). Euler was the first to officially introduce several of today’s standard mathematical notations, including the sigma symbol “∑” to represent the sum of a list of terms, the conventional notation “f(x)” to denote a function of x, the use of the letter “i” to represent √-1, and the systematic labeling of “A, B, C” and “a, b, c” for the angles and corresponding sides on a triangle, respectively (Boyer). One of his better known discoveries is known as “Euler’s Number,” denoted by the symbol “e” which represents the value for the base of natural logarithms in much the same way that “흅” does the circumference of a circle (Euler also helped institute the standard use of “흅,” although he did not initially discover it) (Leonhard Euler). In fact, Euler worked so hard that he lost sight in one, then both of his eyes, one of them becoming infected after a botched operation intended to restore its vision. Yet Euler maintained his strong faith in God, claiming that this faith is what supported him through his painful loss of his vision (Leonhard

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

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

Pierre de Fermat Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages, France. Mr. Fermat's education began in 1631. He was home schooled. Mr. Fermat was a single man through his life. Pierre de Fermat, like many mathematicians of the early 17th century, found solutions to the four major problems that created a form of math called calculus. Before Sir Isaac Newton was even born, Fermat found a method for finding the tangent to a curve. He tried different ways in math to improve the system. This was his occupation. Mr. Fermat was a good scholar, and amused himself by restoring the work of Apollonius on plane loci. Mr. Fermat published only a few papers in his lifetime and gave no systematic exposition of his methods. He had a

Although Euclid (or the school) may have not been first proved by him, (in fact much of his work may have been based upon earlier writings,) he did manage to insert assumptions and definitions of his own to strengthen the various postulates into the form we know today.

Mathematics has contributed to the alteration of technology over many years. The most noticeable mathematical technology is the evolution of the abacus to the many variations of the calculator. Some people argue that the changes in technology have been for the better while others argue they have been for the worse. While this paper does not address specifically technology, this paper rather addresses influential persons in philosophy to the field of mathematics. In order to understand the impact of mathematics, this paper will delve into the three philosophers of the past who have contributed to this academic. In this paper, I will cover the views of three philosophers of mathematics encompassing their