Essay on Philosophy

Being one of the greatest philosophers of his time, Pythagoras created a society of skilled mathematicians who worked together to facilitate mathematics, showed how numbers can be independent, and proved the Pythagorean theorem, making him iconic in mathematics today. His discoveries of simple yet essential methods are prevalent today throughout many mathematical fields in which they are treasured.

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

Socrates is easily one of the most well known names in the history of philosophy. He is even portrayed via the magic of Hollywood time travel in the popular movie “Bill and Ted’s Excellent Adventure” and was more recently quoted inaccurately on a t-shirt as saying, “I drank what?” Despite his fame, Socrates was not the first philosopher by far, and certainly not the earliest to make meaningful contributions to the field of philosophy. Some of the great “Pre-Socratics” include Anaximenes, Parmenides, Xenophane, and Democritus. The philosophical issues of their days were significantly different from the popular discussions today, though no less relevant, and provide ample fodder for the

Ideas in science, especially astronomy and human anatomy, changed how many viewed man and led to a path of enlightenment. One example of the variation in science was the shift from a geocentric to a heliocentric universe. Pre-renaissance the Catholic Church conveyed that the center of the universe was earth. At the time, arguing with the church was considered a sin, so rarely did anyone try to contradict this idea. The geocentric viewpoint had been long affirmed until Nicolaus Copernicus, a Polish astronomer, reversed this idea, solely based off of mathematics and observations. Promptly after during the Renaissance, scholars studied Ptolemy and realized the idea that the center of the universe was actually the sun, not the earth. The heliocentric doctrine that Copernicus came up with was first denied because the Catholic church had claimed the earth, and humans, were at the center of everything, and the universe revolves around man. This was a real epiphany to people at the time because it made them rethink that perhaps without them being the center of the universe they aren't the most important things. This helped to expand means, though out of just religion and themselves. These ideas changed how many viewed man because it was proven that humans were not the center of the

Since the beginning philosophers had been trying to figure out what everything was made of. Thales of Miletus, the first natural philosopher, said that everything was made of water and was the first to introduce the meaning of change. He believed there were two types of change, qualitative change and quantitative change. From there philosophers theorized how things changed over time. Anaximander, a student of Thales, believed that everything in the universe came from an aperion (a boundless and intermediate realm). Next came Anaximenes who said that everything came from air. In which the quantity of air would determine the type of object formed, the colder the tighter and the looser the warmer. Next, Pythagoras believed that everything was

Thales of Miletus is known for being the first systematic philosopher of the Western world. He was the first to reject supernatural explanations and seek reasons behind events. To prove the value of his understanding of the world he used his logic and evidence to predict a good crop of olives and, buying up olive presses, was able to corner the market in oil and make a fortune, which closely relates to in today's world when a monopoly is created meaning the exclusive possession or control of the supply or trade in a commodity or service. He is also known for devising several geometric theories (which allowed him to measure the height of the pyramids from the ground) which was astonishing that someone could have that knowledge and be able to put it all together and create something as great as that. Thales was also the first person to study electricity. It had been noticed that amber, when rubbed, attracted threads of fiber to it. It was the static electricity which Thales’ was drawn to and begin to study. When the negative particle of the atom was named it was called the electron, after the Greek word for amber – elektron. Democritus was said to be the most successful of the ancient philosophers from a scientific standpoint, and yet he was almost forgotten about and seldom mentioned. We know that he believed that the

Thales and Heraclitus, two Pre-Socratic philosophers, proposed two notable, but very different, belief systems to explain the world around them. Thales, the first Western philosopher, introduced a non-mythological way of viewing the world. Prior to Thales, the Greeks believed their gods controlled all natural forces. However, Thales philosophized that everything originated from some fundamental substance. He reasoned that this substance must be water. He based his belief on the idea that this fundamental substance needed to be both flexible and appear in different forms. Although, Thales' s water theory proved incorrect, his belief that the world could be explained in a simpler, non-divine manner opened the door for metaphysics and science.

Pythagoras was not only a mathematician; in fact it is sometimes doubted whether the math we attribute to him was actually his own work or simply reprocessing of the work of others. He was instead generally seen as a religious figure and was the leader of what is sometimes referred to as a “cult.” He was described as “part philosopher, part priest, and part conjuror” and had a lot of bearing in both the religious and scientific views of his time. He believed that religion and science were indeed one and the same, with math serving as a pathway for discovering the workings of the universe. This belief was controversial, and many philosophers referred to Pythagoras sarcastically, but it was a belief that would continue onward throughout Greek history in the minds of other philosophers, such as Aristotle. It was the basis for the interest in mathematics and astronomy, because he taught that by learning the movement of the heavenly bodies, or planets, humans would be able to find the formula for all movement in the universe and predict future events.

When he was given freedom, he formed a school in Samos, called "The Semicircle," but soon left to travel to Italy. He traveled to southern Italy, to the town of Croton, where he founded a religion based school. He also developed a small group of his top followers called the Mathematikoi. In this school, Pythagoras made great discoveries. Some achievements of Pythagoras include, classifying numbers into even and odd, classifying perfect numbers, and classifying triangle numbers. His biggest discovery is most definitely the Pythagorean Theorem. This property's equation states that a^2+ b^2 = c^2, with the variables a, and b acting as the two legs of a right triangle, and c acting as the hypotenuse. The Pythagorean Theorem was the start of basic trigonometry, and geometry. When you hear the phrase Pythagorean Theorem, most people revert to saying that Pythagoras invented it. Well... no. Basically, Pythagoras heard the idea proposed in Babylon, so he stole it for himself and refined it a bit. Even so, the little bit of refining he did was something that the Persians probably couldn't have done. Pythagoras was proud of his achievement, but then one of his own students turned on

Pythagoras was an exceptional thinker who had a crucial impact on the field of mathematics. His unique ways of thinking and problem solving led to him creating a new theorem, entitled the Pythagorean Theorem, which significantly changed what was known about math. Although there are no known books written about or by Pythagoras from that time, he was influential in the math field and its expansion.

There are many great philosophers in this world. Some of which are extremely well known and almost everyone knows their names like Socrates, Plato Aristotle Locke and so very many more. Pythagoras is a less known philosopher who had a lot of discoveries while leading a life in a secretive manner. He was an enigma and the leader of a religious sect cult who believed the universe to consist solely of whole numbers and their ratios. Pythagoras said "Do not talk a little on many subjects, but much on a few." Has one ever wondered where did he learn his vast knowledge of mathematics and religious aspects leading to the Pythagorean cult, or what was all of his discoveries besides

I find it interesting to be speaking about the Greek mathematician Thales, as I first heard about him this semester in my Western Civilization class. According to mathopenref.com Thales was one of the first seven wise men of Ancient Greece.Thales was also one of the earliest Greek philosophers. Thales was the Discoverer of Geometry of lines. After the discovery of geometry lines, Abstract geometry appeared. Thales was a teacher of Anaximander, who was a Greek scientist from Miletus. Thales was the founder of the Ionian school of philosophy also located in Miletus. Miletus was an ancient city of the Ionian Greeks in southwestern Asia Minor. Thales school of philosophy was not only the only school founded in Miletus, Many schools were founded in Miletus. All of the schools were a big attraction to scientist, philosophers, geographers and architects. Thales was known for the theoretical and practical understanding of geometry. Many think that this discovery was not really his but everyone gave him credit for it . He also has been confirmed by many sources to

The pre-Socratics are referred to as the natural philosophers. They tried to explain everything tin the world by some natural phenomena. They were concerned about two main problems. These included cosmology, or the physical nature of the universe and a second principle cosmogony or the nature of change and the creation of the universe and what will become off all things. Empedocles was a Greek pre-Socratics as a Greek pre-Socratic philosopher from a Greek city in Sicily who wanted to figure out the answers to these two problems. According to him, the world is made of four main elements, including: earth, air, fire and water, these four elements is able to create all things by being “mixed in different combinations and proportions”. In an attempt to explain cosmogony or the nature of change he change of things in the universe, he explains that each of the elements “retains its own characteristics in the mixture and each is eternal and unchanging”. Empedocles also proposed a world where the two cosmic forces of love and strife are present. These two forces work upon the four elements in both “creative and destructive ways”. Love is a force of “attraction and combination” and Strife is a force of “repulsion and separation”. Many things were unclear about these forces however, what was true was that the two forces were engaged in an everlasting “battle for control of the cosmos and that they each prevail in turn in an endless cycle”. In an attempt to explain this cycle of

Thinkers within the realm of philosophy possessed a different train of thought that allowed them to make massive discoveries. Thales is regarded as the first recorded philosopher from Miletus. He believed reality was defined by water. Water rests on earth, reflects objects, and conforms to the shape of other objects. During what we call the ancient period, 600-300 BCE, communities lived by water supplies. Water is necessary to have the ability to obtain other means of survival. As opposed to referring to religion, Thales rejected the concept of Gods on Mount Olympus. The reality beyond mythology for Thales relied on the basis of water. Thales touched base with the concept of knowledge through observing and perceiving the way water functioned around him.

The Greek empire flourished in a significant manner due to the early invention of Greek geometry. The first forms of Greek mathematics were discovered from 800 BC. - 600 BC.. However, during this time period, both literature and writing were far more advanced than math was. Eventually Greek math had expanded to other empires quickly advancing mathematicians knowledge of geometry. The first forms of Greek math were only innovations taken from other societies, but Greeks were the first to invent the idea of “Geometry”. After the period of Alexander the Great, Greek geometry was born. Greek geometry is so important that modern countries around the world still use these methods today. Everything we have ever known about modern day geometry was based on Greek techniques. Euclid, a mathematician located in Greece, started combining the works of other mathematicians. He later created a famous book, known as “The elements”. This book covers almost everything that Greek mathematicians have ever discovered, including definitions, postulates, propositions, and different theories. The book was believed to be published around 300 BC. Mathematicians all around Greece started working together to form other theorems. “Geometry existed before creation”, was a famous quote told by a Greek mathematician, Plato. In Greece, one of the main ideas were that laws and rules of life were already made, but had to be discovered. This quote represents that the idea of geometry was always there, but