Euclid’s Elements and the Axiomatic Method Essay

David Hilbert was a German mathematician whose research and study of geometry, physics, and algebra revolutionized mathematics and went on to introduce the mathematic and scientific community with a series of mathematical equations that have yet to be solved. Furthermore, his study of mathematics laid the groundwork for a variety of ongoing mathematic analyses, which continue to influence the world today.

Even though the concept of mathematics has many different ideas of what it is, the concept they are trying to prove is all in one general direction. Everyone sees math as a different set of ideals and theorems to which their work is based and can never truly revolve around one idea which is why the definition of mathematics always appears to be

To begin, the concept of unity follows the Aristotelian proposition that nothing can be added to or taken away from a perfect work of art. Next, proportion, or the harmony of the parts to the whole and to each other is, based the mathematical and geometric relationships discovered by the Ancient Greeks. Finally, clarity refers to the logical

My biggest issue with the soundness of Plato’s final argument however falls between premises six through eight:

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.

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

For Pythagorean shapes and numbers was so important. He believed that the most perfect shape of the nature is circle. Therefore he put the earth in the center of a spherical world. According to Plato the movement of planets is in perfect circles. However now its known that the planetary orbits are ellipses and not

Geometry and mathematics were the cornerstone of Greek life. While the myths of the day were still acknowledged and, for the most part, accepted, it became less prevalent in society.

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

Even though it’s called Ancient Greece, doesn’t mean that all their ideas and lifestyles are ancient. Greeks have influenced lives today in many ways. They are the base of many different creations. Greeks have influenced the world today through education, architecture, government, and many more things. Many people's ideas are still used today and really affect society and how people live.

During his career, Eratosthenes became a well renowned mathematician although he was just short of being the best, he was beat out by Archimedes who was the best in almost every subject. Throughout his life Eratosthenes was called β which is the second letter in the Greek alphabet. In 247 B.C. Eratosthenes was appointed to be the Librarian of Alexandria by Ptolemy III Euergetes. Eratosthenes also created the Sieve of Eratosthenes which is a simple, yet effective way of finding prime numbers. The most notable thing he did was find the circumference of the earth, he did this by adopting a simple

     Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know

Omar was also a poet, philosopher, and astronomer. Omar’s works were translated in 1851, which was research on Euclid’s axioms. In the medieval period, he expanded on Khwarizmi’s and the Greeks mathematic works. He only worked with cubic equations only and focused on geometric and algebraic solutions of equations. In 1145AD, Al-Khwarizmi’s book was translated by Robert Chester, which made it possible for algebra to be introduced to Europe. After algebra was introduced in Europe, European mathematicians developed and expanded on algebra concepts. Even though algebra began in the Arabic countries, once European mathematicians obtained the information of algebra, they became the leaders of mathematical discoveries in the world (“Mathematics”).

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