There have been few movements in world history which have had the same ability to affect future generations than Greek Mathematics and the men who helped to shape this concentration. The important movements and people are only great when historians can say that the aforementioned consisted of a lasting ability to remain important for years as well as its effect upon future generations in the process. “The assertion that Greek Mathematics retains both qualities is self evident.”[1] No student in America, as well as most of the rest of the world, can graduate from the secondary level without at least being introduced, if not inspired by the Greek mathematicians. From, Euclid to Thales and Aristotle and beyond, Greek Mathematics and the men who formed it, despite living more than two thousands years ago, their contributions are not only recognized and appreciated, but many of the theorems and ideologies are still taught as if they were written yesterday. The contributions that the ancient Greeks gave to their peers as well as countless future generations would not be bested for centuries; some historians would argue that the level of contributions to mankind has still not been bested, all these many years. Regardless, the assertion that Greek Mathematicians contributed to the field of mathematics, and as a result, influenced not only other generations but other fields of study; science and astronomy to list a few, is self evident and beyond discussion.

The exact ways in which Greek mathematics was able to contribute to the world, is through the efforts of a few select men, who despite having left this earth more than two thousands years ago, and is still studied and appreciated to this very day. It would first behoove a study of Greek mathematics to first identify what exactly is being referred to when talking about the concentration. “Classical Greek Mathematics refers to Greek mathematics from the time of the Hellenistic Period (from 323 BC) and which was written in the Greek language.”[2] The location for some of the most important contributions occurred in Alexandria in Egypt which attracted Jewish, Persian and Egyptian scholars to the field of mostly Greek thinkers. Greek mathematics concentrated and gave to the world, major contributions in the field of number theory, mathematical analysis and what proofs and ways of though which would greatly contribute to the formation of Calculus; an area of study which taken from Isaac Newton and is the science used to propel satellites into space and man’s first walk on the moon.

It was the contributions of Thales which historians regard as the starting point to what is called Classical Greek Mathematics. Thales was famous for teaching that all substances within the earth, as well as the earth itself were derived from water and that water was the basic substance within the earth and of the earth. However, Thales was most famous for his contributions to the field of Geometry. A thousand years later, Muslim scholars in the Middle East would use and rely upon much of the works of Greek mathematicians in the field of Geometry; especially the work of Thales. His work involved the angles of triangles and how the height of a pyramid, by measuring the shadows of the pyramid when they were of similar length, one would then be able to measure the height of the famous pyramids in Egypt. Within the discoveries within Thales Theorem is the concept of a sect. “a sect is a measure of the angle. Knowledge of two angles and an enclosed leg, allows one to determine by similar triangles the second leg, which will then give the student the distance of the triangle.”[3] This would later be known as Thales Theorem and would be indicative of how Thales, as well as other Greek mathematicians used deductive reasoning within mathematics in order to make Mathematics eventually practical for the masses.

“In the spirit of Greek mathematicians specializing in the concepts of math which can be referred to as practical to the human race, Thales was instrumental in the formation of the modern calendar as we know it today.”[4] He set the seasons of the year and divided the year into the standard 365 days per year. In doing this, Thales required mathematics to calculate the distance of the sun and its movements. This discovery and contribution to the field of, not only mathematics but general knowledge cannot be measured. This continuing theme; contributions to the field of mathematics which not only furthers the concentration of math but also helps the general world and the people who inhabit it, Greek mathematicians should be credited.

Continuing in the field of Geometry, the name of Euclid is connected to the study. Euclid is important because his teachings in the area of Geometry had more relevant and lasting power than perhaps any other mathematician who ever existed. The level of importance of any contribution to a particular field of study is measured by its mass appeal and ability to stay relevant for as long as possible. Euclid’s most famous works, Elements, contains both to a greater degree than perhaps any other work on mathematics ever created. “For more than two thousand years, his Elements were used as the foundation of Geometry and were used primarily in textbooks to a majority of the world’s youth until 1903.”[5] This is an amazing accomplishment and has been the hope of any mathematician or figure in world history; to have their accomplishments last and be recognized as great for hundreds, if not thousands of years. Only a handful of times this hope has become a reality. Euclid’s Elements can be included in this most exclusive list.

The works of another great Greek Mathematician: Pythagoras contains many important and constant elements which can be seen in both the fields of Mathematics and History. The first is that Pythagoras stood on the shoulders of others who had come before. This is seen and recommended for many important figures in History. There are rarely any new ideas and contributions which did not owe at least a degree of its achievements to the achievements of others. Pythagoras’ most important achievement in mathematics was simply proving Euclid’s 47th proposition in Geometry. This became known as Pythagoras’s Theorem and is taught in every high school Geometry class in the United States as well as the world. This theorem states: “that the square of the hypotenuse of a right angled triangle is equal to the sum of the square of the other two sides.” (Netz, 1998 pg. 84) Pythagoras also made another most important contribution. However, he would not be alive to witness it. The Copernican Theory, which was used to teach that the earth was round and revolved around the sun, made famous by Nicholas Copernicus in the 15th century, used as a contributing factor to the basis of the argument, theories and philosophies that was first given to the academic world by Pythagoras. Pythagoras, and rightly so, is know as one of the select founders of mathematics. If his theories had been forgotten a mere hundred years after they were founded ( a feat that many of today’s thinkers and news makers would be very content with) the name, figure and contributions of Pythagoras would have been long forgotten.

Another giant in the field of Greek mathematics was Archimedes. This mathematician dabbled in both the elementary and profound areas of math. His works lead to the foundation of Calculus as well as the now elementary properties of the amount of water that one’s own body was responsible for displacing in a body of water. Also, the concept of the lever and being able to move heavy objects with greater ease can be attributed to Archimedes. The use of mathematic for practical uses was also important among the contributions of this man. Whether it was his work in Geometry or his ability to keep ships afloat with the invention of the Archimedean screw, this mathematician was revered as the greatest mathematician of his time. It would be his love of Geometry that would eventually lead to his death as his response to a Roman soldier who had walked onto and disrupted his plans, resulted in the Roman soldier piercing Archimedes with his sword and killing him. The Roman leader Marcellus erected a tomb to the great mathematician in his honor.

Perhaps more than any of the other above mentioned Greek mathematicians, the works of Archimedes was some of the most practical and widely used discoveries the world has ever known. Such discoveries might not profound the modern Math major in this country’s universities. However, it is unlikely that the modern discoveries of our era, will have the same weight and lasting ability as the discoveries of the Greek mathematicians; specifically Archimedes. This is what keeps the scholars and historians coming back to such figures. The displacement of water, the density of certain medals such as gold and silver, the use of the lever, the advancements in Geometry as well setting the foundation for Calculus, as well as helping to keep Roman ships afloat through the utilization of his invention; the Archimedean screw. Only the name of a fee select figures in modern American history should be invoked in the effort towards any type of response as the American equivalent.

Aristotle is known as the most famous philosopher the world has ever known. His teachings and ability to relay the importance of thought and theory is very important to the field of science and philosophy. However, even though the greatest and most known of his works was not in the field of mathematics, Aristotle is attributed with assisting the thought process within the field. “Aristotle believed in three theoretical sciences, and mathematics was one of them. Aristotle was not primarily a mathematician, but did use and contribute to math, in order to excel in other sciences. Contrary to popular belief, Aristotle was not primarily a mathematician. In fact, most of his work was done in theories of sciences, and philosophy. He really didn’t contribute many math theories. He did, however, contribute greatly to logic, and other sciences, such as biology. His theories discussed planets, position of stars, and human and animal behavior.”[6] Aristotle was also instrumental, like most Greek mathematicians, in the field of Geometry and math logic. His belief that: “a triangle drawn in a semi circle is a right triangle, was one of the best known theories of Aristotle in the field of Mathematics. However, Aristotle gave to the field of mathematics, something much more important that this theory. His ability to encourage logic and pure math as a way of thinking and regarding math as more than just numbers and equations, was an important contribution. Also, Aristotle’s definition of logic is verbal reasoning. “The heart of Aristotle’s logic is the syllogism, the classic example of which is as follows: All men are mortal; Socrates is a man; therefore, Socrates is mortal. The syllogistic form of logical argumentation dominated logic for 2,000 years.”[7] These are the attributes which have helped to endure the legacy of such a teacher, philosophy and mathematician as Aristotle.

What is a key historical and mathematical element to all of the above mentioned Greek mathematicians was the fact that even though the math and science being discovered today is considered to be much more advance than what was discovered by the above mentioned more than two thousand years ago, what is being discovered today using math, could not have been accomplished if not for the achievements of these Greek mathematicians. This is a common theme and one that must not be overlooked. In keeping with the historical perspective and importance of the Greek mathematicians

WORKS CITED

Andrews, J. Biography of Aristotle http://www.andrews.edu/~calkins/math/biograph/bioarist.htm Downloaded September 3, 2007

Artmann, B. Euclid: The Creation of Math Chicago: University of Chicago Press 2004

Christianides, J. Classics in the History of Greek Mathematics Columbia: Springer Press. 2004

Gow, J. A Short History of Greek Mathematics Phoenix: Dover Press 2002

Netz, R. The Shaping of Greek Mathematics London: Cambridge 1998

[1] Artmann, B. Euclid: The Creation of Math Chicago: University of Chicago Press 2004 pg. 118

[2] Netz, R. The Shaping of Greek Mathematics London: Cambridge 1998 pg. 28

[3] Gow, J. A Short History of Greek Mathematics Phoenix: Dover Press 2002 pg. 32

[4] Christianides, J. Classics in the History of Greek Mathematics Columbia: Springer Press. 2004 pg. 98

[5] Artmann, B. Euclid: The Creation of Math Chicago: University of Chicago Press 2004 pg. 237

[6] Andrews, J. Biography of Aristotle http://www.andrews.edu/~calkins/math/biograph/bioarist.htm Downloaded September 3, 2007

[7] Andrews, J. Biography of Aristotle http://www.andrews.edu/~calkins/math/biograph/bioarist.htm Downloaded September 3,

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