24 Jun 2022


Mathematics in Ancient Greece

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Greek mathematics originated from the 3rd century BCE after the development of pre-historic mathematics by the Babylonians and the Egyptians. This was the time when the Greek empire had expanded its sphere of influence to the Asian minor and Mesopotamia (Burton, 2010) . During the time, adopting the contemporary knowledge was essential for every nation that dominated another. Similarly, the Greeks were apt to learn new elements and dynamics in the societies they conquered, and just like any other activity, Greek mathematics was developed through this process. After the Greeks had competently acquired the basics of mathematics, they contributed profoundly to its development in the following years. Particularly, the Greeks had presided over the most momentous and important mathematics revolutions by the pass of the Hellenist period, an era which saw the rise of famous mathematicians such as Euclid, Archimedes, and Diophantus. These mathematicians had mostly studied at Alexandria in Egypt, a great learning center that foresaw the development of mathematics under the beneficent rule of Ptolemies ( Struik, 2012 ). Under the inspiration of Alexander the Great, the Greek Hellenistic Empire was instrumental in developing modern-day mathematics. In fact, it is said that the aforementioned professionals were the first professional scientists to be paid for conducting scientific research. Similarly, Pythagoras of Samos was a Greek philosopher and founder of Pythagoreanism movement. This paper, therefore, seeks to establish the contributions made in the ancient Greek mathematics, discuss the contributing personas, and how the ancient Greek mathematics relates to the modern mathematics. 

The mathematical knowledge of Pythagoras of Samos originated from an understanding of geometry and astronomy from the Egyptians and the Babylonians respectively. History indicates that Pythagoras was inspired by the works of Thales of Miletus, who was a pre-Socratic Greek philosopher, mathematician, and an astronomer (Burton, 2010) . Being more of an astronomer, Thales applied geometry mathematics to calculate pyramids heights and ship distances from the sea. For instance, in determining ship distances from the seas, Thales applied the congruence theorem. Thales was among the seven sages of Greece who are considered as the first of Greek philosophers. Thales had observed the great potential in Pythagoras and spent a lot in nurturing the mathematical spirit he saw in him. 

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Continually, in the 6 th century, Pythagoras initiated a study of numbers in an abstract form. Pythagoras had great devotion for mathematics that it is said he voluntarily joined a Cambyses in 525 BC from Egypt to Babylonia which was intended to extradite captives from Egypt. Having gained much mathematical experience from the two nations, Pythagoras formed a movement to expound on his opinions. Pythagoras then reappeared in his home, Samos, after nearly 50 years of wandering. However, he was banned from his native land by the Polycrates, which made him turn to the westward of Crotona, a prosperous colony in Southern Italy. Pythagoras then formed a movement of 300 young aristocrats who aided in his advocacy ( Restivo, 2013) . Indeed, Pythagoras was diversified in his contentions as he showed an interest in politics, philosophy, and religion. Moreover, Pythagoras married one of his able mathematics pupils, Theano, who later contributed phenomenally in developing the concepts Pythagoras had. After Pythagoras’ death, Theano continued his advocacy of Pythagorean mathematics. In the contemporary world, the Pythagorean Theorem is instrumental in architecture and construction mathematics. 

Euclid of Alexandra was another great Greek mathematician who made remarkable contributions in geometry. Euclid is also referred to as the founder of geometry, and in his work Elements, Euclid taught on Euclidean geometry and derivation of mathematical theorems of the same ( Struik, 2012 ). Also, Euclid sort to solve mathematical problems on perspective, conic sections, spherical geometry, number theory, and rigor (Burton, 2010) . Many of his contributions in Elements were developed to what is today algebra number theory. Euclid’s works are related to the use of the adjective “ Euclidean ” on many mathematical works, even in the present-day computations. For instance, Euclidean axioms possess great validity with the exception of the parallel postulate. Other indicators of Euclid’s mathematician supremacy are the Euclidean space, Euclidean orchard, Euclidean relation, and Euclidean algorithm. 

Plato is another founder and patron of the Greek mathematics, even though he is remembered today as a philosopher. Plato was inspired by Pythagoras and consequentially founded an academy in Athens. Plato used mathematical concepts to elaborate on life realities. Particularly, Plato emphasized geometry as the key to unlocking universal secrets. In his academy, Plato taught mathematics as a branch of philosophy, and in his 15-year course, ten years were dedicated to the study of science and mathematics, which included the study of plane and solid geometry, harmonics, and astronomy. Due to his efforts, Plato was crowned the “maker of mathematics”. Some of the celebrated mathematicians from Plato’s academy were Exodus, Theaetetus, and Archytas (Cornford, 2014). The remarkable mathematical solutions Plato contributed in the ancient Greek mathematics were geared towards clearly stating assumptions, logical deductions, as well as insisting on geometric proofs using a straight edge and a compass. Also, the Three Classical Problems established in squaring a circle, doubling the cube and trisecting the angle were great problems that still prevail in the modern mathematics. It is worth mentioning that Plato was among the first people to pose such problems. 

Finally, Diophantus was a great mathematician of the Hellenistic Greece who lived in Alexandria in the 3 rd century CE. Also known as the “father of algebra”, Diophantus wrote an influential book known as “Arithmetica,” which outlined a collection of algebraic problems ("Diophantus - Hellenistic Mathematics - The Story of Mathematics", 2018) . His contributions were integral in the development of the number theory. In addition, Diophantus contributed to advancing mathematical notations, which was crucial in developing symbolism in algebra. Other contributions from Diophantus touch on powers of the unknown, recognizing fractions, rational numbers, coefficients and equations solutions. 

Conclusively, mathematics in ancient Greece dates back to the 3 rd century BCE, and considerably developed from the Egyptian and Babylonian mathematical approaches. There were a number of influential individuals who led to the growth of mathematics in ancient Greece including Euclid, Archimedes, Diophantus, Pythagoras, and Plato. The developments made by the ancient Greek mathematicians were instrumental in establishing the present-day calculations. Even though most mathematicians of the time have little biographical information, it is undoubtedly true that most of them acquired their mathematical prowess from the Alexandrian school. Thales of Miletus was among the first Greek mathematicians who applied geometry in determining sea distances. He went on to inspire another crop of mathematicians including Pythagoras of Samos who derived from this inspiration the need to expound on algebraic and geometric expressions. Euclid of Alexandria was phenomenal in elucidating axioms, algebra, and mathematical elements, which define the refinement of Euclidean mathematics today. Plato drew inspiration from Pythagoras in his development of philosophical, mathematical approaches. The establishment of Plato’s academy in Athens is a testament that mathematics will continually develop through his rigorous mathematics curriculum. Lastly, Diophantus was a great mathematician of the Hellenistic Greece who is known as the father of algebra for the many contributions he made to developing symbolic algebra, fractions, and rationalism. 


Burton, D. (2010).  History of Mathematics . London: McGraw-Hill Publishing. 

Cornford, F. M. (2014).  Plato's cosmology: the Timaeus of Plato . Routledge. 

Diophantus - Hellenistic Mathematics - The Story of Mathematics. (2018). Retrieved from http://www.storyofmathematics.com/hellenistic_diophantus.html 

Restivo, S. (2013).    Mathematics in society and history: Sociological inquiries  (Vol. 20). Springer Science & Business Media. 

Struik, D. J. (2012).    A concise history of mathematics . Courier Corporation. 

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