History of Mathematics and Ancient Civilization
Mathematics in ancient civilization across Europe and in Egypt is considered a major development not only in science but also normative dimensions of social practice and philosophy of classical and contemporary societies. Ancient human cultures in prehistoric societies exhibited a practical concept of numbers and means of counting larger quantities. Major progress in the history of mathematics and ancient civilization involved the discovery of numbering systems and concepts of fractions which enhanced the practicality of mathematics. The ancient Egyptian and Greek mathematics had a close relationship with the development of writing and measurement systems for performing several practical tasks. The classical Greeks, particularly Athens, also made an immense contribution to the development of ancient mathematics by establishing the algebraic basis for interpreting mathematics. In the course of civilization, advances in Egyptian and Greek mathematics led to inventions of more complex aspects of arithmetic and geometry through deduction and reasoning which forms the foundation of the science and mathematics.
Biography of Pythagoras of Samos
Pythagoras is a Greek mathematician and philosopher who is often considered as the founder of pure mathematics. He was born in the mid-6th century and son to Mnesarchus of Tyre and Pythias of Samos (Zhmud, 2012). He wrote several books on mathematics and philosophy and invented the famous Pythagorean Theorem. He traveled with his parents across Greece and was introduced to Mathematics by teacher Pherekydes during which he encountered Thales who mentored and encouraged him to learn astronomy and mathematics in Egypt. He went to Egypt at around 535 BC where he was admitted to a temple in Diospolis where he interacted with many Egyptian Priests (Zhmud, 2012). Later, when Egypt was invaded by Persia, Pythagoras was taken to Babylon as a prisoner of war where he learned arithmetic and music as well as other Babylonian Mathematical concepts.
When he left Babylon back to Samos, he went to School of Croton in Italy where he taught mathematics and founded Pythagorean Society of Mathematics and Astronomy and proved his Pythagorean Theorem. While in the school of Croton, Pythagoras was enthusiastic in principles of mathematics as well as number systems and mathematical triangle (Zhmud, 2012). He also made a key observation on the mathematical theory of music by establishing a relationship between harmonious tones of vibrating strings to ratios of lengths and numbers. He later died after the attack on Pythagorean Society at School of Croton where he is claimed to have committed suicide. However, Pythagorean Theorem has contributed a lot to the understanding of geometric algebra, properties of numbers and astronomy.
Ancient Civilizations and Mathematics.
Science and mathematics became essential aspects of culture and tradition in ancient Greece and the entire ancient Mediterranean. During the classical age, Greek mathematics transformed from theoretical mathematics to applied mathematics used to solve various problems in natural sciences centered in arithmetic, geometry, astrology and astronomy and music. The evidence of ancient Greek mathematics is found in manuscript books as well as Latin and Arabic translations. Athens became the center of vibrant mathematics activity in Greece during the classical and imperial period (Ferreirós, 2015). Deductive mathematical principles developed in Athenian culture and oral arguments for mathematical philosophy and rhetoric involved institutional settings such as schools and temples.
The most landmark developments in Greek mathematics during the classical period and Hellenistic period include the work of Archimedes’ principles, Pythagorean theorems, Euclid canon principles, Aristoxenous harmonic elements Apollonius, and Pappusamong others (Ferreirós, 2015). However, all these Greek mathematic civilizations focused on geometric constructions. Pythagoras developed concepts of triangles based on Thale’s Intercept theorem on geometric classical problems. Euclid made a contribution to the understanding of Pythagorean scale based on monochord which is quite relevant in today geometry. He developed Euclid’s Elements concepts for Conics which formed the foundation for other greek mathematics discoveries on geometry by Pythagoras, Eudoxus and Archimedes (Ferreirós, 2015). Deductive mathematics became a distinctive mathematical style during the Hellenistic period and informed the construction techniques based on geometry.
Ancient Egyptian and Babylonian mathematics presented different approach principles based on Egyptian hieroglyphics numeric interpretation. The number of systems developed in ancient Egypt was based on grouping of hieroglyphic symbols to form units for performing various arithmetic operations. The major sources of ancient Egyptian mathematics include the Moscow papyrus which shows how Egyptians calculated volumes and areas of objects as well as Ahmes Papyrus which showed multiplication and division techniques based on unit fractions (Imhausen, 2016). Simple algebraic problems regarding addition and subtraction were solved by grouping and regrouping special hieroglyphic symbols while division and multiplication were evaluated using common binary multiples. Later, the invention of unit fractions enhanced the solution for algebraic problems regarding division and multiplication (Imhausen, 2016). Geometry was less developed in ancient Egypt compared to Greek mathematics and was mainly restricted to fractional operations for determining areas, volumes, and similarity.
Apart from the evidence of ancient Egyptian mathematics on papyrus text, the Great Pyramid of ancient Egypt reveals the application of mathematics inaccurate measurements, geometry and directions. Egyptian mathematics was developed to reveal professional distinctions particularly in the application of geometric triangle concept in the construction of pyramids (Imhausen, 2016). Egyptian mathematics was closely related to surveying activities of ancient Egyptians. Egyptians used triangles as a basic unit for measuring distances in surveying. The ancient Egyptian mathematics also played a role in the invention of the calendar. Calendar and the Egyptian pyramids reveal how ancient Egyptian mathematics was sophisticated in regards to geometry and golden ratios.
Mayan culture was among the earliest civilization who contributed to the development of advanced numbering system in ancient mathematics. As a community who had agricultural lifestyle mathematics and astronomy became essential in predicting planting and harvesting seasons during the classical and imperial ages (Edwards, 2015). They developed the concept of zero and Mayan calendar long before other civilizations during the pre-classical era which reveals the Mayan sophisticated mathematical background long before civilization. Unlike other ancient civilizations such as Egyptians and Greek, Mayans’ numerical system considered the concept of zero and developed a symbol for denoting zero in their number system (Edwards, 2015). Ancient Mayan mathematics civilization spread through Central America proving the most intelligent societies in America who influenced the ancient art, sculpture and architecture in the region.
The Mayan knowledge and skills in science and mathematics made their numerical system the best tool for determining astronomical and astrological calculations. The Mayans developed unique systems of symbols of dot and bar to represent numbers from zero to five and special grouping strategies to represent numbers beyond five using those symbols (Closs, 2010). However, the most unique aspect of ancient Mayan mathematics is their approach for representing larger numbers. The Mayan approach involved using base-20 numerical system making 20 a unit for numerical computations involving large numbers such as astronomical calculations. Mayan numerical system also had complex arithmetic procedures governed with rules for performing addition and subtraction based on their symbols.
Ancient Italy was dominated by Hindu-Arabic numbering systems during classical periods which were based on decimal systems and algorithms. Also, most of the Italian documents and existing ancient writing was found in Roman numerals. Roman numerals were considered safer for keeping important commercial transaction texts compared to the Hindu-Arabic system which could be easily altered (Williams, 2008). Italian Mathematics developed significantly during the 16th century when the contributions of Leonard Fibonacci were utilized in the development of the Fibonacci system of numbers useful in the stock market. Other major mathematicians during the 16th century who contributed immensely to Italian mathematics include NiccoloTartaglia and Francesco Bonaventura Cavalieri (Williams, 2008). These mathematicians developed unique ways of solving cubic equations as well as the invention of integral calculus and differential calculus which formed the foundation of modern mathematics. Italian mathematics also became an integral part of understanding astrology, physics, and thermodynamics.
The development of mathematics system in the United States and Canada during the colonial period among Native Americans exhibited complex use of geometric shapes to create symbols for various numeric systems and geometric and arithmetic operations. The Native American cultures considered the geometry and counting as the most fundamental mathematics during pre-colonial ages (Closs, 2010). The outstanding developments in American mathematics and science were the contribution of the famous scientists and mathematicians including Albert Einstein, Isaac Newton and BenjaminBanneker (Ellerton& Clements, 2012). Isaac Newton as a physicist, astronomer, and mathematician, made an immense contribution to the knowledge of calculus which was further developed and published by other mathematicians like Leibniz. After the independence, American mathematics witnessed a rapid expansion in American universities emphasized on research on mathematics leading to various inventions in statistics, axiomatics, topology, and American mathematics further thrived in the 19th and 20th century among the epicenters of mathematical discoveries globally (Ellerton& Clements, 2012).
Ancient Mexico was dominated by the Aztecs who practiced a very unique numbering system for determining measurements and taxations. The early numbering system in Mexico borrowed the concept of the Mayan vigesimal system in which large numbers were represented as a base-20. The paintings of ancient Aztecs retrieved dating to about the 16th century showed drawings and measurements expressed in the vigesimal numeric system (Galaz-García, et al., 2014). It is also identified that the arithmetic calculations were performed by the Aztecs in early Mexico and also some key principles of geometry in measurements acquired from the Mayans. It is also evident that the Zapotec writing, as well as Olmec writing and sequence of numbers, was fundamental in the development of Mexican mathematics (Galaz-García, et al., 2014). The coexistence of various cultures in ancient Mesoamerica influenced the development of writing and mathematics both in Mexico and America.
Closs, M. P. (2010). Native American Mathematics. Austin, TX: University of Texas Press.
Edwards, S. B. (2015). Ancient Maya. Edina, MN: ABDO.
Ellerton, N. F., & Clements, M. A. (2012). Rewriting the History of School Mathematics in North America 1607-1861: Springer Science & Business Media.
Ferreirós, J. (2015). Ancient Greek Mathematics. Mathematical Knowledge and the Interplay of Practices. doi:10.23943/princeton/9780691167510.003.0005
Galaz-García, F., Pardo Millán, J. C., & Solórzano, P. (2014). Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics. Contemporary Mathematics. doi:10.1090/conm/709
Imhausen, A. (2016). The Egyptian Number System. Mathematics in Ancient Egypt. doi:10.23943/princeton/9780691117133.003.0003
Williams, K. (2008). Mathematics in The Marches, Italy. The Mathematical Intelligencer, 31(2), 54-56. doi:10.1007/s00283-008-9017-7
Zhmud, L. (2012). Biography: Sources, Facts, and Legends. Pythagoras and the Early Pythagoreans, 61-104. doi:10.1093/acprof:oso/9780199289318.003.0003
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