Greek mathematics refers to the contributions made by ancient Greek scholars and mathematicians in mathematics. The Greeks, especially during the classical period of the 5th–4th centuries BC, played an important role in the development of mathematics and laid the foundation for many basic concepts still in use today.
Here are some of the key figures and achievements in Greek mathematics:
Thales of Miletus (c. 624 BC – c. 546 BC): Thales is often considered the first Greek mathematician.
Although little is known about his work, it is credited that he introduced deductive reasoning and applied geometry to various problems, such as calculating the height of pyramids.
Pythagoras of Samos (c. 570 BC – c. 495 BC): Pythagoras is known for Pythagorez's theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a^2+b^2=c^2). This theorem revolutionized the study of geometry and has countless applications.
Euclid of Alexandria (c. 300 BC): Euclid's most famous work is The Elements, a comprehensive compilation of mathematical knowledge of his time.
It consists of 13 books covering topics such as geometry, number theory, and irrational numbers. Euclid's work laid the foundation for rigorous mathematical proofs and logical reasoning.
Archimedes of Syracuse (c. 287 BC – c. 212 BC): Archimedes made significant contributions to various fields of mathematics, including geometry, calculus, and mechanics.
He developed methods for calculating area and volume, such as the exhaustion method. Archimedes also proposed the mathematical principles of levers and pulleys.
Apollonius of Perga (c. 262 BC – c. 190 BC): Apollonios is known for his study of conic curves, which are curves formed by cutting cones. He introduced ellipses, parabolas, and hyperbolas and studied their properties extensively.
Alexander's Diophantine (circa 3rd century AD): Diophantine is often referred to as the "father of algebra." His work Arithmetic introduced symbolic algebra and pioneered the study of multiple unknown equations. The Diophantine equation named after him involves finding integer solutions to polynomial equations.
These mathematicians laid the foundations for various branches of mathematics and made lasting contributions to the field. Their work laid the foundation for later mathematical developments, and their ideas have been studied and built to this day.
Here are some additional contributions and features of Greek mathematics:
Eratostine of Guruni (c. 276 BC – c. 194 BC): Eratostini is known for accurately calculating the circumference of the earth using simple geometric principles.
He also made significant contributions to number theory, prime numbers, and the Eratostini sieve (a method of finding prime numbers).
Hipparchas of Nicaea (c. 190 BC – c. 120 BC): Hiparchas is considered one of the greatest astronomers of antiquity.
He developed the first known triangular table, the "chord table", which linked the length of a chord in a circle to its corresponding angle. This work laid the foundation for trigonometry as a mathematical discipline.
Ptolemy (90 BC – 168 BC): Ptolemy was an astronomer, mathematician, and geographer best known for his book Almagest.
This influential paper synthesized the astronomical knowledge of the time and proposed a comprehensive mathematical model of the motion of celestial bodies. Ptolemy's model of the geocentric universe was widely accepted for centuries.
Hellenistic mathematics: During the Hellenistic period (323 BC – 31 BC), Greek mathematics underwent further development.
Mathematicians like Euclid, Archimedes, and Apollo continued to influence mathematical thought, and new scholars emerged, such as Heron of Alexandria, known for his study of mechanics and invention of various machines.
Geometric construction: Greek mathematicians were particularly interested in geometric constructions using only a compass and ruler. They explored issues such as triparting angles, doubling cubes, and squaring circles.
Although the Greeks could not solve all these problems, their research led to important discoveries in geometry.
Bibliography:
【1】Heath，T.L.（1981）。 History of Greek Mathematics (2 volumes). Oxford University Press. This comprehensive book by Thomas Little Heath details Greek mathematics, covering various mathematicians and their contributions.
[2] Boyer, C.B., and Merzbach, U.C. (2010). History of Mathematics (3rd ed.), John Wiley & Sons. This textbook provides a comprehensive overview of the history of mathematics, including sections dedicated to Greek mathematics.
【3】Netz，R.（2004）。 The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations. Cambridge University Press. Reviel Netz explores the development of Greek mathematics and its shift from problem-solving methods to the use of equations and proofs.
[4] Knorr-Bremse (1986). An ancient tradition of geometric problems. Birkhäuser。 Wilbur Knorr-Bremse studied the geometric problems posed and solved by Greek mathematicians, revealing their methods and reasoning.
[5] Van der Waalden, B.L. (1983). Science Awakens II: The Birth of Astronomy. Knodhof International Publishing House. Bartel Leendert van der Waerden's book explores the development of ancient Greek astronomy, including the mathematical aspects of the discipline.
