During the Forum of Philosophy – Reflections on China-West Cultural Exchanges
Held in Athens 7-10 August, 2013
The geographical partition of Greece both mountains and numerous islands dictated its economy, which upon the islands, due to commercial travels the trade attended a remarkable increase. Moreover this geographical partition also dictated the representation of a govermental system , which was based on the structure of the city-state. Thus by definition the city-state controlled a limited number of the population, namely around a few thousand. Either monarchical or democratical , often referred only by name , the city-state was ruled by laws and usually possessed a flourishing economy .
Around the 6th century B.C. this was the case of the Ionian coasts where the wise men ( the word philosopher was introduced in Plato’s epoch ) abolished the cosmogony for the cosmology by studying the real constitution of nature . This movement is known as the passage from the mythological interpretation of nature to the rational one. Thus the rational inquiry commenced in order to attend the truth in philosophy, whereas mathematics constituted its subset. Upon these coasts was born the concept of mathematical proof as a turning point in the history of mathematics, as well as in the history of science.
From the History of Eudemus we are informed that the concept of mathematical demonstration is attributed to Thales of Miletus ( c.624-597 B.C.), who “discovered many propositions and disclosed the underlying principles of many others to his successors “.
Pythagoras ( c.572-497 B.C ) who for political reasons abandoned his native island of Samos ,formed a philosophical school in Croton , in Southern Italy. He created a mathematical type of philosophy whose main doctrine was that ” the integer number is the substance of all things “. In reality the Pythagoreans considered that the basis of all natural phenomena was ruled by numbers , as well as the basis of the universe. Moreover Pythagoras discovered that the harmonics of music were expressed by numerical ratios.
The Platonic Academy (founded in Athens c. 385 ) constituted the highest institution , where scholars under the guidance of Plato ( 429-347 B.C.) were initiated to philosophy, as well as to mathematics . In the Republic, he discussed the type of an appropriate education in order to rule the ideal state. First of all a future monarch is required to learn: arithmetics , geometry ( plane and solid ) , astronomy and harmonics (music ) .” It has a great power of leading the mind upwards and forcong it to reason about pure numbers ,( while ) refusing to discuss collections of material things which can be seen and touched “( Plato , Republic VII 525 transl. by F. Conford . London Oxford University Press 1941) It may be stressed that for Plato , the study of geometry : drwas the soul trowards thruth”.
Euclid’s Elements of Geometry constrituted one of the main themes of the ancient Greek inheritance, which was ruled by the Aristotelian logic. It remains aa an incomparable model of pure mathematics with precise definitions , well ordered axioms , theorems and logically coherent proofs.
At the third and early second centuries B.C. Greek mathematics were dominated by Archimedes of Suracuse (c.287-212B.C.) and Apollonius of Perge ( c.250- 175 B.C.). The first one conceived and elaborated the beginnings
of the infinitesimal calculus , from the ” limit” methods of Eudoxus . He also discovered the law of the lever and its applications in order to find centers of gravity and the basic principles of hydrostatics.
Apollonius in his main treatise the Conics were developed in a corpus the important properties for these curves, which later in the hands of Kepler became thr ideal instrument to express the laws of planetery motions .
Hypatia (c.355-415), Theon’s daughter, marked the end of Greek mathematics.She taught Plato and Aristotle, considering philosophy as a way of religious misticism. She also completed her father’s commentaries on Ptolemy’s Almagest , she worked on the edition of Archimedes’ measurement of the circle , on Apollonius’ Conics and on Diophantus’ Arithmetica. Moreover she trid to preserve the ancient Greek cultural inheritance in Alexandria , where all the institutions the ,Museum .the library and the temples collapsed due to fanatisme of the forts christians .
Ancient Greek and Chinese mathematics: a few commom aspects
The initiation of the rulers to mathematics
The measurement of the hight of a pagoda in Liu Hui’s treatise and the measuremnt of the pyramid by Thales
The mysticism of numbers
Abacus ( suan phan ) and Salamis Abacus
Geometry ( mohist definitions ) – Euclid’s definitions
Theorem of Pythagoras ( Hsuan Thy )
Evaluation of π ( Han arithmetics )
Conics sections