Speech of Christina Fili Professor, member of Greece China Association – Science Department

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