Ancient Greek Mathematics

Griechische Mathematik

The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.
Saint Augustine (354-430)

Poetry is the only place where the power of numbers proves to be nothing Odysseas Elytis, Nobel Prize Literature 1979

Greeks like Thales from the Ionian islands around 600 BC visited Egypt and Babylon. They acquired the practical knowledge accumulated over centuries and promoted it into Science. Greeks obtained Geometry as an art of measuring the land from the Egyptians as Herodotus describes. The influence of Greek mathematics continues through the ages. Arithmetic, music, geometry, and astronomy – pure number, applied number, stationary magnitude, and magnitude in motion respectively – began life in Plato’s Republic and constituted the quadrivium of sciences up to 1600 AD and later. Eudoxus and Archimedes exhaustion methods were only extended by Cauchy and Weierstrass. The discovery of a proof of Fermat’s last theorem in 1993-4 shows how even current mathematical activity originates in Greek mathematical activity. Also the last years we have some remarkable discoveries analyzing the work of Archimedes and Hipparchus. A characteristic Greek discovery that the square root of 2 is not a rational number is for me one of the best examples that Greeks were interested in true science. One has to think that how surprising it is to discover that you cannot express this number in the form a/b where a and b are integer numbers. You can approach it with an accuracy as good as you want if you choose very large numbers for a and b but whatever you choose it will be never exactly the square root of 2. So there is a special type of numbers, the irrational numbers. For engineering purposes even small numbers for a and b would be enough but the proof of the irrationality of the square root of 2, although so simple, shows what the difference is between engineering and pure science.



From Plato's Theaetetus to Gauss's Pentagramma Mirificum: A Fight for Truth (

  • Enquiries about the genesis of formal thinking and about syntactic knowledge representation

  • Individual Biographies from the University of St Andrews of the mathematical work of:

    Anaxagoras , Anthemius , Antiphon , Apollonius , Archimedes , Archytas , Aristaeus , Aristarchus , Aristotle , Autolycus of Pitane , Bryson , Callippus , Chrysippus , Cleomedes , Conon , Democritus , Dinostratus , Diocles , Dionysodorus , Diophantus , Domninus , Eratosthenes , Euclid , Eudemus of Rhodes , Eudoxus , Eutocius , Geminus , Heraclides of Pontus , Heron , Hipparchus , Hippias , Hippocrates , Hypatia , Hypsicles , Leucippus , Marinus of Neapolis , Menaechmus , Menelaus , Nicomachus , Nicomedes , Oenopides of Chios , Pappus , Perseus , Philon of Byzantium , Plato , Porphyry , Posidonius , Proclus , Ptolemy , Pythagoras , Serenus , Simplicius , Sporus , Thales , Theaetetus , Theodorus , Theodosius , Theon of Alexandria , Theon of Smyrna , Thymaridas , Xenocrates , Zeno of Elea , Zeno of Sidon , Zenodorus

    Ancient Greek Mathematics Greek and English Website

    Mathematics LINKS (including links to Biographies from Anaxagoras to Zenodorus)


    Suda On Line: Byzantine Lexicography