... were lengths to which their numbers did not correspond (called irrational lengths), their study of number largely came to halt. For the Greeks, with their emphasis on geometry, mathematics was about number and shape. Only with Greeks did mathematics change from a collection of techniques for measuring, counting, and accounting into an academic discipline having both aesthetic and religious elements. At the start of the Greek period, Thales introduced the idea that precisely stated assertions of mathematics could be logically proved by formal argument. For the Greeks, this approach culminated in the publication, around 350BC, of Euclid's mammoth thirteen volume text Elements, reputedly the second most widely circulated book of all time after the Bible. After the Greeks, although mathematics advanced in several parts of the world - notably in Arabia and China - its nature did not change until the middle of the seventeenth century, when Sir Isaac Newton (in England) ...

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