History
There has long been a standard account of the development of geometry in ancient Egypt, followed by Greek mathematics and the emergence of deductive logic. The modern sense of the term mathematics, as meaning only those systems justified with reference to axioms, is however an anachronism if read back into history. Several ancient societies built impressive mathematical systems and carried out complex calculations based on proofless heuristics and practical approaches. Mathematical facts were accepted on a pragmatic basis. Empirical methods, as in science, provided the justification for a given technique. Commerce, engineering, calendar creation and the prediction of eclipses and stellar progression were practiced by ancient cultures on at least three continents.
Read more about this topic: Informal Mathematics
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“... the history of the race, from infancy through its stages of barbarism, heathenism, civilization, and Christianity, is a process of suffering, as the lower principles of humanity are gradually subjected to the higher.”
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