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
Famous quotes containing the word history:
“Regarding History as the slaughter-bench at which the happiness of peoples, the wisdom of States, and the virtue of individuals have been victimized—the question involuntarily arises—to what principle, to what final aim these enormous sacrifices have been offered.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“The disadvantage of men not knowing the past is that they do not know the present. History is a hill or high point of vantage, from which alone men see the town in which they live or the age in which they are living.”
—Gilbert Keith Chesterton (1874–1936)
“I believe that in the history of art and of thought there has always been at every living moment of culture a “will to renewal.” This is not the prerogative of the last decade only. All history is nothing but a succession of “crises”Mof rupture, repudiation and resistance.... When there is no “crisis,” there is stagnation, petrification and death. All thought, all art is aggressive.”
—Eugène Ionesco (b. 1912)