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:
“Every generation rewrites the past. In easy times history is more or less of an ornamental art, but in times of danger we are driven to the written record by a pressing need to find answers to the riddles of today.... In times of change and danger when there is a quicksand of fear under men’s reasoning, a sense of continuity with generations gone before can stretch like a lifeline across the scary present and get us past that idiot delusion of the exceptional Now that blocks good thinking.”
—John Dos Passos (1896–1970)
“Considered in its entirety, psychoanalysis won’t do. It’s an end product, moreover, like a dinosaur or a zeppelin; no better theory can ever be erected on its ruins, which will remain for ever one of the saddest and strangest of all landmarks in the history of twentieth-century thought.”
—Peter B. Medawar (1915–1987)
“The history of philosophy is to a great extent that of a certain clash of human temperaments.”
—William James (1842–1910)