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:
“America is the only nation in history which miraculously has gone directly from barbarism to degeneration without the usual interval of civilization.”
—Georges Clemenceau (1841–1929)
“When we of the so-called better classes are scared as men were never scared in history at material ugliness and hardship; when we put off marriage until our house can be artistic, and quake at the thought of having a child without a bank-account and doomed to manual labor, it is time for thinking men to protest against so unmanly and irreligious a state of opinion.”
—William James (1842–1910)
“This above all makes history useful and desirable: it unfolds before our eyes a glorious record of exemplary actions.”
—Titus Livius (Livy)