When the archaeologists’ artifact-proven history of mathematics opens 4,000 years ago in Babylon and Mesopotamia, it is already a very sophisticated science. Mathematics may well have had its beginnings much earlier in India or Indochina, as it is an art and science that has traveled consistently westward. Over 3,000 years ago the Greeks made further magnificent contributions to geometry, algebra, and calculation. Then about 2,000 years ago the Roman Empire all but obliterated mathematics. A little more than 1,000 years ago Arabs and Hindus traveling through North Africa began to restore some of the ancient mathematics to the westward-evolving culture. When al-Khwarizmi’s original A.D. 800 treatise on algebra was republished in Latin in Carthage in 1200, it required a further 200 years for his elucidation of the function of zero-the cipher-to be diffused into the university systems of Europe .