The earliest records of advanced, organized mathematics (beyond just counting) date back to the ancient Mesopotamian country of Babylonia and to Egypt of the fourth millennium b.c.. The Egyptian civilization, one of the world's oldest, developed in the valley of the Nile. Its study and use of mathematics developed only in response to the practical needs within agriculture, business, and industry. Specifically, Egyptian mathematics was primarily arithmetic, with an emphasis on measurement, surveying, and calculation in geometry. Its use was elementary, with no trace of the necessity of later abstract mathematical concepts such as proofs and axioms. This mathematics was generally arrived at by trial and error as the way to obtain desired results. However, no records exist that show how the Egyptians reached their conclusions. It is true, though, that they possessed advanced mathematical knowledge, for without it their accomplishments in engineering, astronomy, and...