Timeline of mathematics

This is a timeline of pure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm. ca. 70,000 BC – South Africa, ochre rocks adorned with scratched geometric patterns (see Blombos Cave). ca. 35,000 BC to 20,000 BC – Africa and France, earliest known prehistoric attempts to quantify time (see Lebombo bone). c. 20,000 BC – Nile Valley, Ishango bone: possibly the earliest reference to prime numbers and Egyptian multiplication. c. 3400 BC – Mesopotamia, the Sumerians invent the first numeral system, and a system of weights and measures. c. 3100 BC – Egypt, earliest known decimal system allows indefinite counting by way of introducing new symbols. c. 2800 BC – Indus Valley Civilisation on the Indian subcontinent, earliest use of decimal ratios in a uniform system of ancient weights and measures, the smallest unit of measurement used is 1.704 millimetres and the smallest unit of mass used is 28 grams. 2700 BC – Egypt, precision surveying. 2400 BC – Egypt, precise astronomical calendar, used even in the Middle Ages for its mathematical regularity. c. 2000 BC – Mesopotamia, the Babylonians use a base-60 positional numeral system, and compute the first known approximate value of π at 3.125. c. 2000 BC – Scotland, carved stone balls exhibit a variety of symmetries including all of the symmetries of Platonic solids, though it is not known if this was deliberate. 1800 BC – Egypt, Moscow Mathematical Papyrus, finding the volume of a frustum. c. 1800 BC – Berlin Papyrus 6619 (Egypt, 19th dynasty) contains a quadratic equation and its solution. 1650 BC – Rhind Mathematical Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents one of the first known approximate values of π at 3.