Long before the earliest written records, there are drawings that do indicate a knowledge of mathematics and of measurement of time based on the stars. For example, paleontologists have discovered ochre rocks in a cave in South Africa adorned with scratched geometric patterns dating back to c. 70,000 BC.[2] Also prehistoric artifacts discovered in Africa and France, dated between 35,000 BC and 20,000 BC,[3] indicate early attempts to quantify time.[4]
Evidence exists that early counting involved women who kept records of their monthly biological cycles; twenty-eight, twenty-nine, or thirty scratches on bone or stone, followed by a distinctive scratching on the bone or stone, for example. Moreover, hunters had the concepts of one, two, and many, as well as the idea of none or zero, when considering herds of animals.[5][6]
The Ishango Bone, found in the area of the headwaters of the Nile River (northeastern Congo), dates as early as 20,000 BC. One common interpretation is that the bone is the earliest known demonstration[7] of sequences of prime numbers and Ancient Egyptian multiplication. Predynastic Egyptians of the 5th millennium BC pictorially represented geometric spatial designs. It has been claimed that Megalithic monuments in England and Scotland from the 3rd millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.[8]
The earliest known mathematics in ancient India dates back to circa 3000-2600 BC in the Indus Valley Civilization (Harappan civilization) of North India and Pakistan, which developed a system of uniform weights and measures that used the decimal system, a surprisingly advanced brick technology which utilised ratios, streets laid out in perfect right angles, and a number of geometrical shapes and designs, including cuboids, barrels, cones, cylinders, and drawings of concentric and intersecting circles and triangles. Mathematical instruments discovered include an accurate decimal ruler with small and precise subdivisions, a shell instrument that served as a compass to measure angles on plane surfaces or in horizon in multiples of 40–360 degrees, a shell instrument used to measure 8–12 whole sections of the horizon and sky, and an instrument for measuring the positions of stars for navigational purposes. The Indus script has not yet been deciphered; hence very little is known about the written forms of Harappan mathematics. Archeological evidence has led some historians to believe that this civilization used a base 8 numeral system and possessed knowledge of the ratio of the length of the circumference of the circle to its diameter, thus a value of π.[9] Dating from the Shang Dynasty (1600—1046 BC), the earliest extant Chinese mathematics consists of numbers scratched on tortoise shell [1] [2]. These numbers use a decimal system, so that the number 123 is written (from top to bottom) as the symbol for 1 followed by the symbol for a hundred, then the symbol for 2 followed by the symbol for ten, then the symbol for 3. This was the most advanced number system in the world at the time and allowed calculations to be carried out on the suan pan or Chinese abacus. The date of the invention of the suan pan is not certain, but the earliest written reference was in AD 190 in the Supplementary Notes on the Art of Figures written by Xu Yue.