mathematic now

Long before the earliest written records, there are drawings that 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.[1] Also prehistoric artifacts discovered in Africa and France, dated between 35,000 BC and 20,000 BC,[citations needed] indicate early attempts to quantify time.[citations needed] 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.[2][3]

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[4] 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 from as early as the 5th millennium BC in Egypt,[citations needed] and then subsequently England and Scotland from the 3rd millennium BC,[5] incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design,[citations needed] as well as a possible understanding of the measurement of time based on the movement of the stars. From circa 3100 BC, Egyptians introduced the earliest known decimal system,[citations needed] allowing indefinite counting by way of introducing new symbols. Circa 2600 BC, Egypt's massive construction techniques represent not only precision surveying but also suggest knowledge of the golden ratio.[citations needed]

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.[6]