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!! Lebombo Bone

One of the oldest mathematical artifacts known, a small piece of the fibula of a baboon, found near Border Cave in the Lebombo Mountains between South Africa and Swaziland. Discovered in the 1970s during excavations of Border Cave and dated about 35,000 B.C., the Lebombo bone is marked with 29 clearly defined notches. This suggests it may have been used as a lunar phase counter, in which case African women may have been the first mathematicians since keeping track of menstrual cycles requires a lunar calendar. Certainly, the Lebombo bone resembles calendar sticks still used by Bushmen in Namibia.

!! Ishango Bone

The Ishango bone is the oldest known object containing logical carvings. It was discovered in the Congo in 1960, and has been dated to be 20,000 years old. The bone contains the sequences of notches:

11, 21, 19, 9 11, 13, 17, 19 and 3, 6, 4, 8, 10, 5, 5, 7

* http://en.wikipedia.org/wiki/Ishango_bone

* http://www.simonsingh.net/The_Ishango_Bone.html

It is said that the markings signify that there was a deeper understanding of numbers. It is said that they were fascinated by prime numbers too: row (b) contains all the 4 primes between 10 and 20. row (a) is said to be craved based on the knowledge that 10 - 1, 20 - 1, 20 + 1, 10 + 1 represent some sort of pattern: these are the numbers that differ from 10 and 20 by 1. Row (c) seems to show knowledge of doubling (2 × 3 = 6, 2 × 4 = 8, 2 × 5 = 10), halving ( 6/3 = 8/4 = 10/5 = 2 ) and difference of 2 ( 7 - 5). Definitely this interpretation is highly controversial, as all these seem too advance for the Palaeolithic era.