Below are some artifacts that show evidence for some of the earliest civilizations showing a vague mathematical ability and understanding.
The Ishango Bone:
Some of the earliest evidence of mathematical ability was discovered in the Democratic Republic of the Congo. Jean de Heinzelin de Braucourt (1920-1998) unearthed the Ishango Bone in 1950. The Ishango Bone is assumed to be made from a baboon bone (or the bone of another large, similar mammal) that dates back to the Upper Palaeolithic Period of human history (between 18,000 B.C. and 20,000 B.C. – about 20,000-25,000 years ago).
The bone has a series of etches and is therefore assumed to be some kind of tally stick (a system of counting that is still used in society today). It is also argued that the bones may have possibly been used for non-mathematical reasons and that perhaps the bone was simply just a handle the tally’s were just random engravings for a better grip. However, the engravings seem to be purposefully and carefully placed in non-random fashion, which means it was more likely used as a counting tool.
The bone consists of three columns. The first column suggests that this particular civilization had a vague understanding of doubling and halving – it starts with three tallies, which then double to six tallies. Then there are four tallies which double to eight tallies. Then there are ten tallies that halve to five tallies.
However, the other two columns are the most interesting. All the numbers represented by the tallies are odd (9, 11, 13, 17, 19, 21) – and even more impressive is the fact that the last column contains prime numbers (numbers that only have two factors – 1 and the number itself) between 10 and 20. The numbers engraved into the last two columns add together to 60 and 48 – both numbers of which are even and have factors of 12.
There are too many patterns (for example, the multiples of 12 and the prime numbers) on the Ishango bone alone for it to be considered a coincidence or non-mathematical object. When you couple this with the fact that there have been similar bones discovered in Swaziland (the Swaziland Lebombo bone assumed to be 37,000 year olds) and in Czechoslovakia (a wolf tibia assumed to be about 32,000 years old), this can easily be argued to be one of the oldest artifacts showing mathematical understanding in early historic cultures.
Quipu:
Another piece of evidence showing basic mathematical ability in historic cultures is a ‘quipus’. In 2005, in the Peruivian city, Caral, a quipu was unearthed and dated back to 3000 B.C. (about 5,000 years ago) to the existence of the ancient Incas.
Quipus were common devices used by the Ancient Incas to record and communicate information. They involved knotting individual pieces of string (that could range from 3 to 1000) in order to convey information (such as material resources, calendar information, and, more morbidly, a death calculator (those who were sacrificed victims for the gods). Different types of knots were tied to represent different numbers and different powers of ten.
What is striking about the quipu is that it shows that you don’t need to have developed a written language in order for mathematics to be used and thrive – civilizations have reached advanced ways of keeping records without the written words.
Plimpton 322:
The Plimpton 322 has been referred to as “one of the world’s most famous mathematical artifacts” (as stated by Eleanor Robson).
The Plimpton 322 is a Babylonian clay tablet, assumed to have been unearthed in Senkereh (Southern Iraq) and has been dated to about 1800 B.C. making it roughly 4000 years old. This clay tablet consists of 4 columns and 15 rows. The first three columns lists Pythagorean triples (whole integer numbers that fit into Pythagoras’s theorem ) whereas the fourth column simply lists the row number.
The fact that this Old Babylonian civilization were aware of Pythagorean triples was a massive achievement considering Pythagoras wouldn’t prove this theorem until about 2000 years later (between 570-490 B.C.). It has been theorised that the numbers in the table were simply the solutions for students who were studying, what we now refer to as algebra. If so, this means that this Old Babylonian civilization knew more that just Pythagorean triples.
References:
Pickover, Clifford. The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (Sterling Milestones). Sterling, 2012.
Swetz, Frank. “Mathematical Treasure: Ishango Bone | Mathematical Association of America.” Frank J. Swetz, www.maa.org/press/periodicals/convergence/mathematical-treasure-ishango-bone. Accessed 10 Dec. 2020.
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