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Unit 1

The Primes

1.2 Math at the Dawn of Time

TALLY STICKS

Evidence suggests that the exact beginning of mathematical thought, even the origin of the concept of a "number," predates the advent of written language. The earliest example of recorded mathematical symbols is a sequence of tally marks on the leg bone of a baboon found in Swaziland, dating to around 35,000 years ago. By contrast, the earliest known language writings date to around 6,500 years ago. It is not known for sure what the tally marks on the bone represent, but it is plausible that they represent a record of an early hunter's kills. These tally marks may represent numbers in application, but there may also be evidence that early humans were interested in properties of numbers themselves.

ISHANGO BONE Item 3060 / Oregon Public Broadcasting, created for Mathematics Illuminated, ISHANGO BONE (2008). Courtesy of Oregon Public Broadcasting.

Possible evidence of mathematics more sophisticated than counting comes from another bone dated ten thousand years younger than the Swaziland counting bone. Around 25,000 years ago, by the shores of Lake Edward (which today lies on the border between Uganda and Zaire), the Ishango people lived in a small fishing, hunting, and farming community. This settlement lasted for a few centuries before being buried in a volcanic eruption.

Excavations at this site turned up a bone tool handle with a series of interesting marks. The Ishango bone, as it is now called, has groups of markings, some of which represent primes. Although the exact meaning of these markings is still being debated, the current thought is that they represent some sort of lunar calendar. Regardless of the precise meaning of the markings, the artifact demonstrates that humans were thinking about mathematical concepts, perhaps even the concept of prime numbers, 25,000 years ago, well before the emergence of cities.

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CULTURAL MATH

QUIPU USED FOR COUNTING Item 2251 / Inca, QUIPU. USED FOR COUNTING (fifteen-early sixteenth century). Courtesy of Kathleen Cohen.

Jump 10,000 years forward and a bit to the east from the makers of the Ishango bone, and you're in the emerging Egyptian and Fertile Crescent civilizations. These civilizations had deep understanding of mathematics and used it to achieve unequalled engineering feats.

MATHEMATICS TABLET Item 2250 / Babylonian, MATHEMATICS TABLET SHOWING CALCULATIONS OF VOLUME (ca. 1635 BCE). Courtesy of Kathleen Cohen.

Babylonian clay tablets show an understanding of Pythagorean triples, centuries before the cult of Pythagoras appeared in Greece. However, these were not the only ancient civilizations to develop, presumably independently, familiarity with numbers and number relationships. Mathematical concepts may have spread naturally throughout Africa, and the Middle East, and Asia, but they also appeared early on in Central and South America.

CALENDAR RELIEF Item 2253 / Mayan, CALENDAR RELIEF (fifth-ninth century). Courtesy of Kathleen Cohen.

Evidence suggests that the development of mathematics in early cultures was tied to specific purposes. Much of early mathematical thought was focused on representing and understanding the movements of the heavens, as is evident in the Mayan long count calendar and the constellations of the zodiac. Elsewhere, such as in ancient China, mathematics was put to use in bookkeeping and other business activities. Math's development generally served practical purposes until about 600 BC, when the Greek philosophers began to explore the world of numbers itself.

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Next: 1.3 Number for Number's Sake: The Greeks


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