Mathematical
The 168 etchings on the bone are ordered in three parallel columns along the length of the bone, each marking with a varying orientation and length.[1] The first column, or central column along the most curved side of the bone, is referred to as the M column, from the French word milieu (middle).[1] The left and right columns are respectively referred to as G and D, or gauche (left) and droite (right) in French.[1] The parallel markings have led to various tantalizing hypotheses, such as that the implement indicates an understanding of decimals or prime numbers. Though these propositions have been questioned, it is considered likely by many scholars that the tool was used for mathematical purposes, perhaps including simple mathematical procedures or to construct a numeral system.[4]
Discoverer of the Ishango bone, de Heinzelin, suggested that the bone was evidence of knowledge of simple arithmetic, or at least that the markings were "deliberately planned".[1][5] He based his interpretation on archaeological evidence, comparing "Ishango harpoon heads to those found in northern Sudan and ancient Egypt".[6] This comparison led to the suggestion of a link between arithmetic processes conducted at Ishango with the "commencement of mathematics in ancient Egypt."[6] The third column has been interpreted as a "table of prime numbers", as column G appears to illustrate prime numbers between 10 and 20,[1] but this may be a coincidence.[4] Historian of mathematics Peter S. Rudman argues that prime numbers were probably not understood until the early Greek period of about 500 BCE, and were dependent on the concept of division, which he dates to no earlier than 10,000 BCE.[9]
More recently, mathematicians Dirk Huylebrouck and Vladimir Pletser have proposed that the Ishango bone is a counting tool using the base 12 and sub-bases 3 and 4, and involving simple multiplication, somewhat comparable to a primitive slide rule. However, they have concluded that there is not sufficient evidence to confirm an understanding of prime numbers during this time period.[1][2][10]
Anthropologist Caleb Everett has also provided insight into interpretations of the bone, explaining that "the quantities evident in the groupings of marks are not random", and are likely evidence of prehistoric numerals. Everett suggests that the first column may reflect some "doubling pattern" and that the tool may have been used for counting and multiplication and also possibly as a "numeric reference table".[4]
Astronomical
Alexander Marshack, an archaeologist from Harvard University, speculated that the Ishango bone represents numeric notation of a six-month lunar calendar after conducting a "detailed microscopic examination" of the bone.[6][1][2][7] This idea arose from the fact that the markings on the first two rows adds up to 60, corresponding with two lunar months, and the sum of the number of carvings on the last row being 48, or a month and a half.[6] Marshack generated a diagram comparing the different sizes and phases of the Moon with the notches of the Ishango bone.[6] There is some circumstantial evidence to support this alternate hypothesis, being that present day African societies utilize bones, strings, and other devices as calendars.[1] However, critics in the field of archaeology have concluded that Marshack's interpretation is flawed, describing that his analysis of the Ishango bone confines itself to a simple search for a pattern, rather than an actual test of his hypothesis.[7]
This has also led Claudia Zaslavsky to suggest that the creator of the tool may have been a woman, tracking the lunar phase in relation to the menstrual cycle.[11][12]
Other explanations
Mathematician Olivier Keller warns against the urge to project modern culture's perception of numbers onto the Ishango bone.[2] Keller explains that this practice encourages observers to negate and possibly ignore alternative symbolic materials, those which are present in a range of media (on human remains, stones and cave art) from the Upper Paleolithic era and beyond which also deserve equitable investigation.[2]
Dirk Huylebrouck, in a review of the research on the object, favors the idea that the Ishango bone had some advanced mathematical use, stating that "whatever the interpretation, the patterns surely show the bone was more than a simple tally stick."[1][6] He also remarks that "to credit the computational and astronomical reading simultaneously would be far-fetched", quoting mathematician George Joseph, who stated that "a single bone may well collapse under the heavy weight of conjectures piled onto it."[6] Similarly, George Joseph, in "The Crest of the Peacock: Non-European Roots of Mathematics" also stated that the Ishango bone was "more than a simple tally." Moreover, he states that "certain underlying numerical patterns may be observed within each of the rows marked."[13] But, regarding various speculative theories of its exact mathematical use, concluded that several are plausible but uncertain.