Today's Reading
1. IN THE BEGINNING
Our species, Homo sapiens, has been around for 300,000 years but, as far as we can tell, mathematics is a relatively recent invention. Many artifacts have been lost or simply haven't lasted, so we have only a partial picture. The first traces of human mathematical activity start to appear around 20,000 years ago, in the form of scratched tally marks on animal bones.
One of the oldest and most famous of these is the Ishango bone, which was found along the border between modern-day Uganda and the Democratic Republic of the Congo and dates from 20,00018,000 BCE. The bone is probably the fibula of a baboon, though it could be from a wolf or similar-sized animal. It has a piece of quartz attached to the top, suggesting it may have been used as a tool. Running down its length are three columns populated with tally marks. The scratches may be there simply for gripping the tool, but there may also be more to them than that.
The marks on the first column add up to 48, and the marks on the second and third columns add up to 60. Each of the columns is split into distinct segments, with the third column's split the most interesting. The sixty notches there are split into groups of 11, 13, 17 and 19. These are prime numbers—numbers that can only be divided by 1 and themselves. Prime numbers are undoubtedly some of the most important numbers in mathematics. As later mathematicians will discover, they are the building blocks of all other numbers. To see them here, on a carving from more than 20 millennia ago, is like receiving a message from an alien. It is exhilarating and surprising—yet it is also hard to know exactly what it means.
The mathematical patterns could just be coincidence, but they could also show the numerical sophistication of our ancient ancestors. The numbers 48 and 60 are 4 × 12 and 5 × 12 respectively, hinting that the people who made the scratches had a number system built around the number 12 (rather than 10, as we use today). One of the earliest number systems we know of was built around the number 60, so this is far from implausible. Another option is that the bone was a six-month lunar calendar, with the notches representing phases of the moon. Another, put forward by twentieth-century mathematician Claudia Zaslavsky, was that the bone may have been used by a woman to track her menstrual cycle. Measuring the coming and going of the seasons for planting seeds, or when rivers would flood, also seems like a reasonable possibility. Similar bones have been discovered in other parts of Africa and elsewhere. For tens of thousands of years, it appears that counting has been an integral part of being human.
The very earliest surviving signs of mathematics are much like the Ishango bones. Such relics may show a giant conceptual leap for our species, a moment when we began to think in the mathematical abstract—or they may simply be scratches. Remains of ancient monuments and pottery often feature elaborate geometric designs, but does that mean the makers understood the mathematics behind the displays, or did they just like the patterns?
The earliest mathematics our species developed may not have been written down or have left any physical trace. More contemporary evidence shows that a deep understanding of mathematics can develop through speech alone. The Akan people of West Africa, for example, had a sophisticated set of mathematical tools for dealing with weights and measures that was passed down by word of mouth. The oral nature of their mathematical system made it perfect for doing business with Arab and European merchants between the fifteenth and late nineteenth centuries. However, it also meant that it was demolished by hundreds of years of the Atlantic slave trade. After researchers managed to reconstruct how it worked in 2019, using the few remaining artifacts held in museums, they suggested the system should be given UNESCO World Heritage status because it was so spectacular.
In this case, the system was in use until fairly recently and some artifacts still exist, but there have probably been many other oral mathematical systems that are now lost to time. Counting, and its consequences, was probably integral to many communities and civilizations that never had the need to write anything of this nature down. Or if they did, any trace of it has now perished. These first moments of mathematics are vague and will remain so forever. However, with the advent of written language and the rise of some of the world's biggest civilizations, the picture becomes a little clearer.
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