Mangareva is home to just 2,000 inhabitants. The island is a tiny 18 square kilometres and is located halfway between Easter Island and Tahiti. Yet on this small, remote island, the ancient inhabitants were more mathematically advanced than the rest of Europe when they invented a numerical system for trading.

Research conducted last year and published in the journal Proceedings of the National Academy of Sciences, revealed that the indigenous people of the Polynesian Island invented a binary number system , similar to the one used by computers to calculate, centuries before Western mathematicians did. Andrea Bender, a cognitive scientist at the University of Bergen in Norway, and her colleague Sieghard Beller, were studying the Mangarevans when they noticed that the inhabitants had words for the numbers 1 to 10, but for numbers 20 to 80 they used a binary system, with separate, one-word terms for 20, 40, and 80. For really large numbers, they used powers of 10 up to at least 10 million.

The remote island of Mangareva. Source: Wikipedia

"Those were probably the numbers that were most frequent in their trading and redistribution systems," said Bender. "For that specific range, it was helpful to have these binary steps that make mental arithmetic much easier — they didn't have a writing or notational system, so they had to do everything in their mind."

One of the most famous mathematicians of the 17 th century, Gottfried Wilhelm Leibniz, is known to have invented a binary numeral system. Nowadays, binary numbers – where each position is written as a 0 or 1 – form the foundation of all modern computing systems. But the study showed that the Manareva islanders were using a combined decimal and binary system which had died out by the mid-1400s.

Gottfried Willhelm Leibniz

The Mangarevans traded across long distances for items such as turtles, octopuses, coconut and breadfruit with people on the Marquesas Islands, Hawaii and the islands around Tahiti. It is believed that the binary system helped ancient people to keep track of their trading activities. What is more surprising is that they were able to use a complex number system without needing notation.

The numbering scheme may be the only known example of an extensive binary numeral system that predates Leibniz.

By April Holloway