How many different number systems have humans invented?

Not everyone counts in tens - the Babylonians used base-60, which is why we still have 60 seconds in a minute and 360 degrees in a circle.

The answer

Humans have developed dozens of distinct number systems throughout history. The base-10 (decimal) system dominates today, likely because of our ten fingers, but the Babylonians used base-60 (sexagesimal) from around 3100 BCE - giving us 60-minute hours, 60-second minutes, and 360-degree circles. The Maya civilization used base-20 (vigesimal), counting fingers and toes. The Yuki people of California used base-8 (octal), counting the spaces between fingers. Binary (base-2), formalized by Leibniz in 1679, now underpins all computing. The Telefol people of Papua New Guinea use a base-27 body-counting system, tapping 27 body parts in sequence. French preserves vigesimal traces: quatre-vingts (80) means 'four twenties.' Some Aboriginal Australian languages count only one-two-many, while the Pirahã have no exact number words at all.

Source: Wikipedia

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