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I have include three links. One is a book about Inca mathematical ideas. The Incas did not have a written language which makes it difficult to know its history. Further, mathematical ideas develop slowly and are pass down from generations without formal records, making a "start date" nearly impossible. Certainly, the system of counting existed prior to 1532, which marks the end of the Inca empire. One link says the empire existed for approximately 100 years, but certainly mathematics in the Inca society could have been much older.
The Incas used the sun and moons position in the sky to tell time
The invention is Quipu..
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