Since its discovery, the Sanxingdui Culture has been thoroughly investigated by archaeological, sociological, psychological, and geographic scholars to reveal its political, economic, and cultural landscape. However, the absence of written historical materials by this culture has left a mystery that cannot be fully revealed by modern technology. In this study, a mathematical method based on rigorous and logical reasoning was used to eliminate the influence of subjective factors to the greatest extent possible, which has unparalleled advantages, particularly in deducing the evolution of human history in the absence of written historical materials. First, the concept of ownership was established using the proposed mathematical model. The advantages and disadvantages of the public ownership clan economy and that of private ownership slavery were then compared. The comparisons revealed that a private ownership economy based on slavery was an inevitable choice for the Sanxingdui Culture, which resulted in the impossibility of the emergence of a written language. The use of a mathematical model to effectively interpret the mystery of Sanxingdui Culture not only achieves the goal of using mathematical language to bridge the gap between natural and social sciences but also lays a solid foundation for the unified and coordinated development of the two disciplines.

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