Most ancient cultures primarily wrote out their mathematical texts in words for several reasons:
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Literacy Levels: In many ancient societies, literacy rates were low, and only a small percentage of the population could read or write. Using words made mathematical concepts more accessible to a larger audience, particularly those who might not have been formally educated in mathematics.
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Oral Tradition: Many ancient cultures relied heavily on oral traditions for knowledge transmission. Mathematical practices and concepts were often communicated verbally before being transcribed. Writing out problems in words maintained this oral tradition and made it easier for practitioners to share and teach mathematical ideas.
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Contextual Understanding: Writing problems in words allowed for a clearer contextual understanding of the mathematical ideas being presented. It provided details about the specific situations and relationships involved, which might have been lost in symbolic notation. This context was often crucial for applying mathematical solutions to real-life problems.
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Limited Symbolism: The development of mathematical symbols and notation came much later in history. Early civilizations did not have a standardized system of symbols for mathematical operations, leading to a reliance on descriptive language. As mathematics evolved, so did the symbolic notations, but even then, complex ideas often still required elaborate verbal explanations.
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Teaching Methodologies: Instruction in mathematics typically took place in a hands-on manner, with students learning through examples and explanations. Verbal descriptions fit well with teaching philosophies that emphasized understanding through discussion and dialogue, rather than abstract notation.
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Cultural Preferences: Different cultures had varying philosophical views towards mathematics. The Greeks, for instance, valued rigorous proof and logical reasoning, while others focused on practical application and problem-solving, which often led to a verbal explanation approach. The cultural context influenced how mathematical knowledge was recorded and shared.
In summary, the reliance on verbal descriptions for mathematical texts in ancient cultures was shaped by factors such as literacy rates, oral traditions, the need for contextual understanding, limited symbolism, teaching methodologies, and cultural preferences. These factors combined to create a mathematical environment where written language was favored over symbolic notation.