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<p>The Upaniṣads, foundational texts of Indian metaphysical thought composed between 800 BCE and 200 BCE, employ mathematical symbolism, recursive structures, and pre-formal mathematical reasoning to articulate profound cosmological and philosophical concepts. These texts use numbers as metaphors for unity, multiplicity, and transcendence, underpinning doctrines such as non-duality (<i>advaita)</i>, the fivefold self, and the dissolution of individuality into the ultimate reality <i>(Brahman</i>). This interdisciplinary study explores how numerical constructs, infinity, and geometric imagery reflect philosophical ideas, contextualizing them within the Vedic mathematical tradition and drawing comparisons with Pythagorean, Platonic, Chinese, and Islamic philosophical traditions. By highlighting the integration of logic and spirituality, this paper underscores the Upaniṣads’ enduring relevance to contemporary epistemology, metaphysics, and the philosophy of mathematics. Through textual analysis, comparative philosophy, and historical contextualization, it reveals the Upaniṣads’ unique synthesis of mathematical and metaphysical thought, offering insights into their potential dialogue with modern disciplines such as cognitive science and artificial intelligence.</p>

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Mathematical Symbolism and Philosophical Ideas in the Upaniṣads: A Cross-Disciplinary Inquiry

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Satish Kumar Singh

摘要

The Upaniṣads, foundational texts of Indian metaphysical thought composed between 800 BCE and 200 BCE, employ mathematical symbolism, recursive structures, and pre-formal mathematical reasoning to articulate profound cosmological and philosophical concepts. These texts use numbers as metaphors for unity, multiplicity, and transcendence, underpinning doctrines such as non-duality (advaita), the fivefold self, and the dissolution of individuality into the ultimate reality (Brahman). This interdisciplinary study explores how numerical constructs, infinity, and geometric imagery reflect philosophical ideas, contextualizing them within the Vedic mathematical tradition and drawing comparisons with Pythagorean, Platonic, Chinese, and Islamic philosophical traditions. By highlighting the integration of logic and spirituality, this paper underscores the Upaniṣads’ enduring relevance to contemporary epistemology, metaphysics, and the philosophy of mathematics. Through textual analysis, comparative philosophy, and historical contextualization, it reveals the Upaniṣads’ unique synthesis of mathematical and metaphysical thought, offering insights into their potential dialogue with modern disciplines such as cognitive science and artificial intelligence.