In Episode 37 of Ancient Code, Modern Mind, host Harsh Rain explores the dynamic Indian scientific dialogue following Aryabhata’s Aryabhatiya, focusing on Brahmagupta’s critiques and the Kerala School’s advancements. Building on Episode 36’s comparison with Ptolemy, this episode examines Brahmagupta’s Brāhmasphuṭasiddhānta (628 CE), which sharply criticized Aryabhata’s Earth rotation theory (Golapāda, Gola.9), favoring a static Earth, and disputed parameters like lunar revolutions and Pi’s value (using √10 vs. Aryabhata’s 3.1416). Despite the critique, Brahmagupta’s engagement advanced Indian astronomy by refining Aryabhata’s Kuṭṭākāra method and fostering debate, establishing schools like Ārya-pakṣa and Brāhma-pakṣa. Centuries later, the Kerala School (14th–16th centuries), led by Mādhava of Sangamagrāma, extended Aryabhata’s sine-based trigonometry (Jyā) with infinite series for sine, cosine, and arctangent, precursors to modern calculus, and computed Pi to 11 decimal places. Nīlakaṇṭha Somayājī’s geo-heliocentric model and Jyeṣṭhadeva’s Yuktibhāṣā further refined astronomical models and documented proofs. This episode highlights Indian science’s critical engagement and innovation, cementing Aryabhata’s enduring legacy.

Key Words:
Aryabhata, Brahmagupta, Kerala School, Aryabhatiya, Brāhmasphuṭasiddhānta, Earth rotation, Golapāda, Kuṭṭākāra, Jyā, Pi, Ārya-pakṣa, Brāhma-pakṣa, Mādhava, infinite series, calculus precursors, Nīlakaṇṭha, Yuktibhāṣā, geo-heliocentric, Indian astronomy, scientific dialogue.

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