How did Indian mathematics exchange ideas with Islamic mathematics during the Mughal period?

During the Mughal period, the exchange of mathematical ideas between India and the Islamic world was characterized by a collaborative blending of traditions, particularly within the imperial Mughal courts. Despite broader social and political tensions, astronomers and mathematicians engaged in the mutual translation of scientific works, often moving between Persian and Sanskrit.1

This intellectual cross-pollination resulted in the integration of several key concepts into the Sanskrit jyotisa (mathematical astronomy) tradition, including:

• Spherical Trigonometry: Concepts and results from Greco-Islamic spherical trigonometry were incorporated into Indian texts.1
• Astronomical Tools: Mathematical instruments and advanced astronomical tables were shared and adopted across both traditions.1

This period of exchange built upon a much older history of interaction, as early Indian mathematical treatises had already profoundly influenced the development of Islamic mathematical astronomy following their translation into Arabic in the 8th century. By the Mughal era, this relationship evolved into a more direct, collaborative effort at the court level, ensuring that the mathematical knowledge of both cultures continued to inform and enrich one another.21