Sri Vaishnavism did not arrive at Srirangam as a finished system; it was substantially worked out there. In the eleventh century the temple became the site of sustained theological engagement among a succession of teachers, Nathamuni, who is credited with recovering and organizing the Tamil devotional hymns of the Alvar poet-saints, his grandson's disciple Yamunacharya, and above all Ramanuja, whose synthesis of Vedantic philosophy with Tamil devotional theology at Srirangam produced the qualified non-dualism, Vishishtadvaita, that remains Sri Vaishnavism's central philosophical position. Ramanuja served as the temple's head for a significant portion of his life, and tradition holds that debates conducted within its walls directly shaped positions he later formalized in writing.
That theological work eventually produced an internal division within Sri Vaishnavism itself, between the Tenkalai, or southern, school the Srirangam temple today follows, and the Vadakalai, or northern, school, disagreeing over questions including the relative weight given to Sanskrit versus Tamil scripture and the nature of divine grace. The disagreement is real and long-running, but both schools trace their lineage back through the same eleventh-century Srirangam debates, which makes the temple not merely a shrine housing Vishnu as Ranganatha but the shared point of origin both wings of Sri Vaishnavism still look back to.