Madhva founded Dvaita ("dualist") Vedānta in direct opposition to Śaṅkara's Advaita non-dualism, arguing that reality divides fundamentally into independent reality (svatantra) - Brahman (identified with Viṣṇu) alone - and dependent reality (paratantra), comprising individual souls and inert matter. Rather than treating plurality as illusory appearance (māyā) over a single non-dual reality, Madhva held that the distinctions between God, souls, and matter are all fully real.
Intellectual setting
Madhva wrote as the third of the three major classical Vedānta founders, directly and polemically contesting both Śaṅkara's Advaita and Rāmānuja's qualified non-dualism (Viśiṣṭādvaita), and organized his teaching within a devotional Vaiṣṇava monastic institution centered at Udupi.
Key ideas
The independent-dependent distinction
Madhva divided all reality into one independent entity, Brahman/Viṣṇu, and everything else as dependent upon it, treating souls and matter as genuinely real and really distinct from God rather than as manifestations of a single underlying non-dual substance.
Devotion and graded liberation
Madhva taught that liberation depends on devotion (bhakti) to Viṣṇu and divine grace, and held that souls differ eternally in their intrinsic nature and capacity, so that liberation itself is graded according to each soul's inherent qualities.
Legacy
Madhva's Dvaita Vedānta became one of the three classical schools of Vedānta alongside Advaita and Viśiṣṭādvaita, and it continues to shape South Indian Vaiṣṇava devotional practice and theology to the present day.