The title Shankaracharya designates the head of one of the mathas, monastic seats, traditionally said to have been established by the eighth or ninth century philosopher Adi Shankara at four cardinal locations across India, Sringeri in the south, Dwarka in the west, Puri in the east and Jyotirmath, Badrinath, in the north, each entrusted with a specific Veda and a specific mahavakya, great saying, from the Upanishads, an organizational scheme historians regard as having developed and been formalized over some centuries following Shankara's own lifetime rather than necessarily in the fully elaborated form later tradition attributes directly to him. Adi Shankara himself is credited as the most influential systematic exponent of Advaita Vedanta, the non-dualist school of Hindu philosophy holding that the individual self, atman, is ultimately identical with Brahman, the single underlying reality, a philosophical position his mathas and their successive Shankaracharyas have continued to teach and defend across the intervening centuries.
A fifth matha at Kanchipuram is also widely, though not universally, recognized as part of the same tradition, a point of some historical and institutional disagreement among the mathas themselves regarding the precise original scheme and each seat's exact relative standing, illustrating that even a tradition organized specifically around preserving a single philosophical lineage has not been immune to its own internal disputes over institutional precedence.