information:highlighting, linguistic:paraphrasing, information:filtering, structural:reformatting
Dashanami Sampradaya and mathas

Advaita Vedanta is, at least in the west, primarily known as a philosophical system. But it is also a tradition of renunciation. Philosophy and renunciation are closely related:

Most of the notable authors in the advaita tradition were members of the sannyasa tradition, and both sides of the tradition share the same values, attitudes and metaphysics.

Shankara was a Vaishnavite who came to be presented as an incarnation of Shiva in the 14th century, to facilitate the adoption of his teachings by previously Saiva-oriented mathas in the Vijayanagara Empire. From the 14th century onwards hagiographies were composed, in which he is portrayed as establishing the Daśanāmi Sampradaya, organizing a section of the Ekadandi monks under an umbrella grouping of ten names. Several other Hindu monastic and Ekadandi traditions remained outside the organisation of the Dasanāmis.

According to tradition, Adi Sankara organised the Hindu monks of these ten sects or names under four Maṭhas (Sanskrit: मठ) (monasteries), with the headquarters at Dvārakā in the West, Jagannatha Puri in the East, Sringeri in the South and Badrikashrama in the North. Each matha was headed by one of his four main disciples, who each continues the Vedanta Sampradaya.

According to Paul Hacker, the system may have been initiated by Vidyaranya (14th c.), who may have founded a matha, proclaiming that it was established by Shankara himself, as part of his campaign to propagate Shankara's Advaita Vedanta. Vidyaranya enjoyed royal support, and his sponsorship and methodical efforts helped establish Shankara as a rallying symbol of values, spread historical and cultural influence of Shankara's Vedānta philosophies, and establish monasteries (mathas) to expand the cultural influence of Shankara and Advaita Vedānta.