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Paryaaya
The Ashta Mathas
Madhwaachaarya initially established eight monasteries popularly called “Ashta Mathas”. The head of each matha bears the suffix ‘tirtha’, continuing the style of Madhwaachaarya’s name, Ananda Tirtha.
The names of the eight mathas are Palimaru, Adamaru, Krishnaapura, Puthige, Pejawara, Kaniyoor, Shirooru and Sodhe. As per the order of the names of the mathas mentioned above, two mathas are paired, forming a total of four pairs. That is, Palimaru and Adamaru form a pair, Krishnaapura and Puthige are a pair, and so on. Each pair is called “dwandva”. The idea behind the pairing is to enable one matha to seek help from its partner matha if required.
Paryaaaya
Paryaaya is the exclusive and rotational worship and administration of the Udupi Krishna matha by each of the Ashta mathas. Madhwaachaarya himself established this tradition and laid the Paryaaya tenure as two months, that is, every two months the reins were handed over to the next matha.
The pontiff relinquishing charge hands over the temple keys and a vessel called “Akshaya Patre” to the pontiff taking charge. The new pontiff occupies the seat of Madhwaachaarya called the Paryaaya Peeta or the Sarvagnya Peeta.
This system is being followed unbroken till date.
Paryaaya is a very complex process and an impressive spectacle. For more on the accompanying rituals, you may visit https://sripalimarumatha.org/sri-krishna-pooja-paryaya
The change
In 1532, Vaadiraja increased the tenure of the paryaaya to two years, thus enabling the heads of the mathas to implement changes/improvement if necessary and to travel in order to disseminate Madhwa philosophy.
Vaadiraja, who lived for 120 years, created history by worshipping Krishna through five rounds of paryaaya.
This feat, impossible to match, let alone surpass, was in recent times (2016-2018) accomplished by the Late Sri Vishwesha Tirtha Swamiji of Pejawara Matha. Having been initiated into sanyaasa at the age of eight, he was able to go through five rounds of paryaaya. It is said that he wanted to abstain from occupying the paryaaya peeta as a mark of reverence to Vaadirajaru.

Sri Vishwesha Tirtha (1931-2019) Pejawara Adokshaja Matha
Mathas of Madhwa Tradition
Various followers of Madhwaachaarya founded additional mathas. The list of mathas mentioned below are not comprehensive.
Bhandarkere matha was established by Madhwaachaarya’s guru turned into his disciple, Achyutha Preksha Tirtha.
Subramanya matha was established by Madhwaachaarya’s younger brother, Vishnu Tirtha. Raghavendra Swamy matha, Vyasarayara matha, Uttaradhi matha, Bheemanakatte matha and Sripadaraja matha are other well-known mathas in Karnataka.
Kashi Math of Goud Saraswats, Gaudiya Math of the followers of Chaitanya Mahaprabhu and ISKCON follow the tenets of Tattvavaada.
However, none of these mathas are involved in paryaaya.