Mathas of Achintya Vada Veda Sampradaya have sprung up in Puri right from the days of Chaitanya. After Chaitanya several other followers of Achintya Vada Veda had started a number of organisations which later came to be known as Mathas. One of the very famous Matha of the Achintya Vada philosophy is the Chaitanya Radhakanta Matha. This monastery was a premier monastery of the Rajangila type.

It is said that in the Chaitanya Radhakanta Matha the sadhus as a matter of sacred duty and privileges circumambulate the inner compound of the Jagannath Temple of Puri daily in accompaniment of devotional songs and music or Nama Sankirtan. A special place in the compound of Gundichaghar has been allotted to the monastery where the head of the monastery and his followers are entitled to sit and spend time during the nine-day stay of the deities in this place. This is the spot where the monastery is privileged to offer food to the deities on the day of their arrival and also of their departure from this place.

Many small monasteries have sprung up around Radhakanta matha. There was a place where a man called Bakreswar Pandit resided. This place became a monastery named Sidhabakula Matha and the transformation had come about of a miraculous feat which Chaitanya had once exhibited.

The Gangamata Matha located near Swetganga tank came under the fold of Achintya Vada Veda after the Acharya of the Matha Basudeb Sarbabhauma was defeated by Chaitanya in the discourse of Vedanta. The Gangamata Matha is one of the important Rajangila Matha and its presiding deity is called Rasikraj. The special services which have been bestowed on the Matha include performance of Nama sankirtan at the time of Baladhupa, and offering of scented oil and sweets and delicious preparation to the deities.

Tota Gopinath Matha has also become famous as one of the Mathas of the Achintya Vada Veda order. The followers of this sect hold the view that Caitanya got himself merged in the body of Gopinath, the presiding deity of the Tota Gopinath Matha of Harchandi Street. This monastery has no relationship with the temple. Suna Goswami Matha is also one of the Matha belonging to the Achintya Vada Veda order.

Besides these mathas there are also a few others which belong to Achintya Vada Veda, but they go with Gadwa Madhava sect in their daily activities. These mathas are Habeli, Khajuria, and Indraswami. In the present time the Jhanjapita Matha of Achintya Vada Veda sect which is established by Charana Das Babaji has become an important matha. Some of the ritual services of greatest importance which this matha performs are Namasankirtan, cleaning of Gundichaghar (Gundicha marjana) and Raghava Jhala.

Other Goudiya Vaishnava mathas which correspond to those of Acintya Veda Veda in philosophical doctrines and religious ideology are Purusottam Goudiya Matha, a branch of Chaitanya Matha located at Nadia in West Bengal, Ahula Matha established by Adwaita Mahapravu and Nityananda Nibas or Goswami Matha established by Nityananda Mahapravu.