Bhagwan Shankaracharya knew that after his demise, India will have to face a physical war, ideological war, cultural war. He knew this very well. That is why in order to protect the 4 Vedas he set up 4 Amnaya Mutts in the 4 corners of this country. Amnaya means the Vedas and Amnaya Peetha means Vedic Seat. So, he established 4 Mutts in the 4 directions of India in order to protect the 4 Vedas and the 4 divine abodes of India.
He established the Sri Uttaramnaaya Jyotirmath in the north. The Veda protected by Jyotirmutt is the Atharva Veda, i.e the literature relating to Atharva Veda, the Brahman Grathas, the Aranyak Granthas, the Upanishads, in order to protect these, this mutt was established. He gave this responsibility to the Uttaramnaya Jyotirmutt. He then established a mutt in Badrikasram, which we also know as Joshi Mutt. Then in Dwaraka Bhagwan Shankaracharya established the Sri Dwaraka Kaalika Sharada Mutt. Saamvediya Paschimamnaya Sri Dwaraka Sharada Kalika Mutt. Bhagwan Shankaracharya gave this mutt the responsibility of protecting the Sama Veda.
After that in the east Bhagwan Shankaracharya established the Sri Rigvediya Poorvamnaya Goverdhan Puri Mutt. Rig Vediya Poorvamnaya… as is evident by its name this is a Rig Veda Mutt. This mutt was established to protect the Rig Veda. This Govardhan Mutt will protect the Rig Veda, protect the various branches of the Rig Veda, the Brahman Granthas, Aryanakas, Upa Vedas and the Upanishads. All that which comes under the Rig Veda.
After that in the south Bhagwan Shankaracharya established the Yajurvediya Dakshinamnaya Sringeri mutt. He gave the Yajur Veda to the Sringeri mutt. He gave the responsibility of protecting the Yajur Veda to the Sringeri mutt. It’s not as if he just established the mutts and gave them the responsibility of protecting the Vedas. He gave them this responsibility in a scientific manner, philosophical manner, day-to-day functioning, in an ideological manner, cultural manner. He established these 4 aamnaya mutts as per yoga shastras and in third chapter of the Chandogya Upanishad, there is a description of the Madhu Vidya. He has established these 4 mutts in the 4 corners of India as per that Madhu Vidya and established the 4 Vedas in a systematic manner. Bhagwan Shankaracharya also assigned their respective teerthas, presiding deity, respective goddess to be worshipped, Gotra, Veda, sampraday and the sanyasi order of each of these mutts.