Adi Shankaracharya is an advaita philosopher and wrote commentaries to the prasthāna trayi and composed many stotras on different deities.. It is believed that he established four mutts(denoting four vedas) in four directions of India. They are
East : Pooramnaya Shri Govardhana Peetham (Rigveda-eastern Monastery) located at Jagannadh Puri, Orissa.
West : Paschimamnaya Shri Sharada Peetham (samaveda-western Monastery)— Located At Dwaraka, Jamnagar, Gujarat.
North : Uttaramnaya Shri Jyotish Peetham (atharva Veda-northern Monastery)— Located At Badarinath, Uttarakhand.
South : Dakshinamnaya Sri Sringeri Sarada Peetam (yajurveda-southern Monastery)— Located at Shringeri, Karnataka.
The pontiffs of these monastery institutions are called as Shankaracharyas and recognised equal to Adi Shankaracharya.
But many people believe that Kanchi kamakoti peetham located at Kancheepuram, Tamil Nadu is also established by Adi Shankaracharya. Kanchi Kamakoti peetham in its history states that Adi Shankara established 5 mathas rather than 4. The pontiff of this math is also called as Shankaracharya.
So how many monastery institutions did Adi Shankara establish in his lifetime? What do Shankara Digvijayas state about this?