Question

the four mathas established by Shankaracharya

Answer 1

Adi Shankaracharya wished to grace the Indian subcontinent by establishing five major mathas in the four corners of the peninsula – north (Jyothirmath), south (Sringeri,Kanchi ), east (Puri), west (Dwaraka) – to propagate the philosophy of advaita vedanta and to promulgate the concept of Sanatana dharma, thus

Answer 2

The popular view among historians[who?] is that there were four Mathas or Peethas (religious orders):[1]

The Dakshinānmnāya Sri Sharada Peetham (Main Matha) or the Shri Sringeri Sharada Peetham in Sringeri, Karnataka.

The Uttarāmnāya matha (Northern Matha) or the Jyotirmath Peetham in the city of Jyotirmath, Badrikashram also known as Joshimath, Uttarakhand.

The Pūrvāmnāya matha (Eastern Matha), or the Govardhan Peetham at Puri, Odisha.

The Paśchimāmnāya matha (Western Matha), or the Dwarka Sharada Peetham at Dwarka, Gujarat.

hope it helps