Those who know a little of Sanskrit and Hinduism would know what an Intellectual Giant Adi Shankaracharya was.

But not many know the logic that has gone behind his establishing the four Mutts.

He chose four directions to found the Mutts.

All the Four Vedas are represented

Padmapadacharya (fl. 8th century CE) was an Indian philosopher, a follower of Adi Shankara.

Padmapāda’s dates are unknown, but modern scholarship places his life around the middle of the 8th century; similarly information about him comes mainly from hagiographies. What is known for certain is that he was a direct disciple of Shankara, of whom he was a younger contemporary. Padmapada was the first head of Puri Govardhana matha. He is believed to have founded a math by name Thekke Matham in Thrissur, Kerala. Keralites believe that he was a Nambuthiri belonging to Vemannillom, though according to textual sources he was from the Chola region in South India.

Sureśvara (also known as Sureśvarācārya, c. 750 CE) was an Indian philosopher, who studied under Śankara. Śankara is said to have entrusted to Sureśvara his first monastic institution, the Sringeri Sharada Peetham. Suresvara is believed to have founded the famous Naduvil Matham in Thrissur…

Little is known for sure about Sureśvara’s life. According to a strong tradition within Advaita Vedānta, before he became a disciple of Śankara, Sureśvara was known as Maņdana Miśra, a Mīmāmsāka. After being defeated in debate by Śankara, Miśra renounced his life as a householder, and became a sannyāsin. Whether this Maņdana Miśra was the same as the author of Brahmasiddhi is questioned by modern scholars, on the basis of textual analysis.

Hastamalakacharya (IAST Hastāmalakācārya) (c. 8th century CE) was a disciple of Adi Shankara, the Advaita philosopher. He was made the first Jagadguru (head) of the Dvāraka Pīṭhaṃ, the monastery founded by Adi Shankara in Dwaraka. Hastamalaka founded a matha by name Idayil Matham in Thrissur, Kerala.

The Mādhavīya Śaṃkaravijayam states that when Adi Shankara was at Kollur, he accepted invitations by brāhmaņas to have Bhikşa (alms or food) at their houses. On such an occasion he visited a village called Śrī Bali (present day Shivalli), where every house was said to emit the holy smell of the smoke of Agnihotra sacrifice, to accept Bhikşa. That place was inhabited by about two thousand brāhmaņas who were learned in the Vedas and performed the Yajnas prescribed in the Vedas. There was also a temple dedicated to Shiva and Parvati.

In that village there lived a brāhmaņa, Prabhākara, who was noted for his learning. He had a son who though appearing quite handsome, behaved rather like an idiot. Though upanayanam was performed for him, he did not take to studying the Vedas, instead preferred to sit around doing nothing. Hearing about Adi Shankara’s visit, Prabhākara approached the Acharya (teacher) with a load of fruit and prostrated before him. He also made his son prostrate before him. Prabhākara explained to Adi Shankara that his son behaved rather like an idiot and sat idly throughout the day.

Then, Adi Shankara addressed that young boy and asked him who he was. The boy replied in 12 verses containing the gist of theAdvaita philosophy.Thus Adi Shankara was immensely impressed with him and accepted him as his disciple. He was named Hastāmalaka (one with the amalaka fruit in his hand) since the knowledge of the Self was natural to him like an Amalaka fruit in one’s hand. Adi Shankara took the boy into his party and started towards his next destination..

Totakacharya (IAST Toṭakācārya) (c. 8th century CE) was a disciple of Ādi Śaṅkara, the Advaita philosopher. He was made the first Jagadguru (head) of the Jyotirmaṭha Pīthaṃ, the northern maṭha founded by Ādi Śaṅkara near Badrinath. He founded a maṭha by name Vadakke Matham in Thrissur, Kerala…

he Mādhavīya Śaṅkaravijayam states that when Ādi Śaṅkara was at Śṛṅgeri, he met a boy named Giri. Ādi Śaṅkara accepted the boy as his disciple. Giri was a hard-working and loyal servant of his Guru, Ādi Śaṅkara, though he did not appear bright to the other disciples. One day, Giri was washing his Guru’s clothes, when Ādi Śaṅkara sat down to begin a lesson on Advaita Vedānta. He however did not start the lesson saying he was waiting for Giri to come back from his chores and singing lessons. At this, Padmapada pointed to a wall and said that it would be the same if Ādi Śaṅkara taught to this dumb object as he taught to Giri. Now, Ādi Śaṅkara wanted to reward Giri for his loyalty and devotion. Thus he mentally granted Giri the complete knowledge of all the śāstras (sciences). The enlightened Giri composed extempore the Toṭākāṣṭakam, a Sanskrit poem in the toṭaka metre, in praise of the Guru Ādi Śaṅkara. Thus the dumb disciple Giri became Toṭākācārya.

Look at the way Shankaracharya appointed Pontiffs, from deep south to west and from North to South.

And three of these Mutts  fall into a pattern of being in the same latitude.

Geographically speaking the char Dham make a perfect square with Badrinath and Rameswaram falling on the same longitude and Dwarka (old) and Puri on the same latitude, representing the farthest north, east, west, and south points of India (at that time, before coastlines changed)

Badrinath, coordinates. Longitude.

79.49481879999996

Rameshwaram Longitiude.

79.31292910000002

Dwaraka latitude.

22.2441975

Puri Latitude.

19.8133822

* Present alignment.

Citations.

https://en.wikipedia.org/wiki/Char_Dham

http://www.distancesfrom.in/odisha/puri-latitude-longitude/46.html