When did Hindu mathas (monasteries) start?

This post follows up on my post of a few days back: When did Hindu temples start getting built? Which is the oldest functional Hindu temple? , https://ravisiyer.blogspot.com/2022/09/when-did-hindu-temples-start-getting.html .

Like I mentioned in the above post, this question is also a sensitive question with a variety of conflicting answers from different sources. Eventually I decided to put up a limited post raising the question and sharing responses mainly from wikipedia.

The ancient Hindu sages and teachers were called Rishis. 

From https://en.wikipedia.org/wiki/Rishi :

Rishi (Sanskrit: ऋषि, romanized: ṛṣi) is a term for an accomplished and enlightened person. They find mentions in various Hindu Vedic texts. Rishis are believed to have composed hymns of the Vedas. Post-Vedic tradition of Hinduism regards the rishis as "great yogis" or "sages" who after intense meditation (tapas) realized the supreme truth and eternal knowledge, which they composed into hymns.[1: Hartmut Scharfe (2002), Handbook of Oriental Studies, BRILL Academic, ISBN 978-9004125568, pages 13–15]

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Hindu scripture has lots of references to Rishis. For example, Ramayana refers to the Rishis: Vasishta, https://en.wikipedia.org/wiki/Vasishtha and Viswamitra, https://en.wikipedia.org/wiki/Vishvamitra , and also to other Rishis. I recall these references from my reading of Kamala Subramaniam's Ramayana in English, over past few years.

Many of these Rishis had ashrams with disciples, which are mentioned in Hindu scripture.

But these Rishis were usually not celibate monks, as far as I can recall from my readings of Hindu scripture. Yes, some Rishis were celibate. Rishi Shuka is one such example.

From https://en.wikipedia.org/wiki/Shuka :

Shuka[2][3] (Sanskrit: शुक IAST: Śuka, also Shukadeva Śuka-deva) is a rishi (sage) in Hinduism. He is the son of the sage Vyasa and the main narrator of the scripture Bhagavata Purana. Most of the Bhagavata Purana consists of Shuka reciting the story to the king Parikshit in his final days. Shuka is depicted as a sannyasi, renouncing the world in pursuit of moksha (liberation), which most narratives assert that he achieved.[4]

[References:]

2. Matchett, Freda (2001). Krishna, Lord or Avatara?: the relationship between Krishna and Vishnu. Routledge. ISBN 978-0-7007-1281-6.

3. Hiltebeitel, Alf (2001). Rethinking the Mahābhārata: a reader's guide to the education of the dharma king. University of Chicago Press. ISBN 978-0-226-34054-8.

4. Sullivan, Bruce M. (1990). Kṛṣṇa Dvaipāyana Vyāsa and the Mahābhārata: a new interpretation. BRILL. p. 40. ISBN 978-90-04-08898-6.

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Note that young disciples/students at an ashram of a Rishi were celibate brahmacharis, most of whom would go back to their home towns/villages and get married after their student period is over. Lord Krishna himself was a brahmachari student in Rishi Sandipani's ashram/residence, https://en.wikipedia.org/wiki/Sandipani . Note that the wiki page refers to Rishi Sandipani as Sandipani Muni. Muni means a holy man and I think in this context at least, Muni is same as Rishi. From https://religion.fandom.com/wiki/Sandipani , "Saṁdīpanī Muni was the guru of Bhagavan Śrī Kṛṣṇa. Saṁdīpanī was a ṛṣi/muni/saint of Ujjain."

Rishi Sandipani was married and had at least one son, with Lord Krishna restoring the lost son to Rishi Sandipani and his wife.

But the institution of mathas (monasteries) with sannyasi leaders of the matha, does not seem to have been mentioned in ancient Hindu scripture like Ramayana. So when did such Hindu mathas/monasteries start? That has been a question in my mind for many years.

From https://en.wikipedia.org/wiki/Matha :

A matha (/mʌt/, /mʌtɦ/; Sanskrit: मठ, maṭha), also written as math, muth, mutth, mutt, or mut, is a Sanskrit word that means 'institute or college', and it also refers to a monastery in Hinduism.[1][2] An alternative term for such a monastery is adheenam.[3]

The earliest epigraphical evidence for mathas related to Hindu-temples comes from the 7th to 10th century CE.[4] The most famous Advaita Vedanta mathas or peethams, which came to be affiliated with the Advaita tradition in the 14th century, are Puri Govardhanmaṭha Pīṭhaṃ (Odisha), Sringeri Śārada Pīṭhaṃ (Karnataka), Dvāraka Kalika Pīṭhaṃ (Gujarat) and Badari Jyotirmaṭha Pīṭhaṃ (Uttarakhand), and Kanchi matha (Kanchi Kamakoti Pīṭhaṃ - Tamil Nadu).

The most famous and influential Dvaita Vedanta mathas or peethams are Ashta Mathas (Udupi, Karnataka), Uttaradi Matha (Bangalore, Karnataka), Vyasaraja Matha (Sosale, Karnataka) and Raghavendra Matha (Mantralayam, Andhra Pradesh).[5][6] Other major and influential mathas belong to various schools of Hindu philosophy, such as those of Vaishnavism and Shaivism.[7][8] The monastery host and feed students, sannyasis (monks, renouncers, ascetics), gurus and are led by acharyas. These monasteries are sometimes attached to Hindu temples and have their codes of conduct, initiation and election ceremonies.[9][10] The mathas in the Hindu tradition have not been limited to religious studies, and historical evidence suggests that they were centers for diverse studies such as medieval medicine, grammar and music.[11]

The term matha is also used for 'monastery' in Jainism, and the earliest monasteries near Jain temples are dated to be from about the 5th-century CE.[12]

...

History

Patrick Olivelle mentions the absence of organized ascetic or monastic institutions within Brahmanism until the early medieval period. According to Olivelle, noticing the Advaita leaning of the Sannyasa Upanishads, the major monastries of the early medieaval period belonged to the Advaita Vedanta tradition, preserving and possibly adapting the Sannyasa Upanishads with their Advaita leaning.[15]

Mathas, as simple huts for wandering ascetics, are mentioned in chapter 12.139 of the Mahabharata and section 3.1 of Baudhayana Dharmasutras.[4] Matha-s were regionally known by other terms, such as Ghatika-s and Khandika-s.[16] The oldest verifiable Ghatika for Vedic studies, from inscription evidence is in Kanchi, from the 4th-century CE.[16]

[References:]

1. Tamara I. Sears (2014). Worldly Gurus and Spiritual Kings: Architecture and Asceticism in Medieval India. Yale University Press. pp. 4–9. ISBN 978-0-300-19844-7.

2. Matha, Encyclopædia Britannica Online 2009

3. Also transliterated ādīnam, adinam, aadheenam, aadheenm, etc.

4. Scharfe 2002, p. 172-173.

5. The Illustrated Weekly of India. Bennett, Coleman & Company, Limited, at the Times of India Press. 1972. p. 21. Apart from the eight maths, three important maths outside Udipi have played a significant part in upholding and spreading the message of Dvaita: the Uttaradi Math (Bangalore) and the Raghavendraswami Math (Nanjangud) and the Vyasaraya Math (Sosale). Particularly mention must be made of the outstanding contribution of the late Satyadhyanatirtha of the Uttaradi Math - a giant intellectual indeed.

6. Steven Rosen (30 November 1994). Vaisnavism. Motilal Banarsidass Publishers. p. 132. ISBN 9788120812352.

7. V Rao (2002), Living Traditions in Contemporary Contexts: The Madhva Matha of Udupi, Orient Blackswan, ISBN 978-8125022978, pages 27-32

8. Sears, Tamara I. Housing Asceticism: Tracing the development of Mattamayura Saiva monastic architecture in Early Medieval Central India (c. 8th – 12th centuries AD). PhD. Dissertation 2004. p. 29

9. Johnston 2013, p. 681–683.

10. V Rao (2002), Living Traditions in Contemporary Contexts: The Madhva Matha of Udupi, Orient Blackswan, ISBN 978-8125022978, page 43-49

11. Hartmut Scharfe (2002), From Temple schools to Universities, in Education in Ancient India: Handbook of Oriental Studies, Brill Academic, ISBN 978-9004125568, pages 173-174

12. Paul Dundas (2003). The Jains. Routledge. pp. 123–124. ISBN 978-0415266055.

...

15. Olivelle, Patrick (1992). The Samnyasa Upanisads. Oxford University Press. pp. 14, 16, 18. ISBN 978-0195070453.

16. Hartmut Scharfe (2002), From Temple schools to Universities, in Education in Ancient India: Handbook of Oriental Studies, Brill Academic, ISBN 978-9004125568, pages 169-171 with footnotes

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Pic below is "An Advaita Vedanta monastery and Vidyashankara temple at Sringeri Sharada Peetham, Sringeri, Karnataka." Courtesy:  https://en.wikipedia.org/wiki/File:Vidyashankara_Temple_at_Shringeri.jpg .

[On PC desktop, to open pic in larger resolution (if available), right-click on pic followed by open link (NOT image) in new tab/window. In new tab/window you may have to click on pic to zoom in.]

The key dates related info. in above extracts are "earliest epigraphical evidence for mathas related to Hindu-temples comes from the 7th to 10th century CE" and "The oldest verifiable Ghatika for Vedic studies, from inscription evidence is in Kanchi, from the 4th-century CE". We do not have a clear date for first Hindu matha/monastery in this wiki page.

Encylopedia Brittanica makes a more assertive and specific statement but I wonder how accurate it is. It states that the first Hindu mathas were founded by Adi Shankara in 8th century CE, https://www.britannica.com/topic/matha .

I don't want to draw any conclusions about the date for the first known Hindu matha being setup. I say, known, to distinguish from earlier Hindu mathas which are now unknown.

But I think, based on above info., I can say that the earliest known Hindu mathas were setup in or before 8th century CE (AD). 

[I thank Wikipedia and have presumed that they will not have any objections to me sharing the above extract(s) from their website on this post which is freely viewable by all, and does not have any financial profit motive whatsoever.]