Times
akShobhya tIrtha died 1365.
mAdhava had taken sannyAsa earlier to become vidyAraNya. As per popular tradition he was a yati even when the city was founded in 1336 (1331 says shRngeri website; hampi maTha corroborates this). Historians generally agree. Vidyaranya became peethadhipati in sringeri in 1380 and lived till 1386. (Copper plate of harihara ii )
Vedanta Desika lived 1268–1369.
Some advaitin sources argue that there was no debate. That may be ignored. For example, it seems that GR pATil relies on mAdhava’s sannyAsa being post axobhya’s death. In this he contradicts tradition of both shRngeri and hampI pITha.
vidyAraNya’s identity
Some mAdhva texts (राघवेन्द्र-विजय) say the prativAdI was avaidika. Some mAdhva texts classify advaita as a vaidika mata; while others like madhva-vijaya calls shAnkara-s avaidikas. Further, it is said explained by commenters as applicable to shAnkaras. A commentator clarifies - “मायि-भिक्षुम्”।
shRngeri confusion - see TW.
श्रीवैष्णव-स्रोतांसि
Medieval shrIvaiShNava sources say that the person was an advaitin.
- 3k guruparamparA prabhAva by tRtIya-brahmatantra-parakAla (1394 - 1406), though heavily interpolated
- doDDayAchArya’s vedAnta-deshika-vaibhava-prakAshikA,
- vedAnta-deshika-champU
‘moovaayirappaDi guruparamapara prabhava’ has many interpolations (details TW); but is more accurate compared to other such works regarding dates of rAmAnuja’s melukote stint.
It’s not by itself fool-proof evidence.
However, mAdhva sources supposedly agree with vedAnta deshika’s role in the debate; as do other SV works; which makes that story more likely.
… अप्पोदु विजय-नगरत्तिल् तत्त्ववादिय् आन अक्षोभ्य-मुनिक्कुं
मायावादिय् आन विद्यारण्यनुक्कुं
वेदान्तत्तिल् वादं प्रवृत्तम् आग
इरुवर्गळुडैय अभिप्रायत्तैयुं राज-पत्रिका-मूलमाग
वॆदान्त-देशिकर् सन्निधिक्कि अनुप्पिवैत्तु
याधार्ध्यत्तै अऱिन्दुहॊळ्ळ वेणुम् ऎऩ्ऱु अनुप्पिवैक्क,
वेदान्तदॆशिकरुं“असिना तत्-त्वम्-असिना
परजीव-प्रभेधिना।
विद्यारण्य-महारण्यम्
अक्षोभ्य-मुनिर् अच्छिनत्॥”ऎऱ् ऐऴदि अनुप्पिय् अरुळ,
राजावुं वेदान्तदेशिकर् तिरुवडिहळिल्के प्रवणनाय् इरुक्क,
विद्यारण्यनुं अत्तैनहियामल्
शत-दूषिणियै दूषिक्किऱोम् ऎऩ्ऱु शॊल्लिय् अनुप्प,
देशिकरुं शतदूषिणियै अनुप्पिय् अरुळ,
विद्यारण्यनुम् पार्त्तु ऒरु च-कारत्तिल् मेले कुत्त् इट्टु वरविड,
अत्तैदेशिकरुं कटाक्षित्तु च-कार-समर्धनम् ऎऩ्ऱु ऒरु ग्रन्ध शॆय्दरुळि
अन्दकुत्तिन् मेल् ऒरु कुत्तिट्टु अनुप्पियरुळ,
विद्यारण्यनुम् पार्त्तु,
“विष्णुघण्टावताररै नान् जयिक्क वल्लनोव्” ऎऩ्ऱु ईडु पट्टु
प्रवणनाय् इरुक्क
राजावुं वेदान्त-देशिकर् इडत्तिल् अत्यन्तम् भक्तन् आय् इरुन्दान्॥
doDDayAchArya -
कदाचिद् अक्ष्योभ्य-मुनेश् च विद्या-
रण्यस्य जातं बहुलं विवादम्।
विलिख्य भूपो विबुधाय यस्मै
संप्रेषयाम् आस तम् आश्रयेहं॥७६॥
तत्-त्वम्-असिना ऽसिना
तं विद्यारण्यम् मुनिस् तदा अक्ष्योभ्यः।
अच्छिनद् इत्य् अवदद् यस् तं
सेवे तत्त्व-निर्णये चतुरं॥७७॥
kAlAmukha theory
raghottama YT speculates that the vidyAraNya was Kalamukha (- Madhava Mantri, the disciple of Kalamukha Acharya Kashivilasa Kriyashakti?), of kallu-maTha of muLabAgal.
- That maTha, while now being fully madhva, had a shivalinga (which broke and was replaced) and several shiava figurines.
- Prominent mAdhvas credit jayatIrtha with overcoming vidyAraNya’s arguments through written works, and not axobhya.
This theory is weak on the basis of philosophy discussed.