Generally vidyaarmbam among sri vaishnavas begins with a prayer to Lord Sri Hayagreeva, preceded by obeisance to our Acharyaas. Even today Vijayadasami and Sarsvathi pooja are celebrated in Srivaishnavas homes with the recitation of Sri Hayagreeva sthOthram. (in our home at least!). The Parakala Matham, situated in Mysore, is one the most ancient and premier Srivaishnava religious institutions in the country that came into being for the specific purpose of propagating Sri Ramanujam's Visishtadvaita philosophy. Sri Lakshmi Hayagreeva (the Lord with the horse's face) Haya-horse: greeva-neck: this Lord is the presiding deity for all knowledge - 'Aadhaaram sarvavidhyaanaaam Hayagrivam upaasmahe'- is the principal deity of the Parakala Matham, the icon being one of the most beautiful ever adorning the Matham. Sri Hayagreevar Divya MangaLa vigraham is also the president deity for Sri Poundareekapuram Andavan Ashramam and also greatly revered by Sri Ahobila Matham and Andavan Ashram.
The avataram of Hayagriva Bhagavan took place to restore the Vedas to Brahma. Emperumaan had taught BrahmA the Creation through His breath of VedAs. Then, Brahma could understand how various kalpams had begun due to Emperumaan's vEdOpasEam. He became extremely proud and head strong of his position as the creator and about his powers/jnAnam. Sriman Narayana as usual wanted to teach him and decided to remove his (Brahma's) pride. A couple of water droplets from the lotus seat of the Lord incarnated as two Asuras, Madhu and Kaitabha; Due to Bhgawath sankalpam, one (kaitapan) was of thamO guNA and the other (madhu) was of rajO guNA. They stole the Vedas from Brahma. Emperumaan smiled.
Unable to carry on his work of creation without the Vedas, Brahma rushed to the Lord and pleaded the Lord Narayana for mercy and saving Vedas. BrahmA prostrated to the Lord and said:
"Vedas alone are my eyes; they are my wealth; They are my Lord. The whole world is surrounded by darkness due to the absence of Vedas. How am I to proceed on my creation without the Vedas ? Please arise from the Yoga nithrA and help me Lord! Please give me back my eyes which have been blinded by my own pride."
"veda: mE paramam sakshI: veda: mE paramam param
veda: mE paramam dharma, veda: mE brahma sOtthamam"
Lord Narayana incarnated as Hayagriva, appeared as the white Horse faced, faultless sphatika hued form, satva mUrthy, with Divya tEjas, and lustrous form and destroyed the Asuras and restored the Vedas to Brahma. This avtaaram was made on a AvaNi month, sravaNa nakshthram paurNami thithi. With a lovely long nose, like the heaven surrounded by white bright stars, the asva siras (head of horse) illumined the whole world. The upper world and the lower world became His ears. The rays of Sun's brightest lustres are His hairs at the nape of His neck (pidari). BhUmi became His forhead; Ganga and Saraswathi became two lovely eyebrows; Chandra Sooryar (The Moon and the Sun) became His two eyes; SandhyA dEvathai became His nostrils; Pithru devathAs became His teeth; GolOkam and Brahma lOkam became His two lips; kalaraathri became His neck; The Divya tEjas Sathva mUrthy Sri Hayagreevan thus, in a grandest beautiful manner appeared. He rushed to PaathaaLa lOkam and raised His "uthGitham" in samavEdha swaram and terrified Madhukaitapa asurAs; They hid the VedhAs (which were in the form of babies) and ran away from the scene. Sri Hayagreevar handed over the Vedas to BrahmA and went back. Madhukaitapar searched for the sound which terrified them earlier but found the Vedas missing. They rushed to BrahmA who in turn was terribly scared and sought the help of Sriman Narayanan. Sri Hayagreevar fought with asurAs and killed them. BrahmA continued his work of creation.
There is another version of this avtaar and killing of asurAs. When paraLayam was about to end, Bhagawaan out of His dirt from the ear drum made two small solid balls and dropped on the Lotus leaf and BrahmA activated the PrANa vaayu, which gave life to these two, as madhu and kaitabhar. These asurAs appeared and grew up.
BrahmA started off his creation and Vedhas were snatched away by these two asurAs. When the most compassionate Lord, Parama kaaruNikO Bhagawaan wished to please the asurAs, without killing them, asked them as to what they want as a boon. These two asurAs said "we can give You what You want". That is it! The Lord decided to kill them. They said "Can You kill us only where there is no cover for the sky?". The Lord immediately took Hyagreeva avtaar and removed His cloth on the Thighs, put them on His thighs and killed them. Bhagawaan's legs house the Earth and the space/sky. Since the Lord removed the cloth from His thighs and killed them, He still complied with what they challenged Him. What they thought was impossible to happen, He could make it happen with no effort. He, thus saved the Vedas and saves the world. The moral is: thamas, rajas guNAs are to be destroyed to reach Him.
There is yet another interesting "different" version in BrahmANda PuraaNam- Sri Devi Bhagawatham. There was a asurA, by name Hayagreeva (with horse face) who did his severe penance/ tapas on Parvathi Devi. Parvathi, pleased with his tapas, appeared in his front and the asurA asked for "no death". She said "Impossible-can not be granted". Then the asurA amended the request and said "Except for a horse faced one, no one else can kill me". (thinking that it can never happen!). She consented. He became tremendously proud of his achievement and started harassing every deva and rishi. He troubles all three worlds. He snatched away the Vedas from BrahmA and disappeared. Then is the history. The Lord appeared as Hayagreevar and killed the asurA to save the world and bring back the Vedas.
There is yet another puraaNic narration on Hayagreevar. At Kanchi, Agasthya muni was on severe penance on Sriman Narayanan and the Lord appeared as Hayagreevar and was immensely pleased with his tapas. He blessed the muni with Devi mahaathmyam. This is described in BrahmANda puraaNam Sri Hayagreeva agasthya samvaadham.
During Tripura samhaaram to entice the asurAs, the Lord appeared as "other religious" saint (buddhism?) and appeared as Hayagreevar to mislead the asurAs from the Veda maargham (from the path of Vediv traditions and sayings). Thus, He made them lose their ability to get saved and the Lord won. (As also claimed and reported in Buddhism in a web site as follows: Like Mahakala, Hayagriva is one of the Eight Great Protectors of Buddhism, a guardian and a destroyer of obstacles to enlightenment(!). He is a popular personal, or tutelary, deity among the Gelug order of Tibetan Buddhism. Hayagriva's crown of skulls is surmounted by Hayagriva's attribute, a horse's head, alluding to his origin as a horse-headed Hindu god. The terrific neigh that emanates from this horse's head is said to pierce through the illusory nature of reality. Although he was also popular in Tibet and China, Hayagriva's association with the horse may have had a particular appeal to the Mongols. (This, I read in the Net in some buddhism web site!) Swami Desikan in his "navarathna maalai" says " puRamuyarttha asurargatku puRam uRaittha poyyinaan". (to explain the Lord thus, misleading the asurAs by taking non-vedic religion (Buddhism)).
Since, Lord Hayagreevar killed the asurAs, madhu and kaitapar, He is referred to as Madhusoodhanan.
Bhagavan Ramanuja re-established the Visishtadvaita siddhaantham and commented on Brahma sUthram in his Bhashyam. This excellent, unambiguous vyAkhyaanam was completed by Yathiraajaa and fulfilled his "maanasika guru" Yamaunaacharya's wish (manOratham). Ramanuja "officially" released the commentary at the grand gathering of all sanskrit scholars and Vedic scholars at Saraswathi Peetham in Kashmir, in front of Saraswathi Devi. Goddess Saraswathi, immenslely satisfied at the excellent commentary and the truthful presentation of Brahma sUthram, she honoured the commentary by confering a award calling it "SRI BHAASHYAM". Also, she was extremely happy with Yathiraajaa, she presented to him a Divya mangaLa vigraham of Sri Lakshmi Hayagreevan. Since the, Yathiraaja was performing Thiruvaaraadhanam for Sri Kalshmi Hayagreeva Vigraham daily.
This vigraham, through Thirukurugai piraan, through our AchAryAs, came to Sri Vedanta Desikan. Afetr Swami Desikan's period, this is passed on to Sri Brahma tantra Swami and is now with Mysore Parakala Matham Swami. Even today, the Thiruvaaraadhanam is being performed on this Divya MangaLa vigraham of Lord Sri Lakshmi Hayagreevan. If one has a close loving glance at the Lord Hayagreevan's vigraham, He has four hands, and has a beuatiful Horse face, sitting on a white Lotus. His Lotus Feet wears "salaghai" (paayal). His upper two hands hold Sankhu and ChakrA. His lower right hand offers jnAnOpadEsam to us, bhakthAs. Other hand hold Japamaalaa. Also, it appears as if He is granting us boons. VishNu DharmOttharam, VaishNava Moorthanya DharaNi part describes Hayagreeva Thiruvuruvam (form). There it details eight hands for Hayagreevan, where four hands hold Vedas (four children) and other four hold Sanghu, ChakrA, GadhA, and Padmam. Afterwards, He is blessing us with four hands as detailed above.
Even Sri VishNu puraaNam, details Sun as the Horse faced one for upadEsam. Hayagreeva avtaaram is for VedOpadEsam and granting us jnAnam. (Swami Desikan was initiated into the Great Hayagreeva Manthram). Once Swami Desikan wished to stay at ThiruvaheendraPuram and was proceeding from Kanchi. On the way he stayed at some remote place (that belonged to a grain merchant). There lot of grains were stored and piled in sacks.
There Swami Desikan did not have anything to offer to his Sri Hayagreeva vigraham and hence, offered just water and he also went to sleep, without eating anything (just by drinking few drops of water that he had offered to the Lord). Midnight, the merchant noticed a very big, beautiful white Horse which started eating those grains from a sack. The merchant, thinking that it belongs to Swami Desikan, immediately woke him up to tie the white horse. Swami Desikan has tears rolling down his cheeks, and prostrated to the Lord (who had come as the White Horse) and explained to the merchant and asked him to bring a pot of milk. The excited merchant and others brought milk which the Lord drank happily and disappeared.
Next day morning the merchant chased Swami Desikan, (who had actually started off his journey to Thiruvaheendrapuram) and informed that the whole sack (from which the white horse ate) is full of Gold coins! Swami Desikan smiled and was overwhelmed with joy for His mercy and leelA. That place is called "pon viLaintha kaLampudhoor".