Bṛhannīla Tantra explains the three famous epithets of Tāriṇī thus:
tārakatvātsadā tārā sukhamuktipradāyinī |
The Great Goddess who confers on her upāsakas both bhoga and mokṣa is called ‘Tārā’ as she is the deliverer or savior (from ignorance, misery, dangers, saṃsāra etc.)
upgrāpattāriṇī yasmādugratārā prakīrtitā |
As she delivers one from the greatest of dangers or calamities, she is referred to as ‘Ugratārā’.
līlayā vākpradā ceti tena nīlasarasvatī |
As she confers graceful and potent speech to her upāsakasa (vāksiddhi), she comes to be called Nīlasarasvatī.
The mantra of Nīlasarasvatī is derived by removing the ‘astra’ from the pañcākṣara mantra of Tārā:
tārāstrarahitā tryarṇā mahānīlasarasvatī |
An alternate form of Nīlasarasvatī mantra is obtained by replacing the first bīja of Tārā mantra (praṇava) with Vāgbhava bīja. In śrīkrama Tantra of Bimbāmbikā Sampradāya, the mantra beginning with vadhū-bījā has Ekajaṭā as the deity, that which begins with praṇava is attributed to Nīlasarasvatī and the one that begins with hṛllekhā is associated with Ugratārā. There are various other mantras associated with Nīlasarasvatī including the Vidyārājñī and the potent Caturdaśākṣarī vidyā of the Sādi-Saṃvarodhinī krama which is used by the upāsakas of Ucchiṣṭa Mahāgaṇapati. The thirty-four lettered mantra of Nīlarasvatī is also popularly used by several lineages of Tārā upāsakas today.
It is said that her blue color is symbolic of her ‘tvarita anugraha’ (speedy grace).
While the origins of the worship of Tārā as we know today is certainly Buddhistic [which itself is traced back to the conceptualization of Durgā – Buddhist Tantras discuss a form named Durgottāriṇī Tārā, which is clearly derived from Durgā], Bṛhannīla Tantra narrates an interesting story regarding the origin of Nīlasarasvatī.
After the Asuras were defeated and driven into the depths of the ocean by the Sudarshana Chakra of Mahāviṣṇu, two demons appeared within the dark oceans named Hayagrīva and Soma. These two brothers performed a long penance to propitiate the Goddess in her form as śabdākarṣiṇī and attained from her the boon to attract and capture all words and sound (śabdarāśi) from the world. Due to the śabdākarṣaṇa prayoga performed by the two demons, all sounds and words were extracted from the mouths of the Brāhmaṇas and the personification of all mantras appeared as the crystalline white form of Sarasvatī who was captured by the two Asuras. As tears rolled from her eyes, the two demons restricted her with poisonous snakes and imprisoned her within a blue pool of Hālāhala poison. As a result, the Brāhmaṇas forgot the Veda and all yajnas and yāgas stopped. Due to not obtaining the havis, the Devas lost their potency and became exceedingly weak.
To alleviate the world from this calamity, Lord Nārāyaṇa assumed the form of Mahāmatsya (gigantic fish) sporting four hands that held khaḍga, cakra, śārṅga and cāpa . He dived into the depths of the ocean, destroyed Hayagrīva and Soma after a fierce battle, and rescued Sarasvatī from the poisonous pool. The Goddess was unconscious and was revived by the Lord through Tritāra, Prāsāda and Kāmeśvarī mantras. When the Goddess regained her consciousness, she noticed that she had completely turned blue on account of her having been imprisoned in the Hālāhala kuṇḍa. She expressed deep grief over her changed form which was now of a deep blue hue. Matsyāvatārī Bhagavān consoled her and assured here there was nothing wrong with being blue. He said, ‘The great goddess Umā is blue, and her consort is Nīlakaṇṭha; Indra the king of the devas is blue, the life-giving clouds are blue; the limitless sky is blue, the blemish that adds beauty to the moon is also blue. I am myself blue though I am verily the abode of sattvaguṇa. Do not grieve and from today, you will be known as ‘Nīlasarasvatī’ and will grant mokṣa to the deserving. The ṣaḍakṣara mantra used to revive you will grant one all desires’.
There is a discussion of yet another mantra of Nīlasarasvatī here. If one looks at the geographical origin of Bṛhannīla Tantra, which seems to be Bengal/Orissa, the attempt to frequently associate Tārā/Nīlasarasvatī with Viṣṇu/Kṛṣṇa (Matsyāvatāra in this case) becomes easy to explain. This Tantra is opined to be of a much later origin due to references therein to Durgāsaptaśatī and Gandharva Tantra. Also, the portrayal of the deity as the personification of Veda mantra is interesting to note, especially because of the Buddhist origins of Tārā. It is well-accepted that the popular dhyāna of Tārā provided by Kṛṣnānanda āgamavāgīśa was taken from the popular Buddhist manual Sādhanamālā. Older Buddhist works also describe Nāgārjuna as the propagator of the worship of Ekajaṭā, whose mantra he is said to have brought from Bhoṭa deśa (Tibet). The version of Nīlasarasvatī mantra described in Buddhist Tantras is this:
ॐ पिचु पिचु प्रज्ञावर्धनि ज्वल ज्वल मेधावर्धनि धिरि धिरि बुद्धिवर्धनि स्वाहा |
OM picu picu prajñāvardhani jvala jvala medhāvardhani dhiri dhiri buddhivardhani svāhā |
An alternate tale of origin is also narrated in Bṛhannīla Tantra. Defeated and tortured by the Asuras, the Devas invoke the Supreme Mahākālī who assumes a blue form known as Nīlasarasvatī to destroy the demons and grace the world.