The following is based upon accounts known through oral tradition and texts like the mAdhavIya Sankara vijayam. There exists some controversy about Sankara's date, but most traditions are quite unanimous about other details.
Birth and childhood: Sankara was born to the nambUdiri brAhmaNa couple, Sivaguru and AryAmbA, in a little village called kAlaDi in Kerala. The couple had remained childless for a long time, and prayed for children at the vaDakkunnAthan (VRshAcala) temple in nearby Trichur. Siva is said to have appeared to the couple in a dream and promised them a choice of one son who would be short-lived but the most brilliant philosopher of his day, or many sons who would be mediocre at best. The couple opted for a brilliant, but short-lived son, and so Sankara was born.
Sankara lost his father when quite young, and his mother performed his upanayana ceremonies with the help of her relatives. Sankara excelled in all branches of traditional vaidIka learning. A few miracles are reported about the young Sankara. As a brahmacArin, he went about collecting alms from families in the village. A lady who was herself extremely poor, but did not want to send away the boy empty-handed, gave him the last piece of Amla fruit she had at home. Sankara, sensing the abject poverty of the lady, composed a hymn (kanakadhArA stavam) to SrI, the goddess of wealth, right at her doorstep. As a result, a shower of golden Amlas rewarded the lady for her piety. On another occasion, Sankara is said to have re-routed the course of the pUrNA river, so that his old mother would not have to walk a long distance to the river for her daily ablutions.
sam.nyAsa: Sankara was filled with the spirit of renunciation early in his life. Getting married and settling to the life of a householder was never part of his goal in life, though his mother was anxious to see him as a gRhastha. Once when he was swimming in the river, a crocodile caught hold of his leg. Sankara sensed that he was destined to die at that moment, and decided to directly enter the fourth ASrama of sam.nyAsa right then. This kind of renunciation is called Apat sam.nyAsa. The crocodile released him when he thus mentally decided to renounce the world, and Sankara decided to regularize his decision by going to an accomplished guru. To comfort his anxious mother, he promised that he would return at the moment of her death, to conduct her funeral rites, notwithstanding the fact that he would be a sannyAsI then.
Sankara then traveled far and wide in search of a worthy guru who would initiate him and regularize his vow of sam.nyAsa, till he came to the banks of the river narmadA in central India. Here was the ASrama of govinda bhagavatpAda, the disciple of gauDapAda, the famous author of the mANDUkya kArikAs. Sankara was accepted as a disciple by govinda, who initiated him into the paramahamsa order of sam.nyAsa, the highest kind of renunciation. Seeing the intellectual acumen of his disciple, govinda commanded Sankara to expound the philosophy of vedAnta through commentaries on the principal upanishads, the brahmasUtras and the gItA. Sankara took leave of his guru and traveled to various holy places in India, composing his commentaries in the meantime. At this time he was barely a teenager. He attracted many disciples around him, prominent among whom was sanandana, who was later to be called padmapAda. In this period, Sankara wrote commentaries on bAdarAyaNa's brahmasUtras, the various upanishads and the bhagavad gItA. These commentaries, called bhAshyas, stand at the pinnacle of Indian philosophical writing, and have triggered a long tradition of sub-commentaries known as vArttikas, TIkAs and TippaNis. He also commented upon the adhyAtma-paTala of the Apastamba sUtras, and on vyAsa's bhAshya to patanjali's yogasUtras. In addition to these commentarial texts, Sankara wrote independent treatises called prakaraNa granthas, including the upadeSasAhasrI, Atmabodha, etc.
In addition to writing his own commentaries, Sankara sought out leaders of other schools, in order to engage them in debate. As per the accepted philosophical tradition in India, such debates helped to establish a new philosopher, and also to win disciples and converts from other schools. It was also traditional for the loser in the debate to become a disciple of the winner. Thus Sankara debated with Buddhist philosophers, with followers of sAm.khya and with pUrva mImAm.sakas, the followers of vedic ritualism, and proved more than capable in defeating all his opponents in debate. Sankara then sought out kumArila bhaTTa, the foremost proponent of the pUrva mImAm.sA in his age, but bhaTTa was on his deathbed and directed Sankara to viSvarUpa, his disciple. viSvarUpa is sometimes identified with maNDana miSra.
Sankara's debate with viSvarUpa was unique. The referee at the debate was viSvarUpa's wife, bhAratI, who was herself very well-learned, and regarded as an incarnation of Goddess sarasvatI. At stake was a whole way of life. The agreement was that if viSvarUpa won, Sankara would consent to marriage and the life of a householder, whereas if Sankara won, viSvarUpa would renounce all his wealth and possessions and become a sannyAsI disciple of Sankara. The debate is said to have lasted for whole weeks, till in the end, viSvarUpa had to concede defeat and become a sannyAsI. bhAratI was a fair judge, but before declaring Sankara as the winner, she challenged Sankara with questions about kAmaSAstra, which he knew nothing about. Sankara therefore requested some time, during which, using the subtle yogic process called parakAya-praveSa, he entered the body of a dying king and experienced the art of love with the queens. Returning to viSvarUpa's home, he answered all of bhAratI's questions, after which viSvarUpa was ordained as a sannyAsI by the name of sureSvara. He was to become the most celebrated disciple of Sankara, writing vArttikas to Sankara's bhAshyas on the yajurveda upanishads, in addition to his own independent texts on various subjects.
Establishment of maThas: Sankara continued to travel with his disciples all over the land, all the while composing philosophical treatises and engaging opponents in debate. It is said that none of his opponents could ever match his intellectual prowess and the debates always ended with Sankara's victory. No doubt this is true, given the unrivaled respect and popularity that Sankara's philosophical system enjoys to this day. In the course of his travels, Sankara stayed for a long time at the site of the old ASrama of the Rshis vibhAndaka and RshyaSRnga, in the place known as SRngagiri (Sringeri). Some texts mention that Sankara stayed at Sringeri for twelve years. A hermitage grew around him here, which soon developed into a famous maTha (monastery). sureSvara, the disciple whom he had won after long debate, was installed as the head of this new ASrama. Similar maThas were established in the pilgrim centers of Puri, Dvaraka and Joshimath near Badrinath, and padmapAda, hastAmalaka and troTaka were placed in charge of them. These are known as the AmnAya maThas, and they continue to function today. Their heads have also come to be known as SankarAcAryas, in honor of their founder, and revered as jagadgurus, or teachers of the world. Sankara also organized the community of ekadaNDI monks into the sampradAya of daSanAmI sannyAsins, and affiliated them with the four maThas that he established.
Meanwhile, Sankara heard that his mother was dying, and decided to visit her. Remembering his promise to her, he performed her funeral rites. His ritualistic relatives would not permit him to do the rites himself, as he was a sannyAsI, but Sankara overrode their objections, and built a pyre himself and cremated his mother in her own backyard. After this, he resumed his travels, visiting many holy places, reviving pUjAs at temples that had fallen into neglect, establishing SrI yantras at devI temples as in Kancipuram, and composing many devotional hymns.
Ascension of the sarvajnapITha: In the course of his travels, Sankara reached Kashmir. Here was a temple dedicated to SAradA (sarasvatI), the goddess of learning, which housed the sarvajnapITha, the Throne of Omniscience. It was a tradition for philosophers to visit the place and engage in debate. The victorious one would be allowed to ascend the sarvajnapITha. It is said that no philosopher from the southern region had ever ascended the pITha, till Sankara visited Kashmir and defeated all the others there. He then ascended the sarvajnapITha with the blessings of Goddess SAradA. (A few centuries later, rAmAnuja, the teacher of viSishTAdvaita, would visit the same sarvajnapITha in search of the baudhAyana vRtti. However, a variant tradition places the sarvajnapITha in the south Indian city of Kancipuram.)
Sankara was reaching the age of 32 now. He had expounded the vedAnta philosophy through his writings; he had attracted many intelligent disciples to him, who could carry on the vedAntic tradition; and he had established monastic centers for them in the form of maThas. His had been a short, but eventful life. He retired to the Himalayas and disappeared inside a cave near Kedarnath. This cave is traditionally pointed out as the site of his samAdhi. Other variant traditions place Sankara's last days at Karavirpitham or at Mahur in Maharashtra, Trichur in Kerala or Kancipuram in Tamil Nadu. It is a measure of SankarAcArya's widespread fame that such conflicting traditions have arisen around his name.
True to the traditions of sam.nyAsA, Sankara was a peripatetic monk, who traveled the length and breadth of the country in his short lifetime. His fame spread so far and wide, that various legends are recounted about him from different parts of India. The true sannyAsI that he was, he lived completely untouched by the fabric of society. So much so that even the location of kAlaDi, his birth-place, remained generally unknown for a long time. The credit of identifying this village in Kerala goes to one of his 19th-century successors at Sringeri, SrI saccidAnanda SivAbhinava nRsimha bhAratI. Similarly, the credit of renovating Sankara's samAdhi-sthala near Kedarnath, goes to SrI abhinava saccidAnanda tIrtha, his 20th-century successor at Dvaraka.
According to tradition, maNDana miSra was originally a pUrva mImAm.saka, who debated with Sankara, and lost. He is then said to have become a disciple of Sankara, and taken the name sureSvara.
A number of works on grammar (vyAkaraNa - sphoTasiddhi) and vedic exegesis (pUrva mImAm.sA - vidhiviveka, bhAvanAviveka and mImAm.sAnukramaNikA) have been written by maNDana miSra. He is also the author of vibhramaviveka, a treatise on theories of error, in which he refers both to the "anyathAkhyAti" theory of pUrva mImAm.sA and the "anirvacanIyakhyAti" theory of advaita. Moreover, although he is traditionally held to be a disciple of kumArila bhaTTa, the most famous pUrva mImAm.saka, maNDana clearly holds non-dualistic philosophical views in vidhiviveka and sphoTasiddhi. maNDana also severely criticizes kumArila's mImAm.sA theory of language in the sphoTasiddhi, and following bhartRhari, he upholds the non-duality of Sabda-brahman.
maNDana miSra's treatise on advaita, the brahmasiddhi, consists of four chapters, containing both prose and verse sections. He shows a sharp knowledge of the crucial aspects of all the systems which he refutes in the brahmasiddhi, including nyAya-vaiSeshika, pUrva mimAm.sA, bauddha and jaina schools and other vedAnta schools. He is arguably the first among a galaxy of advaitin scholars who made substantial contributions to other schools of Indian philosophy. There are a number of commentaries to the brahmasiddhi, including brahmasiddhi-TIkA by SankhapANi, abhiprAya-prakASikA by citsukha, and bhAvaSuddhi by AnandapUrNa vidyAsAgara. It is said that vAcaspati miSra's tattva samIkshA, which is not available now, was a commentary on the brahmasiddhi.
The traditional identification of maNDana miSra with sureSvara has been doubted in the modern literature. Much can be said on both sides of this issue. It has been pointed out that maNDana miSra and Sankara are most probably contemporaries, and that maNDana must have known of Sankara's philosophical views when he wrote the brahmasiddhi. Many themes are common to both maNDana and Sankara, e.g. that the reality of the universe lasts only until liberation, which is nothing more or nothing less than realizing the true nature (svarUpa) of the Atman; and that the jIva is really brahman, but appears to be different by false knowledge and limiting adjuncts.
Perhaps this similarity is to be expected, because these are some of the cardinal principles of advaita, and any advaitin of note would necessarily follow these lines. There does seem to be some contrast between maNDana and Sankara on some other issues. maNDana shows a tendency to accommodate what is known as "jnAnakarmasamuccayavAda" - a combined path of jnAna and karma to achieve liberation. On the other hand, Sankara is uncompromising in emphasizing jnAna and denying that karma can directly lead to liberation, except for its role in cittaSuddhi, i.e. as a means of purification. And sureSvara's independent work is titled naishkarmyasiddhi - the achievement of the state of the absence of karma. maNDana and sureSvara also differ on the question of the locus of avidyA. maNDana holds that the avidyA rests on the jIva, and has brahman for its object. sureSvara maintains that avidya both rests on brahman and has brahman for its object. This difference in view about the nature and locus of avidyA is also seen in post-Sankaran advaita. vAcaspati miSra takes the same view as maNDana does, and authors in the bhAmatI sub-school expand their views along these lines. However, the vivaraNa writers mostly follow sureSvara's line of reasoning, and hold that brahman is both the locus and object of avidyA. Many contemporary scholars think that this difference of opinion is a late, post-Sankaran development. In this connection, it is important to remember that maNDana was a contemporary of Sankara, so that this difference of opinion indeed has an old history.
Did maNDana miSra, the author of brahmasiddhi, write several treatises on pUrva mImAm.sA earlier? If so, did maNDana, the pUrva mImAm.saka, change his philosophical views later in his life to become maNDana, the vedAntin? Is maNDana, the pUrva mImAm.saka, the same as maNDana, the vedAntin? Or are they different people? Finally, is maNDana the same as sureSvara? Such questions will probably never be answered to everybody's satisfaction. It is interesting to note in this connection that, in the post-Sankaran advaita literature, the names sureSvara and viSvarUpa are used interchangeably to refer to the vArttikakAra, while maNDana, the author of the brahmasiddhi, is usually referred to only as the brahmasiddhikAra . However, many traditional hagiographies, including the mAdhavIya Sankara-vijaya, identify the two.