Srinivasa Ramanujan

Srinivasa Ramanujan, the greatest of all the twentieth century mathematicians, born at a time, a period, when India was lauded as Ratna Garbha, the nineteenth century.

India, with its ancient culture and its heritage gave birth to so many great persons, throughout its history from time immemorial. But, Ramanujan stands alone on a separate plane(t), because he was a warrior par excellence. He was not armed with weapons, but his own vision.

Throughout the centuries there were men who took first steps down new roads new roads armed with nothing but their own vision, Ramanujan certainly belongs to that class.

‘Ramanujan’ owns his name in such a way that the word itself causes and creates awe among the listeners and if a person tells others that he is a (some) Ramanujan, he was compared and liked to the Ramanujan.

His life was a tamely finished voyage, but not tamely made. His untimely death, he lived thirty two years four months and four days, may have stopped the flow of formulae, and identities, which Hardy once remembered with awe and affection that he was shown some half a dozen formulae per a day, but not the influence he created over many of modern-day number theorists.

Ramanujan left behind a vast number of results in his note books. Many of them were studied and proved by some professors/mathematicians partially. Still many of them are not satisfactorily proved.

Prof. Bruce C. Berndt, of University of Illinois, has spent much of his time, for over two decades to study each and every one of the 3254 entries in the Note books of Ramanujan. These were brought out and published by him, and his colleagues. Also there was a pre-posthumous work, of him, namely ‘The Collected papers’ have been a source for further researches to innumerable researchers world over.

Śruti and Smŗti (Smruthi)

Such a vast number of results is an incredible achievement in such a short life time, but it was made possible by the genius Ramanujan. As earlier said, his work of producing six results a day demonstrates the frantic pace at which he worked.

Once asked by others, Ramanujan replied that he was told those formulas by Namagiri Thayar (or Namagiridevi or Goddess of Namagiri) of Namakkal, his family deity, in his dreams. Some of the modernists ridiculed that statements, but this can be explained, and can be proved true by the ancient Indian tradition of Śruti and Smŗti.

Śruti means hearing, not mere hearing, but hearing to a Guru (teacher) with all concentration in a proper way. In the ancient periods the students were taught vocally but the Gurus, the Vedas and other scriptures. The students listen to them with all concentration, of course concentration personified. That is the reason for the Vedas are called Śrutis. Smŗti means remembrance. It is the art of remembrance that had lead to the preservation of all the Vedic literature.

It was told that Vedas were first told by the Lord Vishnu to the Brahma. Brahma heard them, and by remembering (Smŗti) them passed the knowledge on to the next (further) generations.

The students used to hear (Śruti) from the Guru, and remember the knowledge (Smŗti), and used it for practical purposes. Through the ancient concept Śruti and Smŗti, Ramanujan the student ‘listened to’ his Guru, the Goddess Namagiri Thayar, who used to appear in his dreams, and remembered the formulas told by her In this way, he produced a lot of formulas.

It is human nature to err, and that is the reason why some of his formulas were wrong, but the errors were very little. To be precise, he might not remember all the formulas told by the Goddess Namagiri Thayar, his Guru in his dreams.

Why and how he took Her counsel? What made him to take mathematics as his prime interest? When did he start his voyage in to the ocean of Mathematics? What sort of atmosphere, in which he has grown, thatMade him the man he is? This will be discussed in the following passages. We will start in the following way.Some of Ramanujan’s western friends who thought they knew him, would say that he was not really religious, that his mind was indistinguishable (?) from any brilliant westerner’s, that he was a Hindu only by a mechanical observance, or for form’s sake alone.

Was his mind indistinguishable from any brilliant westerners’? Had any westerner from the late eighteenth century to the dawn of the twenty first century produced results of Ramanujan’s class? Most of those so-called brilliant westerners spent years to even understand his formulae. (Some are there of equal brilliance, but they were tutored in a formal way). Still majority of his work unproved and some of his work is producing stunning applications in modern technologies and theoretical physics.

All the years he was growing up, he lived the life of a traditional Hindu Brahmin. He wore the topknot. He had felt sad and was reluctant when he had to cut his hair and remove his topknot, when he was to go to the west. He never grew moustache and beard. He was always clean shaved.

All his life he was a rigid vegetarian. He frequented local temples. He strictly participated in ceremonies and rituals at home. He regularly invoked his family deity’s name, the Goddess of Namagiri of Namakkal and based his actions on what he had taken to be her wishes.

He attributed to the Gods his ability to navigate through the shoals of mathematical texts written in foreign languages. He could recite from the Vedas, the Upanishads and other Hindu scriptures.

He had penchant for interpreting dreams, a taste for occult phenomena, a mystical bent, upon which his Indian friends unfailingly commented. It was said that he had predicted his death to his wife in his later years.

Ramanujan often lost in talking about Vedas and śastras, the ancient Sanskrit tomes, and gave running commentaries on their meanings.

At the age of twenty-one, he showed up at the house of a teacher, got drawn in to a conversation, and soon was expatiating on the ties he saw between God, zero and Infinity, keeping every one spell bound. It was the way often for Ramanujan. Losing himself in philosophical and mystical monologues, he would make bizarre, fanciful leaps of imagination that his friends and others did not understand but found fascinating any way.

This was evident in his mathematical equations also. They cannot make you understand them with much ease, but fascinate you.

It was no surprise that Ramanujan was inspired and lead by divine hand.It had been to Namagiri, the consort of the Lion-god Narasimha, to whom Ramanujan’s parents, childless then, had prayed for a child. Ramanujan’s maternal grandmother, Rangammal, was a devotee of Namagiri, and was said to enter a trance to speak to her. Many years earlier, before Ramanujan’s birth, Namagiri revealed (to) her that one day the Goddess would speak through her daughter’s son.

Ramanujan grew up hearing the story. All his life he invoked Her blessings, seek Her counsel. It was the Goddess Namagiri, he would tell his friends, to whom he owed his mathematical gifts. Namagiri would bestow mathematical insights in his dreams. Namagiri would tell and wrote equations on his tongue. He was the student and She was the Guru. He would hear from Her (Śruti), and would remember by rechanting the equations (Smŗti), wrote in his notebooks. Being a mortal, he would sometimes forget his lessons, due to which he erred.

What a great and live example to the ancient traditional Guru-Sishya relationship Between Namagiri and Ramanujan? It is to be remembered that Saraswathi is the Goddess of knowledge, and wisdom. Gayathri is the Goddess of Vedic scriptures. It is the great Indian tradition, which gives equal priority to the fairer gender (ladies).

Comparison with Einstein and Mozart

“What Einstein was to physics, Mozart was to music, Ramanujan was to mathematics,” says Clifford Stoll.

was arguably the greatest ever, inarguably the greatest of the twentieth century physicists. He has changed the face of modern day physics.

ఇది నేను శ్రీనివాస రామానుజన్ మీద తయారు చేస్తున్న లాంగ్ ఎస్సే. ఇంతవరకూ ఆయన గురించి టచ్ చేయని రీతిలో ఒక కొత్త పాయింట్ని తీసుకుని రాస్తున్నది. దీనిని Prof. Krishnaswami Alladi గారికి, Prof. K. Srinivasarao (Ex. Director, IMSc, Chennai) గారికీ, మరికొందరు ప్రముఖులకి చూపించటం జరిగింది. వారంతా ఎంతో మెచ్చుకుని ఈ రకం గానే వ్రాయమనీ, పూర్తి చేసిన తరువాత పబ్లిష్ చేయిద్దామనీ అన్నారు. మన తెలుగు బ్లాగర్ల కోసం అందులో కొంత భాగాన్ని నా బ్లాగులో పెడుతున్నాను.