Discovery of a Lost Math System
BY: SUN STAFF
Dec 17, 2010 CANADA (SUN) Sutras and subsutras a major Vedic contribution to complex mathematics; and some history of Srila Bhaktisiddhanta Sarasvati Thakur's study of mathematics (author unknown).
In 1911, a brilliant young Indian professor of mathematics, Venkatraman Sarasvati, threw aside a promising academic career as the faculty head of a new national college, and entered the forest ashram of the Shankaracarya of Shringeri, Mysore to fulfill a burning desire to research and unearth scientific secrets from the sacred texts of the Vedas.
The Vedas have long been acclaimed as the world's oldest and biggest storehouse of spiritual knowledge. The voluminous body of Vedic literature also encompasses various branches of the material arts and sciences: Sanskrit grammar, prosody, lexicography, astronomy, astrology, military science, medicine, surgery, architecture, sculpture, mathematics, engineering sciences, music, fine arts and more. However these branches of Vedic arts and sciences were generally overlooked by mundane Indian academicians and scientists, who meekly swallowed whatever "theory" was dictated to them by their colonial masters, and showed little regard or inclination to conduct original study and research of the profound heritage of Vedic literature.
The cryptic language of the Vedas was also a barrier to most scholars, it ensured that only the best of the intellectuals and the spiritually-inspired would be able to mine its hidden treasures. Professor Venkatraman belonged to that rare creed, an accomplished scholar with deep conviction in the absolute truth of the sacred Vedic texts, and stood above and apart from the rest of the academic crowd.
Born in Tinniveli, Madras, in 1884 to highly pious and learned parents (his father's name is Narasimha Shastri), he topped every examination in every subject in every class he took. In 1899, at age 16, he was awarded the title of "Sarasvati" by the Madras Sanskrit Association for his proficiency in the language of the Vedas. In 1904, he took the external MA examinations of the American College of Sciences, Rochester, New York, in seven subjects -- Sanskrit, Philosophy, English, Mathematics, History and Science -- and scored top honours in all! This is reportedly a world record for academic achievement.
Unlike mundane academics who merely aped Western science and showed a biased, dishonest disregard for Vedic science, Professor Venkatraman had deep spiritual leanings and absolute faith in the truths of the Vedas. This spurred him towards his future calling as a revolutionary mathematician, preacher and religious leader of the country (he would go on to become the Shankaracarya of Govardhana Math, Jagannatha Puri).
Unenlightened remarks on the Vedas from unenlightened academics only served to strengthen his resolve to take up the challenge and disprove them. He wrote:
"And the contemptuous or, at best patronising attitude adopted by some so-called orientologists, indologists, antiquarians, research-scholars etc who condemned, or light-heartedly, nay irresponsibly, frivilously and flippantly dismissed, several abtruse-looking and recondite parts of the Vedas as "sheer nonsense" or as "infant humanity's prattle", and so on, merely added fuel to the fire (so to speak) and further confirmed and strengthened our resolute determination to unravel the too long-hidden mysteries of philosophy and science contained in ancient India's Vedic lore..."
Professor Venkatraman performed tapas (austerities) and yoga in the forests of Shringeri to facilitate his research and contemplation. His endeavour was finally crowned with success when he made a breakthrough in deciphering revolutionary mathematical techniques from his research on the Vedic texts. He described the momentous occasion:
"...after eight years of concentrated contemplation in forest solitude, we were at long last able to recover the long lost keys which alone could unlock the portals thereof."
However he did not claim any personal credit for his success. Instead he said that his findings were encapsulated in 16 Sanskrit sutras (and some corollary subsutras) that he attributed to Vedic sources:
"We were agreeably astonished and intensely gratified to find that exceedingly tough mathematical problems (which the mathematically most advanced Western scientific world had spent huge lots of time, energy and money on and which even now it solves with the utmost difficulty after vast labour involving large numbers of difficult, tedious and cumbersome steps of working) can be easily and readily solved with the help of these ultra-easy Vedic sutras contained in the Parishishta (appendix) of the Atharva Veda in a few simple steps and by methods which can be conscientiously described as mere mental arithmetic."
Mathematical Sutras and Subsutras
The Sanskrit sutras and subsutras revealed by His Holiness Bharati Krishna Tirthaji Maharaja encoded deeper mathematical knowledge. The Maharaja, who later became the Shankaracarya of Puri, wrote 16 volumes on the detailed application of these sutras in mathematics, one volume for each sutra. He was firmly convinced of their wide scope of application and wrote:
"The sutras apply to and cover each and every part of each and every chapter of each and every branch of mathematics (including arithmetic, algebra, geometry - plane and solid, trigonometry - plane and spherical, conics - geometrical and analytical, astronomy, calculus - differential and integral, etc). In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction."
However the original manuscripts of the 16 volumes, given by the Shankaracarya to one of his disciples for safe-keeping prior to being published, were lost without trace. During his last few years, the Shankaracarya embarked on re-writing his lost works from memory. After completing the manuscript of one introductory volume, the Shankaracarya attained samadhi in 1960. His sole volume on Vedic mathematics summarises the application of some of the above sutras. That's all the world is left with, until another genius of similar calibre as the late Shankaracarya of Puri emerges to research and decipher further scientific knowledge from these sutras and other portions of the Vedic texts.
Then Almost All Lost Again
Emerging triumphantly from his self-imposed eight-year "sabbatical" in the forest ashram, Professor Venkatraman was initiated into the holy order of sannyasa (renunciate) as Bharati Krishna Tirthaji Maharaja by Trivikrama Tirthaji Maharaja, the Shankaracharya of Sharadapith in Benares (Varanasi) in 1919 at the age of 35. Within two years, he became the next Shankaracharya there. He was marked out for greater responsibility by the Shankaracharya of Govardhana Pith in the holy city of Jagannatha Puri, Shri Madhusudana Tirtha, who wanted to hand over his position due to failing health. This is the same magnanimous personality who some twenty years earlier had cordially received and assisted the great Vaishnava scholar and devotee, Shrila Bhaktisiddhanta Sarasvati Thakura, the foremost mathematician and Vedic astrologer of his time.
From 1902-1904, Shrila Bhaktisiddhanta was staying in the Bhakti Kutir of his father, Shrila Bhaktivinoda Thakur, in Jagannatha Puri, just 100 yards from the Govardhana Matha. He frequently visited the Matha and discoursed with Shri Madhusudana. This is described in the newly-released biography, Sri Bhaktisiddhanta Vaibhava compiled by his grand-disciple, HH Bhakti Vikasa Swami:
"Sri Madhusudana, head of the Matha, treated Sri Siddhanta Sarasvati respectfully, personally guided him in his research, and gave him free access to the extensive Matha library. In fact, Sri Siddhanta spent so much time discussing monism with Sri Madhusudana Tirtha that some people suspected that he might join the impersonalists' camp." (Srila Bhaktisiddhanta would go on to found the Gaudiya-Vaisnava Matha and open up 64 temples and preaching centres in India. His disciple, Srila Bhaktivedanta Swami Prabhupada, would later found the International Society for Krishna Consciousness and spread the bhakti movement around the world.) In 1925, Shankaracharya Madhusudana fell seriously ill and insisted on handing over his mantle to Bharati Krishna Tirthaji Maharaja, who in deference to his order, appointed Sri Svarupanandji to head Sharadapith and went to Jagannatha Puri to become the Shankaracharya there and dedicated the rest of his life travelling and preaching both philosophy and science. Among the books on philosophy he wrote is a title on Sanatana Dharma (the Eternal Religion of the Soul). His lectures and demonstrations on mathematics were well-received by academicians and students in colleges and universities all across the country and were also highlighted by the media.
The Maharaja wrote 16 volumes on the detailed application of his 16 Sanskrit sutras in mathematics, one volume for each sutra. He was firmly convinced of their wide scope of application: "The sutras apply to and cover each and every part of each and every chapter of each and every branch of mathematics (including arithmetic, algebra, geometry - plane and solid, trigonometry - plane and spherical, conics - geometrical and analytical, astronomy, calculus - differential and integral, etc). In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction."
The manuscripts of the 16 volumes were deposited in the house of one of his disciples in Nagpur for safe-keeping prior to being published. However before they could be published, the manuscripts vanished. This tremendous loss of scientific knowledge remains an unsolved mystery till today. Some reports alleged that the manuscripts were illegally acquired and taken out of the country by a foreigner. When the loss of his works was finally reported to the Maharaja, he remained unperturbed and said that everything was still there in his memory and that he could re-write the entire 16 volumes all over again from his retentive memory. But as the Shankaracharya, he had many more pressing duties and demands on his time to attend to first.
In 1957, at the age of 73, the Shankaracharya finally started on the task of re-writing the 16 volumes from memory. He completed the first manuscript, an introductory volume, before embarking, in February 1958, on a three-month tour of the United States and the United Kingdom where he gave hundreds of classes, lectures and demonstrations on science and religion. This is the first time in history that a Shankaracharya broke with established tradition and crossed the Indian Ocean to preach. He dazzled rapt audiences in colleges, universities, churches and other public institutions with his discourses. He gave demonstrations of his mathematical wizardry on television too. He also left behind his sole manuscript to be published in the USA.
After returning to India in May 1958, the Shankaracharya continued his strenuous schedule of travelling and preaching until his health deteriorated. The following year, he fell seriously ill. On February 2, 1960, the Shankaracharya attained samadhi in Mumbai at age 76. His manuscript was brought back to India and published posthumously by his followers under the title Vedic Mathematics. The task of re-writing the 16 volumes was thus left uncompleted. However with the single manuscript that he has left behind, he has successfully planted the seeds in a fertile research field for future scientists and mathematicians to explore and expand.
With the sutras, mathematical formulae and shortcuts, clues and pointers in his introductory volume, the Shankaracharya has bequeathed to modern science a magnificent link to the knowledge of the ancients. Although some academicians, unable to find fault with his mathematics, chose instead to question the authenticity of his Sanskrit sutras, their carping has been overshadowed by the tremendous interest in his work by students in India and other parts of the world who are benefiting from the simple, speedy techniques of calculation he unearthed. The ground-breaking work of the mathematics professor who became renunciate preacher and Shankaracharya continues to be a boon for students facing competitive examinations today.
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