Bharati Krishna Tirtha
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Swāmī Bhāratī Kṛṣṇa Tīrtha (March 1884 – February 2, 1960) was the Śankarācārya of Govardhana matha in Puri, Orissā (now Odishā) from 1925 to 1960. He is particularly known for his book Vedic Mathematics.
Venkatarāman Shastrī was born in March 1884 to an orthodox Tamil Brahmin family. His father was P. Narasimha Shastrī, originally a tehsildar at Tirunelveli in Madras Presidency who later became the Deputy Collector of the Presidency. His uncle, Chandrasekhar Shastrī, was the Principal of the Mahārāja's college in Vizianagaram, while his great-grandfather, Justice C. Ranganāth Shastrī was a judge in the Madras High Court.
Venkatarāman Shastrī joined National College in Trichinopoly. After that he moved to the Church Missionary Society College and eventually the Hindu College, both in Tirunelveli. Shastri passed his matriculation examination from Madras University in January 1899, where he also finished the first.
Although Venkatarāman always scored high in subjects like mathematics, sciences and humanities, he was also proficient in languages and particularly good at Sanskrit. According to his own testimonials, Sanskrit and oratory were his favourite subjects. Due to his skill at the language, that he was awarded the title "Saraswati" by the Madras Sanskrit Association in July 1899 at the age of 16. At about that time, Venkatraman was profoundly influenced by his Sanskrit guru Vedam Venkatrai Shastri.
Venkatarāman passed B.A. examination in 1902. He then appeared for the M.A. Examination for the American College of Sciences in Rochester, New York from the Bombay centre in 1903. He also contributed to W. T. Stead's Review of Reviews on diverse topics like religion and science. During his college days, he also wrote extensively on history, sociology, philosophy, politics, and literature.
Early public life
Venkatarāman Shastrī worked under Gopal Krishna Gokhale in 1905 for the National Education Movement and the South African Indian problems. However, his inclination towards Hindu studies led him to study the ancient Indian holy scriptures, Adhyātma-Vidyā. In 1908, he joined the Sringeri Matha in Mysore to study under Svāmī Satchidānanda Śivābhinava Nrsimha Bhāratī, the Śankarācārya of Sringeri. However, his spiritual practise was interrupted when he was pressured by nationalist leaders to head the newly started National College at Rajamahendri. Prof. Venkatarāman Shastrī taught at the college for three years. But in 1911, he suddenly left the college to go back to Sringeri Matha.
Returning to Sringeri, Venkatarāman spent the next eight years studying advanced Vedanta philosophy with Satchidānanda Śivābhinava Nrsimha Swamigal.
He also practised vigorous meditation, Brahma-sadhana and Yoga-sādhāna, in the nearby forests during those years. It is believed that he attained spiritual self-realization during his years at Sringeri Matha. He would leave the material world and practice Yoga meditation in seclusion for many days. During those eight years, he also taught Sanskrit and philosophy at local schools and ashrams. He delivered a series of sixteen lectures on Śankarācārya's philosophy at Shankar Institute of Philosophy, Amalner (Khandesh). During that time, he also lectured as a guest professor at institutions in Mumbai, Pune and Khandesh.
Initiation into Sannyāsa order
After Venkatarāman's eight-year period of spiritual practice and study of Vedānta and Vedic philosophy, he was initiated into the holy order of sannyāsa in Varanasi by Jagadguru Śankarācārya Svāmī Trivikrāma Tīrtha of Sharada Peetha, Sringeri, on July 4, 1919 and on this occasion he was given the title Swami and the new name "Svāmī Bhāratī Kṛṣṇa Tīrtha".
Śankarācārya of Sharada Peetha
Svāmī Bhāratī Kṛṣṇa Tīrtha was installed as Śankarācārya of Sharada Peetha in 1921 after just two years of sannyāsa. After assuming the pontificate, he was given another title, Jagadguru, as is the tradition. The Swami then toured India from corner to corner giving lectures on Sanātana Dharma, Vedic philosophy and Vedanta.
Śankarācārya of Govardhana Matha
Around the time the Svāmī became Śankarācārya of Sharada Peetha, the Śankarācārya of Govardhana matha, Svāmī Madhusudhana Tīrtha, was in failing health and was greatly impressed by Bhāratī Kṛṣṇa. Madhusudana requested Bhāratī Kṛṣṇa to succeed him at Govardhana Matha. Bhāratī Kṛṣṇa respectfully declined the offer. In 1925, however, Śankarācārya Svāmī Madhusudhana Tīrtha's health took a serious turn and Svāmī Bhāratī Kṛṣṇa Tīrtha had to accept the Govardhana Matha gaddi. In 1925, Svāmī Bhāratī Kṛṣṇa Tīrtha assumed the pontificate of Govardhana Matha, and relinquished the gaddi of Sharada Peetha. He installed Svāmī Svarupānanda as the new Śankarācārya of Sharada Peetha.
In 1921, the Shankaracharya was one of the seven arrested in what became known as the "Karachi case". Maulanaa Mohammed Ali, Maulana Shaukat Ali, Dr. Kitchlu, Nissar Ahmed, Pir Ghulam Mujaddid, and Bharati Krishna Tirtha were charged with preaching in favour of a fatwa issued by the Muslim religious heads of India advocating all Muslims to not cooperate with the government. While the Shankaracharya was eventually acquitted, the others were sentenced to two years imprisonment.
After becoming the Śankarācārya of Govardhana Matha, Svāmī Bhāratī Kṛṣṇa Tīrtha toured several countries for thirty-five years to spread the values of peace, harmony and brotherhood, and to spread the message of Sanātana Dharma. He took upon himself the task of contributing to the renaissance of Indian culture.
While being a pontiff, he wrote a number of treatises and books on religion, sciences, mathematics, world peace, and social issues. In 1953, at Nagpur, he founded an organisation called the Sri Vishwa Punarnirmana Sangha (World Reconstruction Association). Initially, the administrative board consisted of Bhāratī Kṛṣṇa's disciples, devotees and admirers of his spiritual ideals for humanitarian service, but later distinguished people would also contribute to the mission. The Chief Justice of India, Justice B.P. Sinha, served as its President. Dr. C. D. Deshmukh, the ex-Finance Minister of India and ex-Chairman of the University Grants Commission served as its Vice-President.
In February 1958, he went on a trans-oceanic tour to the United States to speak on world peace and Vedānta, staying for three months in Los Angeles, California, traveling via the United Kingdom. This was the first trip outside India by a Śankarācārya. The tour was sponsored by the Self-Realization Fellowship of Los Angeles, the Vedantic society founded by Paramahansa Yogananda in America. At that time, Albert Rudolph, or "Rudi", became one of his students.
He attended national and international religious conferences and Yoga workshops. He believed in the Vedāntic ideal of Pūrnatva which, literally translated, means "all-round perfection and harmony". He remained the Śankarācārya of Govardhana Matha until his death in 1960.
Bhāratī Kṛṣṇa Tīrtha's book, Vedic Mathematics, is a list of sixteen terse sūtras, or "aphorisms", discussing strategies for mental calculation. Bhāratī Kṛṣṇa claimed that he found the sūtras after years of studying the Vedas, a set of sacred ancient Hindu scriptures. 
For arithmetic, Bhāratī Kṛṣṇa gives several algorithms for whole number multiplication and division, (flag or straight) division, fraction conversion to repeating decimal numbers, calculations with measures of mixed units, summation of a series, squares and square roots (duplex method), cubes and cube roots (with expressions for a digit schedule), and divisibility (by osculation).
Several tests and techniques for factoring and solving certain algebraic equations with integer roots for quadratic, cubic, biquadratic, pentic equations, systems of linear equations, and systems of quadratic equations are demonstrated. For fractional expressions, a separation algorithm and fraction merger algorithms are given. Other techniques handle certain patterns of some special case algebraic equations. Just an introduction to differential and integral calculus is given.
Geometric applications are reviewed for linear equations, analytic conics, the equation for the asymptotes, and the equation to the conjugate-hyperbola. Five simple geometric proofs for the Pythagorean theorem are given. A 5-line proof of Apollonius' theorem is given.
Advanced topics promised included integral calculus (the centre of gravity of hemispheres, conics), trigonometry, astronomy (spherical triangles, earth's daily rotation, earth's annual rotation about the sun and eclipses), and engineering (dynamics, statics, hydrostatics, pneumatics and applied mechanics).
In his final comments, he asserted that the names for "Arabic" numerals, the "Pythagorean" Theorem and the "Cartesian" co-ordinate system are historical misnomers; rather, according to Tirthaji, these mathematical insights were enumerated and formalised first by Indian mathematicians of the Hindu tradition, for whom credit ought to be acknowledged.
- "Understanding ancient Indian mathematics". The Hindu. India. 26 December 2011.
- Manjula Trivedi, "My Beloved Gurudeva", dedication to Bhāratī Kṛṣṇa, in Bhāratī Kṛṣṇa's Vedic Mathematics, page i.
- Manjula Trivedi, page i.
- Manjula Trivedi, page ii.
- Manjula Trivedi, pages i-ii.
- Manjula Trivedi, page iii.
- Manjula Trivedi, page iii
- Manjula Trivedi, page iv.
- South Asian Studies. South Asia Institute, University of Heidelberg, Delhi Branch. 1978. pp. 416, 417.
- Prasad, Rajendra (1946). Autobiography (PB). Penguin Books India. p. 136. ISBN 9780143068815.
- Manjula Trivedi, page v-vi.
- Manjula Trivedi, page vi.
- Publication announcement by N.H. Bhagwati, Vice-Chancellor, Banaras Hindu University, March 27, 1965, after title page, Vedic Mathematics
- Agrawala, V. S. (1992). General Editor's note. Vedic Mathematics (pp. v-viii) Motilal Banarsidass Publishers Private Limited.
- Myths and reality : On ‘Vedic mathematics’. S.G. Dani. School of Mathematics, Tata Institute of Fundamental Research. Frontline, 22 October and 5 November 1993.
- The Fraud of Vedic Maths. Hartosh Singh Bal. Open Magazine. 14 August 2010.
- Table of Contents, Vedic Mathematics
- Table of Contents,Vedic Mathematics
- Pages 354-360, Vedic Mathematics
- Pages 350-351, Vedic Mathematics
- Page 352, Vedic Mathematics
- Pages 361-362, Vedic Mathematics
- Page 353, Vedic Mathematics
- Trivedi, Manjula, My Beloved Gurudeva, Sri Vishwa Punarnirmana Sangha, Nagpur (1965).
- Svāmī Bhāratī Kṛṣṇa Tīrtha, Vedic Mathematics, Motilal Banarsidass, Delhi (1992). ISBN 81-208-0164-4
- A Pictorial Biography of Bharti Krishna Tirthaji Maharaja, includes Historic Pictures and Newspaper Article
- A biography of Sri Bharati Krishna Tirthaji (1884–1960) at the Wayback Machine (archived 9 April 2005)
- Puroshattam D. Chidgupkar and Mangesh T. Karad (2004). "The Implementation of Vedic Algorithm in Digital Signal Processing" (PDF). Global Journal of Engineering Education.
- S.G. Dani. "Vedic Mathematics": a dubious pursuit.