Vedic Mathematics (book)
Vedic Mathematics is a book written by the high-ranking Hindu cleric Bharati Krishna Tirthaji and first published in 1965. It contains a list of mental calculation techniques claimed to be based on the Vedas. The mental calculation system mentioned in the book is also known by the same name or as "Vedic Maths". Its characterization as "Vedic" mathematics has been criticized by academics, who have also opposed its inclusion in the Indian school curriculum.
Although the book was first published in 1965, Tirthaji had been propagating the techniques since much earlier, through lectures and classes. He wrote the book in 1957 during his tour of the United States.:10 The typescripts was returned to India in 1960 after his death. It was published in 1965, five years after his death as 367 pages in 40 chapters. Reprints were made in 1975 and 1978 with fewer typographical errors. Several reprints have been made since the 1990s.:6
Tirthaji claimed that he found the sutras after years of studying the Vedas, a set of sacred ancient Hindu texts. However, Vedas do not contain any of the "Vedic mathematics" sutras. First, Tirthaji’s description of the mathematics as Vedic is most commonly criticised on the basis that, thus far, none of the sūtras can be found in any extant Vedic literature (Williams, 2000). When challenged by Professor K.S. Shukla to point out the sutras in question in the Parishishta of the Atharvaveda, Shukla reported that the Tirthaji said that the sixteen sutras were not in the standard editions of the Parishishta, and that they occurred in his own Parishishta and not any other.
The book contains 16 sutras, each of which lists a mental calculation technique. Prof. S. G. Dani of IIT Bombay points out that the contents of the book have "practically nothing in common" with the mathematics of the Vedic period or even the subsequent Indian mathematics. Tirthaji has liberally interpreted three-word Sanskrit phrases to associate them with arithmetic.
|1||Ekadhikena Purvena||Anurupyena||By one more than the previous one|
|2||Nikhilam Navatashcaramam Dashatah||Sisyate Sesasamjnah||All from 9 and the last from 10|
|3||Urdhva-Tiryagbyham||Adyamadyenantyamantyena||Vertically and crosswise|
|4||Paraavartya Yojayet||Kevalaih Saptakam Gunyat||Transpose and adjust|
|5||Shunyam Saamyasamuccaye||Vestanam||When the sum is the same that sum is zero|
|6||Anurupye Shunyamanyat||Yavadunam Tavadunam||If one is in ratio, the other is zero|
|7||Sankalana-vyavakalanabhyam||Yavadunam Tavadunikritya Varga Yojayet||By addition and by subtraction|
|8||Puranapuranabyham||Antyayordashake'pi||By the completion or non-completion|
|9||Chalana-Kalanabyham||Antyayoreva||Differences and Similarities|
|10||Yaavadunam||Samuccayagunitah||Whatever the extent of its deficiency|
|11||Vyashtisamanstih||Lopanasthapanabhyam||Part and Whole|
|12||Shesanyankena Charamena||Vilokanam||The remainders by the last digit|
|13||Sopaantyadvayamantyam||Gunitasamuccayah Samuccayagunitah||The ultimate and twice the penultimate|
|14||Ekanyunena Purvena||Dhvajanka||By one less than the previous one|
|15||Gunitasamuchyah||Dwandwa Yoga||The product of the sum is equal to the sum of the product|
|16||Gunakasamuchyah||Adyam Antyam Madhyam||The factors of the sum is equal to the sum of the factors|
The first edition of the book edited by Prof. Vasudeva Saran Agrawala, who indicates that there is no evidence that the sutras are "Vedic" in their origin.:6 The techniques mentioned in the book do not date back to the Vedic period either. For example, multiple techniques in the book involve the use of decimal fractions, which were not known during the Vedic times: even the works of later mathematicians such as Aryabhata, Brahmagupta and Bhaskara do not contain any decimal fractions.
Tirthaji's claimed that the sutras are relevant to advanced mathematical techniques such as successive differentiation or analytical conics have also been dismissed by the academics. S. G. Dani calls "ludicrous" the Tirthaji's claim that "there is no part of mathematics, pure or applied, which is beyond their jurisdiction". S. G. Dani also points out that Tirthaji's methods were not unique, although they may have been invented by him independently (he held an MA in mathematics). Similar systems include the Trachtenberg system or the techniques mentioned in Lester Meyers's 1947 book High-speed Mathematics. Alex Bellos points out that several of the calculation tricks can also be found in early Modern European treatises on calculation.
Use in schools
The book was previously included in the school syllabus of Madhya Pradesh and Uttar Pradesh.:6 Some schools and organizations run by Hindu nationalist groups, including those outside India, have also included Tirthaji's techniques in their curriculum. The Hindu nationalists have also made several attempts to have Tirthaji's "Vedic mathematics" system included in the Indian school curriculum via the NCERT books.
A number of academics and mathematicians have opposed these attempts on the basis that the techniques mentioned in the book are simply arithmetic tricks, and not mathematics. They also pointed out that the term "Vedic" mathematics is incorrect, and there are other texts that can be used to teach a correct account of the Indian mathematics during the Vedic period. They also criticized the move as a saffronization attempt to promote religious majoritarianism.
Dani points out that while Tirthaji's system could be used as a teaching aid, there was a need to prevent the use of "public money and energy on its propagation, beyond the limited extent". He pointed out that the authentic Vedic studies had been neglected in India even as Tirthaji's system received support from several Government and private agencies.
Vedic mathematics is now taught by several schools and organisations in India as well as other parts of the world. The Chinmaya International Foundation, a foundation of the Chinmaya Mission, is among the proponents of the Vedic Mathematics system.
- Alex Bellos (2010). "3". Alex's Adventures in Numberland. Bloomsbury.
- S. G. Dani (December 2006). "Myths and reality : On ‘Vedic mathematics’". Originally published as a 2-part article in Frontline, 22 October and 5 November 1993. The updated version appears in Kandasamy and Smarandache (2006).
- W.B. Vasantha Kandasamy; Florentin Smarandache (December 2006). Vedic Mathematics: Vedic Or Mathematics: A Fuzzy and Neutrosophic Analysis. American Research Press. ISBN 978-1-59973-004-2. Retrieved 23 May 2013.
- Biographical sketch by Manjula Trivedi, 1965 in book Vedic Mathematics, pages x, xi.
- The Fraud of Vedic Maths. Hartosh Singh Bal. Open Magazine. 14 August 2010.
- K.S. Shukla, Vedic mathematics — the illusive title of Swamiji’s book, Mathematical Education, Vol 5: No. 3, January–March 1989
- K.S. Shukla, Mathematics — The Deceptive Title of Swamiji’s Book, in Issues in Vedic Mathematics, (ed: H.C.Khare), Rashtriya Veda Vidya Prakashan and Motilal Banarasidass Publ., 1991.
- R. K. Thakur (1 November 2009). Vedic Mathematics. Unicorn Books. ISBN 978-81-7806-177-1. Retrieved 23 May 2013.
- Neither Vedic nor Mathematics
- Legitimisation of Vedic mathematics, astrology opposed. The Hindu, 14 August 2001.