Vedic Mathematics is a book written by the Indian monk Bharati Krishna Tirtha, and first published in 1965. It contains a list of mainly 16 mathematical techniques, which the author claimed were retrieved from the Vedas and supposedly contained all mathematical knowledge. These claims have been since rejected in their entirety. Krishna Tirtha failed to produce the claimed sources, and scholars unanimously note it to be a mere compendium of tricks for increasing the speed of elementary mathematical calculations with no overlap with historical mathematical developments during the Vedic period. However, there has been a proliferation of publications in this area and multiple attempts to integrate the subject into mainstream education by some governments.
Contents
The book contains metaphorical aphorisms in the form of sixteen sutras and thirteen sub-sutras, which Krishna Tirtha claimed to allude to significant mathematical tools. The range of their asserted applications spans from topic as diverse as statics and pneumatics to astronomy and financial domains. Tirtha claimed that no part of advanced mathematics lay beyond the realms of his book and propounded that studying it for a couple of hours every day for a year equated to spending about two decades in any standardized education system to become professionally trained in the discipline of mathematics. Contra the hyperbolic claims of the author and publisher, the book is primarily a compendium of tricks that can be applied in elementary, middle and high school arithmetic and algebra, to gain faster results. The sutras and sub-sutras are abstract literary expressions prone to creative interpretations; Krishna Tirtha exploited this to the extent of manipulating the same shloka to generate widely different mathematical equivalencies across a multitude of contexts.
Publication history and reprints
Although the book was first published in 1965, Krishna Tirtha had been propagating the techniques much earlier through lectures and classes. He wrote the book in 1957. It was published in 1965, five years after his death, and included forty chapters in 367 pages. A foreword by Tirtha's disciple Manjula Trivedi claims that he had originally written 16 volumes—one on each sutra—but the manuscripts were lost before publication. Reprints were published in 1975 and 1978 to accommodate typographical corrections. Several reprints have been published since the 1990s.
Reception
of the Indian Institute of Technology Bombay notes the book to be of dubious quality. He believes it did a disservice both to the pedagogy of mathematical education by presenting the subject as a bunch of tricks without any conceptual rigor, and to science and technology studies in India by adhering to dubious standards of historiography. He also points out that while Tirtha'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" except in a limited way and that authentic Vedic studies were being neglected in India even as Tirtha's system received support from several government and private agencies. Jayant Narlikar has voiced similar concerns. Hartosh Singh Bal notes that whilst Krishna Tirtha's attempts might be somewhat acceptable in light of his nationalistic inclinations during colonial rule, it set the grounds for further ethno-nationalistic abuse of historiography by Hindu Nationalist parties; Thomas Trautmann views the development of Vedic Mathematics in a similar manner. Others have viewed the works as an attempt at harmonizing religion with science. Some have however praised the methods and commented on its potential to attract school-children to mathematics and increase popular engagement with the subject.
Originality of methods
Dani believes Krishna Tirtha's methods to be a product of his academic training in mathematics and long recorded habit of experimentation with numbers; nonetheless, he considers the work to be an impressive feat. 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 certain European treatises on calculation from the early Modern period.
Computation algorithms
Some of the algorithms have been tested for efficiency, with positive results. However, most of the algorithms have higher time complexity than conventional ones, which explains the lack of adoption of Vedic mathematics in real life.
Integration into mainstream education
The book had been included in the school syllabus of Madhya Pradesh and Uttar Pradesh, in 2017. Dinanath Batra had conducted a lengthy campaign for the inclusion of Vedic Maths into the National Council of Educational Research and Training curricula. Subsequently, there was a proposal from NCERT to induct Vedic Maths, along with a number of fringe pseudo-scientific subjects, into the standard academic curricula. This was only shelved after a number of academics and mathematicians, led by Dani and sometimes backed by political parties, opposed these attempts based on previously discussed rationales and criticized the move as a politically guided attempt at saffronization. Concurrent official reports also advocated for its inclusion in the Madrassah education system to modernize it. After the BJP's return to power in 2014, three universities began offering courses on the subject while a television channel, catering to the topic, was also launched; generous education and research grants have also been allotted to the subject. Meera Nanda has noted hagiographic descriptions of Indian knowledge systems by various right-wing cultural movements, which deemed Krishna Tirtha to be in the same league as Srinivasa Ramanujan.
