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{{Short description|1965 book by Bharati Krishna Tirtha}}
{{For|developments in mathematics in the Vedic period|Indian mathematics#Vedic period}}
{{good article}}
{{use dmy dates|date=November 2019}}
{{Infobox book
| name = Vedic Mathematics
| image = Vedicmathematics.jpg
| author = [[Bharati Krishna Tirtha]]
| country = [[India]]
| subject = [[Mental calculation]]
| publisher = [[Motilal Banarsidass]]
| pub_date = 1965
| pages =
| isbn = 978-8120801646
| oclc = 217058562
| dewey =
| congress =
| wikisource =
}}
'''''Vedic Mathematics''''' is a book written by Indian ''[[Shankaracharya]]'' [[Bharati Krishna Tirtha]] and first published in 1965. It contains a list of mathematical techniques which were falsely claimed to contain advanced mathematical knowledge.<ref>{{Cite book|title=The history of mathematics : a brief course|last=Cooke|first=Roger L.|publisher=[[Wiley (publisher)|Wiley]]|year=2013|isbn=978-1-118-46029-0|location=Hoboken, N.J.|page=212|chapter=Overview of Mathematics in India|oclc=865012817}}</ref> The book was posthumously published under its deceptive title by editor V. S. Agrawala,{{sfnp|Shukla|2019}} who noted in the foreword that the claim of Vedic origin, made by the original author and implied by the title, was unsupported.<ref name="SGDani1993">{{harvp|Dani|2006}}.</ref>

Neither Krishna Tirtha nor Agrawala were able to produce sources, and scholars unanimously note it to be a compendium of methods for increasing the speed of elementary mathematical calculations sharing no overlap with historical [[Indian mathematics#Vedic period|mathematical developments during the Vedic period]]. Nonetheless, there has been a proliferation of publications in this area and multiple attempts to integrate the subject into mainstream education at the state level by [[right-wing]] [[Hindu nationalist]] governments.<ref name="Varma-2015" /><ref name="The Hindu-2001" />

== Contents ==
The book contains [[metaphorical]] [[aphorisms]] in the form of sixteen ''[[sutra]]s'' and thirteen sub-sutras, which Krishna Tirtha states allude to significant mathematical tools.<ref name="SGDani1993" /> The range of their asserted applications spans from topic as diverse as [[statics]] and [[pneumatics]] to astronomy and financial domains.<ref name="SGDani1993" /><ref name="Hogendijk-2004">{{Cite journal|last=Hogendijk|first=Jan|author-link=Jan Hogendijk|date=March 2004|title=De Veda's en de berekeningen van goeroe Tirthaji|url=http://www.fi.uu.nl/wiskrant/artikelen/233/233maart_hogendijk.pdf|journal=Nieuwe Wiskrant|volume=23|issue=3|pages=49–52}}</ref> Tirtha stated 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 standardised education system to become professionally trained in the discipline of mathematics.<ref name="SGDani1993" />

[[Science and technology studies|STS]] scholar [[S. G. Dani]] in '''Vedic Mathematics': Myth and Reality''<ref name="SGDani1993" /> states that the book is primarily a compendium of "tricks"{{efn|{{harvp|Dani|2006}}: "The book really consists of a compilation of tricks in elementary arithmetic and algebra, to be applied in computations with numbers and polynomials. By a 'trick' I do not mean a sleight of hand or something like that; in a general sense a trick is a method or procedure which involves observing and exploring some special features of a situation, which generally tend to be overlooked; for example, the trick described for finding the square of numbers like 15 and 25 with 5 in the unit’s place makes crucial use of the fact of 5 being half of 10, the latter being the base in which the numbers are written."}} 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 (for example, "as much less" or "one less than previous one") 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.<ref name="SGDani1993" />

===Relationship with the Vedas===
According to Krishna Tirtha, the sutras and other accessory content were found after years of solitary study of the [[Vedas]]—a set of sacred ancient Hindu scriptures—in a forest. They were supposedly contained in the ''[[pariśiṣṭa]]''—a supplementary text/appendix—of the [[Atharvaveda]].<ref name="SGDani1993" /> He does not provide any more bibliographic clarification on the sourcing.<ref name="SGDani1993" /> The book's editor, V. S. Agrawala, argues that since the Vedas are defined as the traditional repositories of all knowledge, any knowledge can be assumed to be somewhere in the Vedas, by definition; he even went to the extent of deeming Krishna Tirtha's work as a ''pariśiṣṭa'' in itself.{{sfnp|Shukla|2019}}

However, numerous mathematicians and STS scholars (Dani, [[Kim Plofker]], K.S. Shukla, [[Jan Hogendijk]] et al.) note that the Vedas do not contain any of those sutras and sub-sutras.<ref name="SGDani1993" /><ref name="Bal-2010">{{Cite magazine|last=Bal|first=Hartosh Singh|date=12 August 2010|title=The Fraud of Vedic Maths|url=https://openthemagazine.com/art-culture/the-fraud-of-vedic-maths/|magazine=The Open|access-date=25 November 2019}}</ref><ref>{{Cite book|title=Mathematics in India|title-link= Mathematics in India (book) |last=Plofker|first=Kim|date=18 January 2009|publisher=[[Princeton University Press]]|isbn=9780691120676|pages=16|chapter=Mathematical Thought In Vedic India|author-link=Kim Plofker|chapter-url=https://books.google.com/books?id=DHvThPNp9yMC}}</ref><ref name="Hogendijk-2004" /> When Shukla, a mathematician and historiographer of ancient Indian mathematics, challenged Krishna Tirtha to locate the sutras in the [[Parishishta]] of a standard edition of the [[Atharvaveda]], Krishna Tirtha stated that they were not included in the standard editions but only in a hitherto-undiscovered version, chanced upon by him; the foreword and introduction of the book also takes a similar stand.<ref name="SGDani1993" />{{sfnp|Shukla|2019}} Sanskrit scholars have observed that the book's linguistic style is not that of the [[Vedic period]] but rather reflects modern Sanskrit.<ref name="SGDani1993" />

Dani points out that the contents of the book have "practically nothing in common" with the mathematics of the [[Vedic period]] or even with subsequent developments in [[Indian mathematics]].<ref name="SGDani1993" /> Shukla reiterates the observations, on a per-chapter basis.{{sfnp|Shukla|2019}} For example, multiple techniques in the book involve the use of [[decimal fractions|decimals]]. These were unknown during the Vedic times and were introduced in India only in the sixteenth century;<ref name="Hogendijk-2004" /> works of numerous ancient mathematicians such as [[Aryabhata]], [[Brahmagupta]] and [[Bhaskara I|Bhaskara]] were based entirely on fractions.<ref name="SGDani1993" /> From a historiographic perspective, Vedic India had no knowledge of differentiation or integration.<ref name="SGDani1993" /> The book also claims that [[analytic geometry]] of [[Conic section|conics]] occupied an important tier in Vedic mathematics, which runs contrary to all available evidence.<ref name="SGDani1993" /><ref name="Hogendijk-2004" />

== Publication history and reprints ==
First published in 1965, five years after Krishna Tirtha's death, the work consisted of forty chapters, originally on 367 pages, and covered techniques he had promulgated through his lectures.<ref name="SGDani1993" /> A foreword by Tirtha's disciple Manjula Trivedi stated that he had originally written 16 volumes—one on each sutra—but the manuscripts were lost before publication, and that this work was penned in 1957.<ref name="Bal-2010" /><ref name="SGDani1993" /><ref name="WBFlorentin2006">{{cite book|url=https://arxiv.org/ftp/math/papers/0611/0611347.pdf|title=Vedic Mathematics: Vedic Or Mathematics: A Fuzzy and Neutrosophic Analysis|author1=W.B. Vasantha Kandasamy|author2=Florentin Smarandache|date=December 2006|publisher=American Research Press|isbn=978-1-59973-004-2|access-date=23 May 2013}}</ref>{{rp|10}}

Reprints were published in 1975 and 1978 to accommodate typographical corrections.<ref>Biographical sketch by Manjula Trivedi, 1965 in book Vedic Mathematics, pages x, xi.</ref> Several reprints have been published since the 1990s.<ref name="WBFlorentin2006" />{{rp|6}}

== Reception ==
[[S. G. Dani]] of the [[Indian Institute of Technology Bombay]] (IIT 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 collection of methods without any conceptual rigor, and to [[science and technology studies in India]] (STS) by adhering to dubious standards of historiography.<ref name="SGDani1993" />{{Efn|Dani's efforts to debunk the myth of Vedic Maths have been lauded by fellow mathematicians. Over {{Cite book|url=https://books.google.com/books?id=eFFyBgAAQBAJ|title=Recent Trends in Ergodic Theory and Dynamical Systems|last1=Bhattacharya|first1=Siddhartha|last2=Das|first2=Tarun|last3=Ghosh|first3=Anish|last4=Shah|first4=Riddhi|date=26 January 2015|publisher=[[American Mathematical Society]]|isbn=9781470409319|page=3}}, [[M. S. Raghunathan]] admires his efforts in this regard.}} 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.<ref name="SGDani1993" /> [[Jayant Narlikar]] has voiced similar concerns.<ref>{{Cite book|url=https://books.google.com/books?id=_l6eBQAAQBAJ|title=The Scientific Edge: The Indian Scientist from Vedic to Modern Times|last=Narlikar|first=Jayant V.|date=4 August 2003|publisher=[[Penguin UK]]|isbn=9789351189282}}</ref>

[[Hartosh Singh Bal]] notes that whilst Krishna Tirtha's attempts might be somewhat acceptable in light of his nationalistic inclinations during colonial rule—he had left his spiritual endeavors to be appointed as the principal of a college to counter [[Macaulayism]]—it provided a fertile ground for further ethnonationalist abuse of historiography by Hindu nationalist parties; [[Thomas Trautmann]] views the development of Vedic Mathematics in a similar manner.<ref name="Bal-2010" /><ref>{{Cite book|url=https://www.questia.com/read/125525910/languages-and-nations-conversations-in-colonial|title=Languages and Nations : Conversations in Colonial South India.|last=Trautmann|first=Thomas R.|publisher=[[University of California Press]]|year=2002|isbn=9780520931909|pages=45|oclc=476020847|access-date=21 October 2019|archive-date=21 October 2019|archive-url=https://web.archive.org/web/20191021152652/https://www.questia.com/read/125525910/languages-and-nations-conversations-in-colonial|url-status=dead}}</ref> [[Meera Nanda]] has noted hagiographic descriptions of Indian knowledge systems by various right-wing cultural movements (including the BJP), which have deemed Krishna Tirtha to be in the same league as [[Srinivasa Ramanujan]].<ref name="Nanda-2000" />

Some have, however, praised the methods and commented on its potential to attract school-children to mathematics and increase popular engagement with the subject.<ref>{{Cite journal|last=Pandey|first=Pushp Deep|date=2003|title=Public engagement with mathematics in India|url=https://www.currentscience.ac.in/php/show_article.php?volume=084&issue=07&titleid=id_084_07_0862_0863_0&page=0862|format=DjVu|journal=[[Current Science]]|volume=84|issue=7|pages=862–863|issn=0011-3891|jstor=24108037}}</ref><ref>{{cite news|url=http://www.thehindu.com/todays-paper/tp-in-school/everything-vedic-in-vedic-maths/article6508218.ece|title=Everything Vedic in 'Vedic Maths'|last1=Glover|first1=James|date=17 October 2014|work=[[The Hindu]]|access-date=4 January 2016|url-access=registration}}</ref><ref>{{Cite web|url=https://www.youtube.com/channel/UCb7w5aTnt7YeXBcVCY0mgFw|title=tecmath|website=YouTube|language=en|access-date=2020-03-14}}</ref> Others have viewed the works as an attempt at harmonising religion with science.<ref>{{Cite journal |last=Crisman |first=Karl-Dieter |date=9 August 2019 |title=Reviews |journal=The American Mathematical Monthly |volume=126 |issue=7 |pages=667–672 |doi=10.1080/00029890.2019.1606573 |issn=0002-9890 |s2cid=215770851}}</ref>

=== Originality of methods ===
Dani speculated that Krishna Tirtha's methods were a product of his academic training in mathematics{{efn|Krishna Tirtha had a [[Master of Arts]] in Mathematics.<ref name="SGDani1993" />}} and long-recorded habit of experimentation with numbers.<ref name="SGDani1993" /> Similar systems include the [[Trachtenberg system]] or the techniques mentioned in Lester Meyers's 1947 book ''High Speed Mathematics''.<ref name="SGDani1993" /> [[Alex Bellos]] points out that several of the calculation methods can also be found in certain European treatises on calculation from the [[early Modern period]].<ref name="alex">{{cite book|chapter-url=https://books.google.com/books?id=Cp8oyheDhfUC|title=Alex's Adventures in Numberland|last=Bellos|first=Alex|publisher=[[Bloomsbury Publishing|Bloomsbury]]|year=2010|isbn=9781408808863|chapter=Something about nothing}}</ref>

=== Computation algorithms ===
Some of the algorithms have been tested for efficiency, with positive results.<ref>{{Cite journal|last1=Kasliwal|first1=Prabha S.|last2=Patil|first2=B. P.|last3=Gautam|first3=D. K.|date=1 January 2011|title=Performance Evaluation of Squaring Operation by Vedic Mathematics|journal=IETE Journal of Research|volume=57|issue=1|pages=39–41|doi=10.4103/0377-2063.78327|doi-broken-date=1 July 2025 |doi-access=free|s2cid=120316446|issn=0377-2063}}</ref><ref>{{Cite book|title=2013 International Multi-Conference on Automation, Computing, Communication, Control and Compressed Sensing (IMac4s)|last1=Huddar|first1=S. R.|last2=Rupanagudi|first2=S. R.|last3=Kalpana|first3=M.|last4=Mohan|first4=S.|publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]|year=2013|isbn=978-1-4673-5090-7|pages=465–469|chapter=Novel high speed vedic mathematics multiplier using compressors|doi=10.1109/iMac4s.2013.6526456|s2cid=11124644}}</ref><ref>{{Cite book|title=2009 International Conference on Advances in Computing, Control, and Telecommunication Technologies|last1=Mehta|first1=Parth|last2=Gawali|first2=Dhanashri|publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]|year=2009|isbn=978-1-4244-5321-4|pages=640–642|chapter=Conventional versus Vedic Mathematical Method for Hardware Implementation of a Multiplier|doi=10.1109/ACT.2009.162|s2cid=6773150}}</ref><ref>{{Cite book|title=2012 International Conference on Devices, Circuits and Systems (ICDCS)|last1=Kunchigi|first1=V.|last2=Kulkarni|first2=L.|last3=Kulkarni|first3=S.|publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]|year=2012|isbn=978-1-4577-1546-4|pages=360–364|chapter=High speed and area efficient vedic multiplier|doi=10.1109/ICDCSyst.2012.6188747|s2cid=19077488}}</ref> However, most of the algorithms have higher [[time complexity]] than conventional ones, which explains the lack of adoption of Vedic mathematics in real life.<ref>{{Citation|last1=Sen|first1=Syamal K.|title=5 - Conclusions|date=1 January 2016|url=http://www.sciencedirect.com/science/article/pii/B9780081007747000053|work=Zero|pages=93–142|editor-last=Sen|editor-first=Syamal K.|publisher=[[Academic Press]]|isbn=978-0-08-100774-7|access-date=23 November 2019|last2=Agarwal|first2=Ravi P.|editor2-last=Agarwal|editor2-first=Ravi P.}}</ref>

== Integration into mainstream education ==
The book has been included in the school syllabus of the Indian states of [[Madhya Pradesh]] and [[Uttar Pradesh]], soon after the [[Bharatiya Janata Party]] (BJP), a right-wing nationalist political party, came to power and remade the education system to emphasise historically dubious notions like that that Vedic Mathematics represented a genuinely ancient and inherently superior Indian and Hindu system of mathematics, knowledge, and thinking.<ref name="WBFlorentin2006" />{{rp|6}}<ref name="Nanda-2000">{{Cite book|chapter-url=https://books.google.com/books?id=QkcuQFBXLFQC|title=The Sokal Hoax: The Sham that Shook the Academy|last=Nanda|first=Meera|publisher=[[University of Nebraska Press]]|year=2000|isbn=9780803219243|pages=206–213|chapter=The Science Wars in India|author-link=Meera Nanda}}</ref><ref>{{Cite journal|last=Behera|first=Navnita Chadha|date=1 July 1996|title=Perpetuating the divide: Political abuse of history in South Asia|journal=Contemporary South Asia|volume=5|issue=2|pages=191–205|doi=10.1080/09584939608719789|issn=0958-4935}}</ref><ref>{{Cite book|title=The Foreign Encounter in Myth and Religion: Modes of Foreign Relations and Political Economy|last=Pijl|first=Kees Van Der|publisher=[[Pluto Press]]|year=2010|isbn=978-0-7453-2316-9|volume=2|pages=98|chapter=Warrior Heroes in the Indo-European Lineage|jstor=j.ctt183h05v.7|doi=10.2307/j.ctt183h05v.7}}</ref>

[[Dinanath Batra]] had conducted a lengthy campaign for the inclusion of Vedic Mathematics into the [[National Council of Educational Research and Training]] (NCERT) curricula.<ref>{{Cite journal|last=Taylor|first=McComas|date=2 October 2014|title=Hindu Activism and Academic Censorship in India|journal=South Asia: Journal of South Asian Studies|volume=37|issue=4|pages=717–725|doi=10.1080/00856401.2014.956679|s2cid=144408510|issn=0085-6401}}</ref> Subsequently, there was a proposal from NCERT to induct Vedic Mathematics, along with a number of fringe pseudo-scientific subjects (Vedic Astrology et al.), 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 criticised the move as a politically guided attempt at [[saffronisation]].<ref name="Hogendijk-2004" /><ref>{{Cite web|url=http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html|title=Neither Vedic Nor Mathematics |website=www.sacw.net|access-date=20 October 2019}}</ref><ref name="The Hindu-2001">{{Cite news|url=https://www.thehindu.com/todays-paper/tp-miscellaneous/tp-others/legitimisation-of-vedic-mathematics-astrology-opposed/article27971872.ece|title=Legitimisation of Vedic mathematics, astrology opposed|date=14 August 2001|work=[[The Hindu]]|access-date=25 November 2019|language=en-IN|issn=0971-751X}}</ref><ref>{{Cite web|url=https://archives.peoplesdemocracy.in/2001/aug19/aug192k1_education1.htm|title=Stop this Fraud on our Children|website=archives.peoplesdemocracy.in|access-date=20 October 2019 |archive-url=https://web.archive.org/web/20160314160716/https://archives.peoplesdemocracy.in/2001/aug19/aug192k1_education1.htm |archive-date=2016-03-14}}</ref><ref>{{Cite journal|last=Hasan|first=Mushirul|date=1 December 2002|title=The BJP's intellectual agenda: Textbooks and imagined history|journal=South Asia: Journal of South Asian Studies|volume=25|issue=3|pages=187–209|doi=10.1080/00856400208723498|s2cid=143341141|issn=0085-6401}}</ref><ref>{{Cite book|url=https://www.questia.com/read/117286858/a-place-at-the-multicultural-table-the-development|title=A place at the multicultural table the development of an American Hinduism|last=Kurien|first=Prema A.|publisher=[[Rutgers University Press]]|year=2007|isbn=9780813540559|pages=164|chapter=Re-visioning Indian History: Internet Hinduism|jstor=j.ctt5hj9tk|oclc=703221465|chapter-url=https://muse.jhu.edu/chapter/620190|chapter-format=PDF|url-access=subscription|access-date=21 October 2019|archive-date=21 October 2019|archive-url=https://web.archive.org/web/20191021152653/https://www.questia.com/read/117286858/a-place-at-the-multicultural-table-the-development|url-status=dead}}</ref>

After the BJP's return to power in 2014, three universities began offering courses on the subject of Vedic Mathematics while a television channel catering to the topic was also launched; generous education and research grants have also been allotted to the subject despite a lack of genuine scientific, mathematical, historical, or religious basis for doing so.<ref>{{Cite news|url=https://www.telegraph.co.uk/news/worldnews/asia/india/11331533/Indias-next-gift-to-the-world-could-be-Vedic-mathematics.html|title=India's next gift to the world could be Vedic mathematics|journal=[[Daily Telegraph]]|last=Nelson|first=Dean|date=7 January 2015|access-date=20 October 2019|language=en-GB|issn=0307-1235}}</ref><ref>{{Cite book|url=https://www.questia.com/read/120041069/the-clash-within-democracy-religious-violence|title=The Clash Within : Democracy, Religious Violence, and India's Future.|last=Nussbaum|first=Martha Craven|publisher=[[Harvard University Press]]|year=2008|isbn=9780674030596|pages=222|oclc=1006798430|author-link=Martha Nussbaum|url-access=subscription}}</ref><ref>{{Cite book|chapter-url=https://www.questia.com/read/120580887/scientific-values-and-civic-virtues|title=Scientific values and civic virtues|last=Nanda|first=Meera|publisher=[[Oxford University Press]]|year=2005|isbn=9780198038467|editor-last=Koertge|editor-first=Noretta|pages=224|chapter=Postmodernism, Hindu Nationalism, and “Vedic Science”|doi=10.1093/0195172256.001.0001|oclc=62288153|author-link=Meera Nanda|chapter-url-access=subscription}}</ref><ref name="Varma-2015">{{Cite news|url=https://timesofindia.indiatimes.com/home/education/news/Vedic-maths-Not-quite-adding-up/articleshow/45839520.cms|title=Vedic maths: Not quite adding up |website=[[The Times of India]]|date=11 January 2015 |access-date=22 October 2019}}</ref> The topic was introduced into the elementary curriculum of [[Himachal Pradesh]] in 2022.<ref>{{Cite web |title=Himachal to introduce Sanskrit language, Vedic mathematics in elementary classes |url=https://www.indiatoday.in/education-today/news/story/himachal-to-introduce-sanskrit-language-vedic-mathematics-in-elementary-classes-1902006-2022-01-19 |access-date=2024-03-04 |website=India Today |date=19 January 2022 |language=en}}</ref><ref>{{Cite web |last=IANS |title=As Himachal introduces chanting of slokas in schools, critics target govt for 'saffronising' education |url=https://www.deccanherald.com/india/as-himachal-introduces-chanting-of-slokas-in-schools-critics-target-govt-for-saffronising-education-1101459.html |access-date=2024-03-04 |website=Deccan Herald |language=en}}</ref> The same year, the government of [[Karnataka]] allocated funds for teaching the subject. This move by the BJP provoked criticism from academics and from [[Dalit]] groups.<ref>{{Cite news |last=R |first=Jayanth |date=2022-09-15 |title=Reserved funds to be used to teach 'Vedic' maths for SC/ST students |url=https://www.thehindu.com/news/national/karnataka/reserved-funds-to-be-used-to-teach-vedic-maths-for-scst-students/article65895866.ece |access-date=2024-03-04 |work=The Hindu |language=en-IN |issn=0971-751X}}</ref><ref>{{Cite web |last=Belur |first=Rashmi |date=15 September 2022 |title=Now, Karnataka govt to introduce vedic maths for SC/ST kids |url=https://www.deccanherald.com/india/karnataka/st-kids-1145457.html |access-date=2024-03-04 |website=Deccan Herald |language=en}}</ref>

==Editions==
* {{cite book |author=Swami Sri Bharati Krsna Tirthaji Maharaja |editor=V. S. Agrawala |title=Vedic Mathematics: Sixteen Simple Mathematical Formulae from the Vedas |place=Varanasi |publisher=[[Motilal Banarsidass]] |edition=First |year=1965 |url=https://archive.org/details/dli.scoerat.13528vedicmathmetics |url-access=registration |ref=none}}

== Notes ==
{{Notelist}}

==References==
{{Reflist}}

===Works cited===
* {{cite book |first=S. G. |last=Dani |author-link=S. G. Dani |orig-year=1993 |chapter=Myths and reality: On 'Vedic Mathematics' |chapter-url=https://www.tifr.res.in/~vahia/dani-vmsm.pdf |editor1-first=W. B. Vasantha |editor1-last=Kandasamy |editor2-first=Florentin |editor2-last=Smarandache |year=2006 |title=Vedic Mathematics, 'Vedic' or 'Mathematics': A Fuzzy & Neutrosophic Analysis |place=Gallup, New Mexico |publisher=Multimedia Larga |isbn=978-1-59973-004-2 |url=https://arxiv.org/ftp/math/papers/0611/0611347.pdf |archive-url=https://web.archive.org/web/20220106084127/https://www.tifr.res.in/~vahia/dani-vmsm.pdf |access-date=23 May 2013|archive-date=6 January 2022 }}
*{{Cite book |title=Studies in Indian Mathematics and Astronomy: Selected Articles of Kripa Shankar Shukla |last=Shukla |first=K. S. |publisher=[[Springer Publishing]] |year=2019 |isbn=978-981-13-7325-1 |editor-last=Kolachana |editor-first=Aditya |series=Sources and Studies in the History of Mathematics and Physical Sciences |location=Singapore |chapter=Vedic Mathematics: The deceptive title of Swamiji’s book |pages=697–704 |doi=10.1007/978-981-13-7326-8 |editor-last2=Mahesh |editor-first2=K. |editor-last3=Ramasubramanian |editor-first3=K. |url=https://books.google.com/books?id=k86aDwAAQBAJ}}

{{Authority control}}

[[Category:Books about Hinduism]]
[[Category:Books about the history of mathematics]]
[[Category:Indian non-fiction books]]
[[Category:Mental calculation]]
[[Category:1965 non-fiction books]]
[[Category:Pseudohistory]]
[[Category:20th-century Indian books]]
[[Category:Pseudomathematics]]
[[Category:Hindutva]]

Vedic Mathematics - Revision history

AntoniaWhetsel0: stub