While Vedic mathematics may evoke associations with Hindutva, it fundamentally represents a system of straightforward arithmetic capable of handling intricate calculations.
Let’s address the question: Why should there be objections when children are required to memorize multiplication tables up to 19? So, why should anyone protest if students are taught a method, specifically Vedic mathematics, that enables them to multiply numbers like 199 by 199 without relying on multiplication tables?
The revival of interest in Vedic maths can be traced back to Jagadguru Swami Sri Bharathi Krishna Tirthaji Maharaj, who published a book on the subject in 1965. Subsequently, the Bharatiya Janata Party government in Uttar Pradesh, Madhya Pradesh, Rajasthan, and Himachal Pradesh introduced Vedic mathematics into the school curriculum. However, this move was viewed by some as an attempt to promote Hindutva, as Vedic philosophy was portrayed as the repository of all human wisdom. The ensuing controversy surrounding the teaching of Vedic maths is primarily because it became linked with fundamentalism and obscurantism, concepts diametrically opposed to science. Critics argue that embracing Vedic maths implies endorsing a Hindu renaissance.
But does this argument hold water? Indian mathematics has long been recognized for its depth, extending beyond the discovery of zero. Krishna Tirtha is credited with uncovering 16 mathematical formulae that were part of the parishishta (appendix) of the Atharva Veda, one of the four Vedas (See box). Tirtha’s elegant formulae enable intricate mathematical calculations, encompassing factorization, highest common factors, simultaneous, quadratic, cubic, and biquadratic equations, partial fractions, elementary geometry, and even differential and integral calculus (See box). Nonetheless, Tirtha has his critics, both within and outside the scientific community, who question the scientific validity of Vedic mathematics.
A common criticism is that the Vedic maths text focuses primarily on middle and high school-level formulations, emphasizing a series of problem-solving tricks. Critics also highlight that the Atharva Veda appendix, which contains Tirtha’s 16 mathematical formulae, cannot be found in any existing texts. Another criticism centers on the quality of the book’s writing itself.
Notably, prominent mathematician S G Dani, a professor at the Tata Institute of Fundamental Research in Bombay, has voiced his critique of Vedic mathematics. He wrote in The Times of India, “The book (Tirtha’s Vedic Mathematics) apparently gathered wider respectability around the mid-1980s following a statement in Parliament by the then human resources minister. Inclusion of such spurious material as Vedic not only corrupts the intellectual process of a proper study of history, but is also unhealthy for society in view of their being prone to abuse in various ways. It is absurd and outrageous to build up a false framework of history to whip up pride; our mathematical heritage offers plenty to be proud of, without resorting to such gimmickry.”
Part of the controversy surrounding Vedic maths arises from the perception that the book is genuinely Vedic and the involvement of politicians who have embraced it. However, on the opposing side are mathematicians like Dani, who stress the importance of dispelling unfounded myths about the antiquity and capabilities of the book, as they can lead to misguided approaches to both history and mathematics, potentially negatively impacting an entire generation of children.
Deceptive Characteristics
To assess the strengths and weaknesses of Vedic mathematics, one must consider the works of ancient Indian mathematicians like Aryabhata I (AD 475), Brahmagupta (622), Bhaskara II (1150), and possibly Sangama Grama Madhava and Narayana Pandita (14th century). This suggests that it might be more accurate to refer to it as Indian rather than Vedic mathematics.
Indeed, much of Tirtha’s work may seem tailored to middle and high school levels, but appearances can be deceiving. The Indian mathematical tradition leans toward inductive and intuitive methods, seldom explicitly stating rigorous proofs. This inductive and intuitive approach, similar to some of Srinivasa Ramanujan’s work, is distinct from a deductive approach. When I S Bhanu Murthy attempted to prove some of Tirtha’s formulae, he discovered that a few profound theorems of number theory were involved.
Therefore, not all of Tirtha’s work can be dismissed as elementary. A substantial portion of it pertains to arithmetic and enhances computational skills, offering pedagogical value.
Tirtha’s work provides numerous examples that refute claims that it’s merely a collection of computational tricks. It is true, however, that the Atharva Veda’s appendix, which contains the 16 formulae attributed to Tirtha, cannot be found in complete form. Only abbreviated references exist. Additionally, the techniques in Tirtha’s book concerning division and recurring decimals are absent from the works of early Indian mathematicians. Nonetheless, Tirtha’s techniques for squares, square roots, cubes, and cube roots align with the work of Aryabhata I, Sridhara (750), and Bhaskara II.
This raises two possibilities: either Tirtha rediscovered lost parts of the Atharva Veda, or he independently developed the formulae, which would indicate his status as a greater mathematician than he professed to be. Regardless of whether the formulae are officially part of the Atharva Veda’s appendix, their practical utility is undeniable.
A Wealthy Tradition
Beyond Tirtha’s work, there is a compelling case for a closer examination of ancient Indian mathematics. Methods employed by Aryabhata I for determining square and cube roots, as well as those by Sridhara and Bhaskara II to solve equations, are significantly faster than conventional methods. Therefore, why not incorporate these techniques into mathematics education? Why not teach students Bhaskara II’s and Brahmagupta’s approaches to solving equations?
Numerous aspects of geometry were explored by ancient Indian mathematicians, with pi serving as an example. Various series were developed to approximate pi, including Lilavati’s estimations of 22/7 and 3927/1250.
Ancient Indian mathematics does not encapsulate the entirety of mathematical wonder, and many modern mathematical concepts were beyond the comprehension of early mathematicians. However, a rational and scientific approach is needed to extract from these early works what is useful and relevant to contemporary needs. Dismissing Vedic maths as fundamentalist and obscurantist goes against the scientific spirit and merely reflects a dogmatic attitude, which, like fundamentalism, is an adversary of science.
Vedic maths represents a historical legacy belonging to all of humanity, and one can appreciate its value without subscribing to the notion of a Hindu rashtra.
