Many School Boards of India are in the process of formalizing the instructions on Vedic Mathematics. Ever since Prime Minister spoke of “Vedic Mathematics” in his radio address Maan-ki-Baat, a controversy that once appeared after publication of the book on the subject in English (1965) written by Jagatguru Shankaracharya Bharathi Krishna Tirtha (1884-1960) of Govardhan Math (Puri) has resurfaced. The discussion at that time had centered around the fact that sixteen mathematical formulae that Bharathi Tirtha had expounded were not part of any known version of the Atharva Veda. However, these formulae provided interesting computational tricks of solving middleschool arithmetic. The purpose of this piece is not to undermine in any way the traditional Indian knowledge system but urges the need to put that in proper perspective.

Though Atharvaveda had some discourse on arithmetic, remarkable development of Astronomical studies took place in India in 2nd millennium BCE. Astronomy at that time developed as an auxiliary discipline associated with the study of Veda. Vedanga Jyotisha accurately identified the Winter Solstice around 1400 BCE. This knowledge was taken to a logical conclusion in Surya Siddhanta (505 CE), perhaps the best-known Indian text on the subject, describing the motions of the sun, moon and various planets relative to various constellations in a geocentric system. The text estimated with reasonable precision the equatorial diameter of various astronomical bodies in the solar system, and calculated their orbits. The book was translated into Arabic in the 8th century.

Aryabhata (476-550 CE), was the first to state that the apparent westward motion of stars every day was due to rotation of the earth around its axis taking approximately four minutes less than 24 hours. He also stated that the apparent luminosity of the moon and other planets in the solar system is essentially reflected sunlight. Aryabhata explained how to predict with reasonable precision the occurrences of eclipses. Before the development of the Heliocentric Theory (that earth and other planets are moving around the Sun) by Copernicus in the 16th century, Aryabhata’s was perhaps the most remarkable contribution in the field of Astronomy. Varahamihira (6th century), Brahmagupta (7th Century), Bhaskar – I (7th Century), Bhaskar – II (12th Century), Narayan Pandita (14th Century) and Madhava Sangamagrama (14th/15th Century) made spectacular contributions in the field of Mathematics and Astronomy. The most notable work of Varahamihira, a contemporary of Aryabhata, was Panchasiddhantika, a concise collection of Indian and GrecoRoman astronomy.

Varahamihira praised the Greeks for being “well trained in sciences” indicating thereby awareness of the Indian scholars about the developments in other parts of the world.

Brahmagupta’s Brahmasphutasiddhanta is the “earliest known text to treat zero as a number in its own right rather than as simply a placeholder digit in representing another number as was done by the Babylonians or as a symbol for lack of quantity as was done by Ptolemy and the Romans”. In the book, Brahmagupta also described operations of negative numbers. In his astronomical contribution, he asserted that the area under the illuminated part of the moon every day can be explained from the relative position of the Sun and Moon and the angles between them. His contemporary, Bhaskara – I, was the first to write the Indian numeral system with a circle for the zero. Sindh was invaded by the Arabs in 712 CE. Brahmagupta’s works were translated into Arabic by Muhammad Al-Fazari. The book was further translated into Latin in 1126 CE. Arabian mathematician AlKhwarizmi (800-850 CE) wrote a text on Indian Arithmetic which was further translated into Latin in 13th century. Thus, the wonders of Indian mathematicians gradually became part of the global knowledge system.

Bhaskara – II (Bhaskaracharya) made many remarkable improvements upon existing knowledge in the field of Spherical Trigonometry and in areas that we today recognize as derivatives and integrals. He had the preliminary notion of ‘infinitesimal’. Narayan Pandit further developed the ideas of differential calculus found in the work of Bhaskara – II. Madhava Sangamagrama, the Malayali mathematician, developed the concept of infinite series functions. In Europe the first such series was developed by James Gregory (1667). European Mathematicians of the 17th century viz. Descarte, Fermat, Pascal and Isaac Barrow made various refinements and extensions in the existing knowledge of derivatives and integrals. Newton (1642-1726) and Leibniz (1646-1716) took all of these disparate ideas into a coherent framework and had set up the foundation of Calculus.

UGC recently issued draft guidelines for training of faculty members of Universities and Colleges in the Indian Knowledge System, which besides others prescribes courses on Vedic Mathematics. It does not make much sense to formally introduce the instructions on Vedic Mathematics at school level. A sidereal day as per traditional Indian mathematics consisted of 60 ‘danda’. Each ‘danda’ consisted of 60 ‘paul’ and each ‘paul’ consisted of 60 ‘bipaul’. Is it required for students in India to know all these details in addition to hour-minutes-seconds as a unit of time? Perhaps what we need is to sensitize our students on the history of development of Mathematics and Astronomy in our country and explain the relevance of such work in the evolution of modern Mathematics, and not the introduction of so-called Vedic Mathematics as an additional course for all students.

(The writer is a former civil servant.)