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NCERT’s recently released Class 7 mathematics textbook includes multiple mentions of ancient Indian contributions to the subject and says concepts such as algebra were first developed by Indian mathematicians.
This is the second part of NCERT’s (National Council of Educational Research and Training) Ganita Prakash textbook for Class 7. Part 1, which also contained such references, was released earlier this year.
Part 2 cites examples from Sanskrit texts, includes problems and solutions related to the work of ancient Indian mathematicians, and also talks about an ancient Indian text on geometry.
NCERT Director Dinesh Prasad Saklani said that part of the purpose behind introducing such concepts is to teach students “correct history” without a “skewed” colonial view.
A chapter on integers, for instance, points to mathematician Brahmagupta’s 7th-century CE text Brahmasphutasiddhanta as being the “first time that rules for multiplication and division of positive and negative numbers were articulated”. It calls this “an important step in the development of arithmetic and algebra”. This is followed by Brahmagupta’s rules on using positive and negative numbers and a maths problem related to them. The textbook says Indian contributions to algebra are among the earliest known work in the field.
A chapter on algebraic equations refers to ‘bijaganita’, “also now known as algebra”, and says that “forming expressions using symbols and solving equations with such expressions was an important component of mathematical explorations in ancient India”. The chapter refers to Brahmagupta’s work on adding, subtracting and multiplying unknown numbers using letters, saying this is among the earliest known works in algebra.
Tracing algebra to Indian mathematicians, the chapter says: “In the 8th century, Indian mathematical ideas were translated into Arabic. They influenced a well-known mathematician named Al-Khwarizmi, who lived in present-day Iraq. Around 825 CE, he wrote a book called Hisab al-jabr wal-muqabala, which means ‘calculation by restoring and balancing’”. It adds that these ideas spread, and by the 12th century, Al-Khwarizmi’s book was translated into Latin and brought to Europe. “The word al-jabr from his book gave us the word algebra, which we also still use today,” it says.
It lists symbols that ancient Indian mathematicians from the time of Brahmagupta used to represent unknowns, along with an example of a maths problem mentioned in the 12th-century text Bijaganita by Bhaskaracharya.
Dhruv Raina, a historian, philosopher of science and former JNU professor, told The Indian Express: “The Arabs were profoundly influenced by the work of Indian mathematicians, particularly Brahmagupta. They improvised upon these methods to create what we consider algebra today. The Arab mathematicians were great synthesisers and innovators with the knowledge they acquired from ancient Greek, Indian and Chinese traditions.”
A chapter on geometry, ‘Constructions and Tilings’, elaborates on the Sulba-Sutras and the text’s method to construct a perpendicular bisector using a rope. “Ancient mathematicians from different civilisations, including India, knew exact procedures to construct perpendiculars and perpendicular bisectors. In India, the earliest known texts containing these methods are the Sulba-Sutras. These are ancient geometric texts dealing with the construction of fire altars for rituals,” it says.
The old Class 7 textbook did not contain any reference to ancient Indian mathematicians. NCERT has been bringing out new school textbooks in line with the National Education Policy (NEP) 2020 and the National Curriculum Framework. The NEP calls for incorporating ‘Indian Knowledge Systems’ in the curriculum.
Asked about the rationale behind including these aspects, Saklani said: “The purpose is threefold. One, to teach students correct history. For too long, the history of mathematics has been presented in India from a colonial European perspective, giving a skewed view. This can only be fixed through presenting history correctly and accurately…” “Two, to make the subject more interdisciplinary, and thereby improve learning… Three, to develop a sense of pride and inspiration in students,” he said.
