Rigveda to Sindhu-Sarasvati civilisation: NCERT Class 9 math book focuses on ancient India

E-PaperSubscribeSubscribeEnjoy unlimited accessSubscribe Now! Get features like A new Class 9 mathematics textbook by the National Council of Educational Research and Training (NCERT) calls the Sindhu-Sarasvati civilisation the first systematic use of grid-based thinking, says Ujjayini (Ujjain in Madhya Pradesh) marked the central longitude meridian in the ancient world, and credits the Rigveda for setting the stage for the modern number system. The new book extensively integrates Indian Knowledge System (IKS) and opens with a verse from Vedanga Jyotisha. (HT Photo)The 196-page textbook titled Ganita Manjari Part 1 – which prominently features ancient mathematics techniques and the work of several ancient Indian scholars – was released on Tuesday. The earlier book only made limited references to ancient India. But the new book extensively integrates Indian Knowledge System (IKS) and opens with a verse from Vedanga Jyotisha, which according to NCERT is “amongst the world’s very oldest texts on astronomy..” ALSO READ | NCERT rolls out new Class 9 science book The textbook credits ancient Indian mathematician Baudhayana for “laying the foundation of coordinate geometry” and states that while 14th-century mathematician Madhava “birthed the area of mathematics, known as calculus,” ancient Indian thinker Brahmagupta “formalised the notion and use of zero and the negative numbers as algebraic entities.” The earlier Class 9 mathematics textbook cited the Indus Valley Civilisation, highlighting “highly developed and very well planned” cities and the practical use of mensuration, and referred to the Sulbasutras—“manuals of geometrical constructions” – from the Vedic period used for building ritual altars. However, the text characterised these developments as largely “practical oriented” and “unsystematic”. The new textbook says “grid-based thinking” and the geometry required to define the locations of points in space “indeed has deep roots in Bharat” with first systematic use of grids occurring thousands of years ago “on a massive urban scale-in the Sindhu-Sarasvati Civilisation, where city streets were constructed with striking precision….This was a coordinate system in practice.” The textbook states Baudhayana later used East-West and North-South lines for his “deep geometric constructions, developing the Baudhayana-Pythagoras Theorem and thus laying the foundation of coordinate geometry.” ALSO READ | Now-deleted NCERT chapter on judiciary was a collective effort, Professor tells Supreme Court A paragraph in the same chapter reads, “Ujjayini was described in the ancient world at least as early as the 4th century BCE in the early Siddhantas-as the point marking the central longitude meridian from which all other locations were measured..” The chapter also states that it would be “impossible” to study four-quadrant Cartesian planes without Brahmagupta’s work as he “formalised the notion and use of zero and the negative numbers as algebraic entities”. The old textbook did not discuss the discovery of zero. The new textbook traces the origins of zero to ancient Indian thought, noting that the Rigveda “set the stage for the number system based on powers of 10.” It adds that the development of place value “paved the way” for “the concept of zero,” described as “perhaps the most important mathematical invention.” Contrasting with other civilisations such as Babylonians and Mayans that used placeholders, the book credits Brahmagupta for transforming the void into a number, a “monumental leap” influenced by Indian philosophical traditions. The textbook links the concept of zero to philosophical traditions, noting that in the Upanishads and Buddhist literature, shunyata or “emptiness” was a “profound state” associated with meditation and stillness. It explains that shunya (zero) and “zeroness” reflected the idea of “emptying one’s mind”. ALSO READ | NCERT granted deemed-to-be university status by Centre, to award its own degrees The text adds that this notion of “nothingness as a concept” evolved beyond philosophy and eventually entered mathematics through the works of Aryabhatta and Brahmagupta. “Thus, the philosophical concept of emptiness crystallised into the mathematical zero,” it says. While the old textbook briefly noted the works of Aryabhatta in a chapter on number systems, the new textbook states that in 499 CE, the ancient mathematician provided a value of 62832/20000=3.1416 for π and he described it as “asanna i.e., ‘approaching’ or ‘approximate’ – a profound insight suggesting that the ratio could not be given exactly as one simple fraction.” The new textbook states that Brahmagupta suggested the use of 3.1622 for π which “..become the dominant approximation in the Arab world and medieval Europe for centuries after.” The textbook further states Madhava’s formula-given in the form of an ‘infinite series’ was a ‘tectonic shift for mathematics.’ “By moving from the geometric cutting of circles to the analytical summing of numbers, Madhava birthed the area of mathematics known as calculus. His infinite series enabled him to calculate π to 11 decimal places (3.14159265358), proving that the relationship between a circle’s circumference and its diameter was a window into an entirely new area of mathematics,” the textbook states. The old textbook had stated, “The Greek genius Archimedes was the first to compute digits in the decimal expansion of π..” In the foreword, NCERT director Dinesh Prasad Saklani wrote, “This textbook also highlights the rich history of mathematics in India, spanning thousands of years. By learning about mathematical developments in India and across the world, students can develop a deeper sense of cultural rootedness…” Aligned with the National Curriculum Framework for School Education (NCFSE) 2023 and the National Education Policy (NEP) 2020, the textbook was developed by a 26-member Textbook Development Team (TDT), including professor Manjul Bhargava of Princeton University, who also serves as co-chairperson of the 20-member National Syllabus and Teaching Learning Material Committee (NCTC). Part 1, comprising eight chapters, will be implemented from the 2026–27 academic session, replacing the earlier Class 9 mathematics textbook first published in 2006, later reduced from 15 to 12 chapters in 2022–23. Some experts disagreed with the textbook’s claims. Professor SG Dani of UM-DAE Centre for Excellence in Basic Sciences (CEBS), University of Mumbai, said Baudhayana’s statement of the Pythagoras theorem was not in terms of coordinate systems and not even in terms of lengths, but rather in terms of areas. “The parallel drawn here is therefore quite phoney,” he said. Amber Habib, professor of mathematics at Shiv Nadar University (SNU), Noida, disputed some claims about Brahmagupta. “It is wrong to depict Brahmagupta as the creator of negative numbers. Chinese mathematicians were using negative numbers to solve systems of linear equations a thousand years before Brahmagupta,” he added. Habib said the work of Madhava and other scholars was a key precursor to modern calculus. “However, it was not the earliest development in this field. That distinction is widely attributed to Greek mathematician Archimedes, nearly 16 centuries earlier.”