A newly released Class 8 mathematics textbook by the National Council of Educational Research and Training (NCERT) has formally acknowledged ancient Indian mathematician Baudhayana as the earliest known scholar to have formulated the theorem on right-angled triangles, centuries before it came to be associated in the modern world with Greek mathematician Pythagoras. The revised textbook places India’s mathematical heritage at the centre of learning, presenting classical concepts through indigenous historical, cultural and architectural examples.

The textbook, titled Ganita Prakash (Part 2), states that Baudhayana was the first person in history to express what is today widely known as the Pythagorean Theorem in a general and essentially modern form. The theorem states that in a right-angled triangle with side lengths a, b and hypotenuse c, the relationship a² + b² = c² holds true. While the theorem is commonly attributed to Pythagoras, who lived around 500 BCE, the NCERT text emphasises that Baudhayana lived several centuries earlier, around 800 BCE, and articulated the same mathematical principle with clarity and rigour.

The book explains that the theorem is therefore sometimes referred to as the “Baudhayana–Pythagoras Theorem” to acknowledge both traditions and ensure clarity about the mathematical result being discussed. It notes that Pythagoras admired and studied the theorem but lived a couple of hundred years after Baudhayana, making the Indian scholar’s contribution historically prior.

Drawing directly from ancient sources, the textbook quotes multiple verses from Baudhayana’s Sulba Sutra, a foundational mathematical and geometrical text composed as part of Vedic ritual literature. One of the key verses cited states that “the diagonal of a square produces a square of double the area,” which the book explains is a clear geometric statement of the right-angled triangle theorem. The text further elaborates how Baudhayana demonstrated that the areas of the squares constructed on the two shorter sides of a right-angled triangle together equal the area of the square constructed on the hypotenuse.

The textbook highlights that Baudhayana did not merely state the theorem in abstract terms but also provided practical numerical examples. In the Sulba Sutra, he listed several sets of integers such as (3, 4, 5) and (5, 12, 13) that satisfy the equation a² + b² = c². These sets, the book explains, are now commonly referred to as Pythagorean triples but are also described as Baudhayana triples or Baudhayana–Pythagoras triples. The text adds that such right-angled triangle triples can be generated in infinitely many ways, underlining the depth of mathematical understanding present in ancient Indian scholarship.

Linking ancient mathematics to later developments in global mathematical thought, the NCERT book notes that the study of such integer triples inspired the celebrated French mathematician Pierre de Fermat in the 17th century. Fermat made a bold general statement about equations involving sums of powers of integers, famously writing in the margin of a book that no solutions exist for equations involving powers greater than two, such as the sum of two cubes equalling another cube. He claimed to have a “truly marvellous proof” but added that the margin was too small to contain it.

This assertion came to be known as Fermat’s Last Theorem and remained one of mathematics’ greatest unsolved problems for more than 300 years. According to the textbook, the theorem was finally proven in 1994 by British mathematician Andrew Wiles, who had been inspired by the problem since childhood. By tracing this intellectual lineage, the NCERT text places ancient Indian mathematics within a broader global narrative of mathematical discovery and continuity.

The revised textbook makes it clear that this emphasis on Indian contributions is part of a deliberate pedagogical approach. The ‘About the Book’ section states that Indian rootedness has been consciously kept in mind while selecting contexts for explaining mathematical concepts. The contributions of Indian mathematicians have been integrated into problem-solving exercises to help students appreciate India’s rich mathematical heritage and its lasting global influence.

Background information provided in the textbook draws from the Indian Science Heritage website maintained by the National Council of Science Museums. According to the site, Baudhayana was an ancient Indian mathematician and likely a Vedic priest associated with the Yajurveda tradition. He lived around 800 BCE and predated other notable mathematicians such as Apastamba. His work formed part of the Sulba Sutras, texts that dealt with geometric principles needed for constructing ritual altars, blending religious practice with precise mathematical reasoning.

This is the second part of NCERT’s Ganita Prakash textbook for Class 8, following Part 1, which was released earlier in the year and also featured references to ancient Indian mathematical contributions. The new volume contains seven chapters and consistently uses examples drawn from Indian monuments, art and culture to explain abstract mathematical ideas.

For instance, the book points out that some of the oldest known fractal patterns in human-made art may be found in Indian temples, including the Kandariya Mahadev Temple in Khajuraho, as well as temples in Madurai, Hampi, Rameswaram and Varanasi. These examples are used to illustrate mathematical ideas while simultaneously connecting students to India’s architectural and artistic heritage.

The ‘About the Book’ section further notes that efforts have been made across all chapters to establish connections between mathematics and other disciplines such as art, social science and natural science. Concepts and problems are linked to everyday life situations, making mathematics more relatable and grounded in lived experience.

Academic experts have largely welcomed the approach. Eknath Ghate, senior professor at the School of Mathematics at the Tata Institute of Fundamental Research (TIFR), Mumbai, said that the claims made in the textbook appear reasonable and well-founded. He added that India’s contributions to mathematics deserve recognition and that it is encouraging to see ancient Indian mathematicians being appropriately acknowledged in school curricula.

With this revised textbook, NCERT aims not only to teach mathematical principles but also to foster a deeper appreciation among students for the historical roots of knowledge. By situating global mathematical ideas within India’s own intellectual traditions, the book seeks to build confidence, curiosity and a sense of continuity between past scholarship and modern learning.