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Salience of Bhāratīya Gaṇita

Appreciating the importance of educating constructs from Indian mathematics to children

One may wonder how can the subject of Mathematics or Gaṇita be called as “Indian Mathematics” or “Bhāratīya Gaṇita”. Various civilizations around the world have contributed their original thought processes to advance humanity's collective knowledge. The subject of Bhāratīya Gaṇita refers to a particular domain that helps us understand how the knowledge tradition in India advanced in the field of mathematics, blossoming in the cultural and scientific context of the Indian ethos.

The history of Bhāratīya Gaṇita spans all the way from the Vedic era to until a few centuries back, where this knowledge tradition thrived in its own unique way and made significant breakthroughs. Thanks to the tireless efforts of various esteemed scholars, this knowledge tradition is now available to us in a form that helps us understand the nuances of our Bhāratīya Gaṇita Paramparā.

Among the scholars of eminence in the current times, Anaadi Foundation would like to especially thank the invaluable works of Prof. M.D. Srinivas, Prof. M.S. Sriram and Prof. K. Ramasubramanian, not only for their impactful research but also for inspiring a host of young scholars to delve deep into ancient scientific texts and bring them out in modern notations for the world to appreciate.

There is indeed a treasure trove of mathematical ideas, pedagogical tools and nuanced reasoning in Indian mathematics that can certainly augment and elevate education of mathematics. One can find inspiration to overcome apprehensions towards math and go on to enjoy mastering various techniques and approaches unique to Bhāratīya Gaṇita.

Fields Medalist Prof. Manjul Bhargava, who is one of the architects of NEP 2020 and the new NCF, said back in 2014 to a reporter that, “Students in India should be taught about the great ancient Indian mathematicians like Paṇini, Piṅgala, Hemacandra, Āryabhaṭa and Bhāskara. Their stories and works inspired me, and I think they would inspire students across India.”

One of the unique features of Indian sciences is that a surprisingly large corpus of scientific literature is written in Sanskrit. Works in mathematics, astronomy, etc. have all been composed in verses that can be easily set to melodious music. Indian mathematicians have shown the high-end skill to weave principles of mathematics into sūtras and delightful verses, without losing clarity or precision. This was essential for the oral tradition to enable easy memorization through the chanting of verses. Indian mathematicians certainly did not stop there. They infused stories, worldly wisdom, values, appreciation for nature and so many other characteristics, paving way for a unique pedagogy.

For instance, here is a beautiful verse written by Bhāskarācāya (12th century CE) in his mathematical work Līlāvatī:

पार्थः कर्णवधाय मार्गणगणं क्रुद्धो रणे सन्दधे

तस्यार्धेन निवार्य तच्छरगणं मूलैश्चतुर्भिर्हयान् ।

शल्यं षड्भिः अथेषुभिस्त्रिभिरपि छत्रं ध्वजं कार्मुकं

चिच्छेदास्य शिरः शरेण कति ते यानर्जुनः सन्दधे ॥

The meaning for the above verse is as follows:

An enraged Pārtha (Arjuna), in order to slay Karṇa in battle, nocked a succession of arrows [on his bow]. Having countered his (Karṇa’s) series of arrows with half of that (Arjuna’s own), [he stopped] the horses by four times the square root [of his total arrows], [immobilised] Śalya by six arrows, then [destroyed] the umbrella, flag and bow by three arrows, [and] cut his head by one arrow. How many were those [arrows], which Arjuna nocked [on his bow]?

This problem can be modeled as:

This story is very enticing too! Imagine a class where children chant the verse together, enjoy the details of the story (Who is Śalya? How did he end up in the Kaurava camp? Is kārmukam the bow of Karṇa?)

Here we see that Bhāskarācāya poses a puzzle that requires solving a quadratic equation, but it is unlike a question we see in our current text books that would give a bland equation and declare “Solve for x”. Here is a narrative based on which one must model an equation. And the story is very enticing too! Imagine a class where children chant the verse together, enjoy the details of the story (Who is Śalya? How did he end up in the Kaurava camp? Is kārmukam the bow of Karṇa?) and mentally solve this quadratic equation and eliminate the negative root as well!

All this is the promise of Indian pedagogy to mathematics. There are great pedagogical merits to learning mathematics the Bhāratīya Gaṇita way!

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