*Dr. Shubhankar Mishra
Mathematics is not just an abstract subject; it plays a fundamental role in our daily lives, influencing our decisions and actions. We often find ourselves asking questions such as, “When is my birthday?” “What’s today’s date?” “What time is it?” and “When should I leave for school, college, or work, and when can I relax?” These inquiries demonstrate our reliance on numerical knowledge, which is closely connected to mathematics. From the moment we wake up to when we go to bed, we use mathematical principles to organize our time and manage our tasks efficiently.
Mathematics is an essential discipline that empowers us to understand and manipulate numbers. With a rich history of innovation, it has shaped our world for millennia. By acknowledging this remarkable legacy, we can inspire young people to appreciate and engage with the diverse cultural origins of mathematics, fostering a deeper enthusiasm for this vital field.
Understanding mathematics is crucial for scientific progress. In ancient times, astrology was known as « Nakshatra Vidya, » which means the science of studying celestial objects and constellations. At the same time, mathematics was revered as « Rashi Vidya, » the science of numbers. The significant advancements in number systems, the invention of zero, place value, arithmetic, geometry, and algebra in ‘Incredible India’ serve as powerful testaments to a rich legacy of knowledge and scientific inquiry. This foundation continues to empower ground-breaking discoveries and innovative technologies that shape our world today.
During our childhood, we often listened to captivating tales from our grandmother, a beloved storyteller. One such tale took us deep into the heart of an ancient Indian narrative, inspired by the questions of a curious daughter. In this story, the daughter, driven by an insatiable thirst for knowledge, asks her father, “O Father! How do planets maintain their stability in the vastness of space? What prevents them from simply falling?” With a warm smile, the father shared his profound understanding of the law of gravity.
In this tale, the father is the legendary Bhaskar II, a distinguished mathematician of ancient India, also known as Bhāskarāchārya, while his curious daughter is named Lilāvati. Their dialogue, expressed in Sanskrit verses, foreshadows the insights of Isaac Newton (1643-1727), whose formulation of the law of gravity emerged nearly 600 years later. This highlights the brilliance of the ancient Indian sage Bhāskarāchārya’s understanding.
Bhāskarāchārya, a renowned mathematician, was born in Bijapur, Karnataka, India in 1114 A.D. His father, Maheshwar Bhatt, was also a distinguished mathematician, which inspired Bhāskarāchārya’s early interest in the subject. He acquired extensive knowledge in mathematics, astrology, the Vedas, poetry, grammar, and more, leaving behind an impressive legacy in his field. Bhāskarāchārya’s lifelong dedication to mathematics and astronomy exemplifies his commitment and hard work. His invaluable contributions to arithmetic and astronomy have solidified his status as one of the greatest mathematicians of ancient India.
Bhāskarāchārya, a remarkable mathematician, wrote Siddhanta Shiromani (which broadly translates into English to ‘Crown of Treatises’) at the impressive age of thirty-two, demonstrating his extraordinary intellect. This early achievement not only highlights his brilliance but also serves as an inspiration for many. Composed in Sanskrit around the year 1150 AD, this extensive work on mathematics and astronomy is divided into four distinct sections: Pati Ganita (Arithmetic), Beej Ganita (Algebra), Grahaganita (astronomical mathematics), and Golādhyāya (spherics, or the study of spheres). Each section is so comprehensive and profound that many scholars consider them to be independent works in their own right.
‘Pati Ganita,’ also known as ‘Lilāvati,’ simplifies fundamental mathematical concepts such as the number system, zero, fractions, and mensuration. ‘Beej Ganita’ explores positive and negative quantities, explaining that the square of any number—whether positive or negative—is always positive. This demonstrates the interconnectedness of mathematics with other fields. Meanwhile, ‘Golādhyaya’ delves into astronomy, spherical trigonometry, and cosmology, further highlighting this interdisciplinary approach. Additionally, the book presents a remarkable portrayal of the changing seasons, showcasing not only Bhāskarāchārya’s mathematical genius but also his poetic elegance.
It is believed that Bhāskarāchārya wrote « Lilāvati, » also known as « Pati Ganita, » to help his beloved daughter, Lilāvati, become proficient in mathematics. His dedication to her education reflects a deep commitment to learning and knowledge. The book « Lilāvati » is a treasure trove of mathematical concepts, including arithmetic, algebra, and geometry, which Bhāskarāchārya meticulously explained to his daughter.
An intriguing legend surrounds this arithmetic-focused book. According to the tale, Bhāskarāchārya, using his expertise in astrology, predicted that Lilāvati would remain childless. Concerned about her future as a parent, he calculated an auspicious moment for her wedding and devised a unique method for telling time—a small perforated bowl placed in a water vessel. As the bowl gradually filled with water and sank, it signalled the perfect moment for the ceremony. He cautioned Lilāvati to keep her distance from the vessel, but fate had other plans.
Lilāvati, full of playful curiosity, approached the vessel while wearing her bridal attire. In the process, a pearl from her dress fell into the water, causing a minor disruption in the calculations that were crucial for determining a favourable moment for her marriage. Consequently, the auspicious moment eluded her, and she found herself remaining unmarried.
Upon witnessing his daughter’s unfortunate fate, Bhāskarāchārya was deeply sad. In an effort to honour her memory and ensure her name lived on, he dedicated his mathematical masterpiece, « Lilāvati, » to her. This ensured that her name would be remembered for generations to come. This touching story not only emphasizes the significance of a name but also celebrates the ancient Indian cultural values and traditions, particularly the deep love and the importance of legacy, which are universal and can be found in every culture.
Lilāvati’, a young woman of exceptional talent, and her story with Bhāskarāchārya highlight the profound value of education and the deep, meaningful connections between knowledge and family. In the book « Lilāvati’, » a variety of mathematical challenges are ingeniously presented, transforming into engaging dialogues between a father and his daughter. These challenges are not just exercises but intriguing puzzles that stimulate the mind and foster a love for learning. In one enlightening exchange, Bhāskarāchārya asks Lilāvati’, « If you understand addition and subtraction, what is the sum of 2, 5, 32, 193, 18, 10, and 100? If you subtract that sum from 10,000, what will remain? »
The book contains thirteen chapters that explore a variety of mathematical topics, each with practical applications. It covers essential definitions and provides insights into interest calculations, as well as arithmetic and geometric progressions. Additionally, it addresses topics in plane geometry, solid geometry, the shadows cast by objects, and Kuttaka (an algorithm, often translated as pulverizer or grinder), among others, all with real-world relevance.
Bhāskarāchārya’s other notable work, Karan Kautuhal (Calculation of Astronomical Wonders), holds great significance in the fields of mathematics and astronomy. This treatise not only explores various astronomical concepts but also offers insightful explanations, enlightening the reader. It describes how a solar eclipse occurs when the Moon passes in front of the Sun and how a lunar eclipse takes place when the Earth casts its shadow on the Moon.
Bhāskarāchārya’s contributions to mathematics and astronomy are not just historical footnotes; they significantly influence these fields even today, shaping the very fabric of modern science. He proposed that any number divided by zero is infinite and that the sum of any number and infinity remains infinite. These ideas are fundamental principles in modern mathematics. In astronomy, his groundbreaking concept of instantaneous motion revolutionized the discipline, providing a foundation for more accurate calculations of planetary movements. These lasting contributions highlight the relevance and ongoing impact of Bhāskarāchārya’s work, a legacy that continues to shape the contemporary scientific landscape.
It is no exaggeration to say that ancient Indian thinkers played a crucial role in shaping the principles later proposed by modern Western scientists. Many Western scholars appear to have studied the works of Indian intellectuals such as Bhāskarāchārya, Kanād, and Aryabhata before formulating their own theories. The widespread translation of Bhāskarāchārya’s writings into numerous foreign languages not only highlights the global significance of ancient Indian knowledge and scientific traditions but also enlightens us about the interconnected history of science. His lasting impact on modern science serves as a testament to the enduring influence of his contributions, which continue to enrich our understanding of the world.
As we reflect on the profound and invaluable contributions of Bhāskarāchārya, it is essential to honour those who have profoundly shaped our understanding of the world. The naming of India’s satellites Bhaskara-I and Bhaskara-II is not just a tribute to history; it is a celebration of innovation and an intellectual legacy that transcends time, a legacy that we, as inheritors of Bhāskarāchārya’s intellectual tradition, can take pride in and be inspired by.
Bhāskarāchārya, who left us in 1179 AD at the age of 65, bequeathed a treasure trove of mathematical and astronomical insights that continue to shape our understanding of the world. His work, as relevant and influential today as it was in his time, demonstrates the enduring impact of theoretical knowledge on real-world challenges. In commemorating his legacy, we not only honour his passion for inquiry and innovation but also take pride in our rich intellectual heritage, a heritage that is not confined to the past but lives on in our present and future.
Let us honour and celebrate Bhāskarāchārya, ensuring that his contributions inspire and guide future generations.
* The writer is an Indian government representative at the World Hindi Secretariat in Mauritius as Deputy Secretary General. The views expressed are personal.
