S Balachandra Rao obit: Pillar of classical Indian astronomy, defender of rational thought
From programming ancient algorithms on 1980s computers to defending scientific integrity in digital age, Dr Rao was against distortion of India's scientific heritage
The world of the history of astronomy and mathematics mourns the passing of Dr S Balachandra Rao, who breathed his last in the early hours of May 14, 2025.
The 80-year-old scholar, former principal and professor of Mathematics at National College, Bangalore, leaves behind his wife Anasuya Shiraly, sons Kedar and Karthik, and an extraordinary legacy of 30 plus books and several research papers in esteemed journals like the IJHS, JAHH and Ganita Bharati that explored the intricate aspects of classical Indian astronomy.
Cosmic reckoning
Born on December 24, 1944, in the small town of Thyagarti near Sagar in Karnataka, young Balachandra's curiosity about the universe first sparked under the starry skies of his hometown. After early schooling in Sagar, he moved to Bangalore's Seshadripuram High School, where a mathematics teacher's poignant telling of Ramanujan's story lit a lifelong passion.
His mother, Radha Bayi, nurtured this passion with tales of India's ancient thinkers, always factual, never mythological. He recalled that his mother's tales "used to inspire me with real stories of great heroes and thinkers of ancient and medieval India. She would never narrate ghost stories and the like."
At Basavanagudi National College, he excelled in mathematics and Sanskrit, a rare combination that would later define his career. His PhD in Fluid Mechanics under renowned professor N Rudraiah at Bangalore University showcased his analytical brilliance. Yet, his heart remained drawn to the stars.
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Decoding the sky
The 1980s computer revolution found Dr Rao writing BASIC programs on a humble SPECTRUM home computer to test ancient astronomical algorithms. He digitally revived methods from seminal texts like the 5th-century Surya Siddhanta (on planetary motions), Brahmagupta's 7th-century Khandakhadyaka (eclipse predictions), and Ganesha Daivajna's 16th-century Grahalaghavam (computational shortcuts).
Later, with collaborator Padmaja Venugopal, he published definitive studies explaining celestial phenomena in the classical Indian astronomical manuscripts. Their works explored asta (transits of inner planets across the Sun), samagama (when the moon eclipses stars), and yuddha (the dramatic conjunctions when planets appear to meet in the night sky).
A folio from Tithi Cintāmaṇi. Photos: Dr S Balachandra Rao's collection
This ground-breaking research culminated in two seminal works: Eclipses in Indian Astronomy and Transits and Occultations in Indian Astronomy. These volumes are a landmark in the scholarship of India's astronomical heritage, offering remarkable insight into the computational logic behind ancient celestial algorithms.
The astrology paradox
Ironically, Dr Rao's path to astronomy began with astrology. While copying his sister's marriage horoscope at sixteen, he noticed curious patterns that would later inform his scientific work. He observed how the lunar nodes Rahu and Ketu maintained a separation of exact 180 degrees, how Mercury and Venus never strayed far from the Sun in their orbits, and how New Moons always showed perfect Sun-Moon alignment.
These empirical observations of cosmic mechanics first ignited his fascination with celestial patterns.
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This early interest took a decisive turn when at 18, Balachandra met his lifelong mentor Dr H Narasimhaiah, whose rationalist world-view and Marxian-Gandhian principles reshaped his thinking. Exposure to diverse philosophies from Marxism, Advaita, and Bertrand Russell's writings led him to completely abandon astrological pursuits.
Yet that early fascination with horoscopes would later inspire one of his most important works, Astrology: Believe It or Not?. Dr. Rao's unique perspective makes the book so powerful: having once immersed himself in astrological study, he approached the subject not as an outsider, but as someone who truly understood its claims, and could dismantle them with scientific precision.
“It is rather ironical that my pursuit of planets started with astrology rather than the science of astronomy...In retrospect, I feel I wasted two years or more studying (but not practising!) astrology," he had recalled.
Revolutionary insights
Dr Rao's research revolutionised our understanding of classical Indian astronomy.
Dr S Balachandra Rao with his wife Anasuya Shiraly
He uncovered why brilliant mathematicians like Brahmagupta (7th century CE) developed sophisticated techniques like successive approximation (Asakṛt) for precise calculations, yet later astronomers preferred simpler methods. Along with scholar Roddam Narasimha, Dr Rao explained this through the notion of "computational positivism", India's unique approach favouring practical, efficient calculations over complex Greek-style axiomatic geometry.
Pioneers like Ganesha Daivajna exemplified this by replacing tricky sine/cosine functions with simpler algebraic formulas that gave good enough results faster.
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At the 2006 World Sanskrit Conference in Edinburgh, Dr Rao made striking comparisons between global astronomy traditions.
He showed how Kerala's Nilakantha Somayaji (1444-1550) proposed a revolutionary "quasi-heliocentric" model where planets orbited the Sun, while the entire solar system circled Earth, the same compromise model Danish astronomer Tycho Brahe would propose 150 years later.
This work highlighted how Indian astronomers developed innovative cosmic models while maintaining their distinctive computational style focused on real-world usability over theoretical perfection. Dr Rao's studies revealed India's astronomical tradition as deeply original and refreshingly practical in its mathematical approach to the cosmos.
Defending science from myths
Dr Rao became a prominent voice against the distortion of India's scientific heritage. When a former senior science administrator claimed that 'Aryabhata had discovered gravity centuries before Newton', Dr Rao responded. While acknowledging Aryabhata's remarkable insight that objects cling to Earth's surface, he distinguished this from Newton's formulation of gravity as a quantifiable universal force.
“Aryabhata did us credit, but we can't claim that he discovered gravity...In his treatise Aryabhatiya, he says that all particles cling to the surface of the Earth. Still, he does not mention an attractive force," he explained.
Pointing out that Newton's notion of gravity is a universal, quantifiable force between two objects with mass, he added, "Newton is respected for the discovery because of quantification of the amount of gravity."
His measured approach celebrated India's authentic contributions without nationalist exaggeration.
This balanced perspective characterised his books – Vedic Mathematics and Science in Vedas and Tradition, Science and Society, systematically separating genuine mathematical concepts from fake pseudo-scientific claims about ancient texts. These works were translated into Kannada and honoured by the Kannada Sahitya Parishat with awards.
Mentor of stars
Beyond his 35-year tenure at National College, Dr Rao's influence extended across multiple institutions.
As director of Bharatiya Vidya Bhavan's Gandhi Centre and professor at the National Institute of Advanced Studies, he guided interdisciplinary research bridging science and the humanities. His editorial role at the Indian Journal of History of Science helped maintain rigorous standards in the field while encouraging young researchers and innovative explorations in the history of science.
He cultivated a generation of scholars, including Dr S K Uma, with whom he translated rare manuscripts like the Grahalaghavam, and researchers like V Vanaja, M Shailaja, and Rupa Raviprasad, who continue to advance his work. His ability to nurture young talent by inspiring exacting standards created a lasting academic legacy.
Lasting legacy
From programming ancient algorithms on 1980s computers to defending scientific integrity in the digital age, Dr Rao's intellectual journey mirrored the evolving challenges of studying India's astronomical heritage.
Why is research in India's scientific history lagging? When posed this question, Dr Rao recently responded bluntly: "Two crippling factors - the growing plague of 'ideological bigotry' and shamefully inadequate funding for research and education compared to other nations."
Dr Rao’s rigorous research and way of life showed us how to appreciate our scientific heritage, not with blind reverence or dismissive unbelief, but with clear-eyed curiosity, a critical approach that ensures India's scientific history remains vibrant and relevant for future generations.
