In AD 628, a sage from India, residing on a mountain in Rajasthan, made a groundbreaking mathematical discovery. This sage, the renowned mathematician Brahmagupta (598–670), delved into Indian philosophical notions of nothingness and the void, ultimately producing a treatise that essentially created and defined the concept of zero.
Brahmagupta was born near the hill station of Mount Abu in Rajasthan. At the age of 30, he authored a 25-chapter treatise on mathematics, immediately recognized for its exceptional brilliance and depth. He was the first mathematician to treat the zero symbol—initially represented as a mere dot—as a number in its own right, rather than just a symbol of absence. This approach necessitated the development of rules for arithmetic using this new symbol alongside the other nine numbers.
These foundational rules of mathematics enabled, for the first time, the expression of any number up to infinity with just ten symbols: the nine numerals devised by previous Indian mathematicians and the newly defined zero. These rules continue to be taught in classrooms worldwide.
Brahmagupta also innovated by formulating a set of arithmetic rules for handling positive and negative numbers, recorded in Sanskrit verse. In other writings, he appears to have been the first to describe gravity as an attractive force, a full thousand years before Isaac Newton.
However, Brahmagupta was not isolated in his achievements. He considered himself as building upon the work of a preceding Indian genius, Aryabhata (476–550). Aryabhata’s work provided a remarkably accurate approximation of the value of pi—3.1416—and explored spherical trigonometry in detail. The simplicity of calculations using his system had direct implications for astronomy, allowing him to compute planetary movements, eclipses, the size of the Earth, and the precise length of the solar year to an accuracy of seven decimal places.
He also accurately proposed a spherical Earth that rotated on its axis. “By the grace of Brahma,” Aryabhata wrote, “I dived deep in the ocean of theories, true and false, and rescued the precious sunken jewel of true knowledge by the means of the boat of my own intellect.”
The intellectual contributions of Brahmagupta and Aryabhata, synthesizing the mathematical wisdom of ancient India, traveled first to the Arab world and then further west, introducing not only essential mathematical concepts like zero but also the numeral system we use today. Despite this, the British education system still largely credits ancient Greece for the significant scientific advances of antiquity. While we learn about figures like Pythagoras and Archimedes in primary school, mathematicians of equal stature from India remain largely unknown to the public, with names like Brahmagupta and Aryabhata unfamiliar outside academic circles.
It was these Indian mathematicians who perfected the numeral system now universally used—a near-universal language. Yet in the West, we often mistakenly attribute our numeral system to the Arabs, from whom we adopted it, rather than to the Indians who actually invented it.
In Britain, there remains a surprising lack of awareness about India’s historically significant role as a central economic and cultural force in the ancient and early medieval world. Though largely unrecognized in the West, Indian scholarship, spiritual insights, and philosophical ideas are foundational to our world. Much like ancient Greece influenced Rome and the broader Mediterranean and European worlds, India at this time was exerting a similar influence over Southeast and Central Asia, and even China. This influence spread not through conquest but through the sheer appeal and sophistication of its culture.
For around 1,500 years, from approximately 250 BC to 1200 AD, India was a confident exporter of its diverse civilization, creating an “Indosphere” where its cultural impact was dominant. Throughout this period, the rest of Asia eagerly absorbed a comprehensive range of Indian soft power—in religion, art, music, dance, technology, astronomy, mathematics, medicine, language, and literature.
India produced not just pioneering merchants, astronomers, and scientists, but also spiritual leaders, monks, and missionaries from various strands of Indic religious thought, both Hindu and Buddhist. These religious worlds often mingled, sometimes competed, and occasionally clashed, but collectively, they came to dominate vast regions of Asia. Today, over half of the world’s population lives in areas where Indian religious and cultural ideas have been, or once were, predominant, with Indian deities capturing the imaginations of millions.
This vast spectrum of early Indian influence has always been evident, manifesting in the Buddhism of countries like Sri Lanka, Tibet, China, Korea, and Japan; in the place names of Burma and Thailand; in the murals and sculptures depicting the Ramayana and Mahabharata in Laos and Cambodia; and in the Hindu temples of Bali. Yet, the monsoon-driven maritime trade routes that connected these diverse regions into a cohesive cultural unit—a broad “Indosphere” stretching from the Red Sea to the Pacific—have never been widely recognized or named.
If India’s transformative effect on the surrounding religions and civilizations was so crucial to world history, why is its extraordinary cultural diffusion not more widely acknowledged? This lack of recognition is likely a lingering effect of colonialism, specifically Victorian Indology, which often undermined and devalued Indian history, culture, science, and knowledge. During the Victorian era, figures like Thomas Babington Macaulay confidently asserted that “a single shelf of a good European library was worth the whole native literature of India and Arabia.”
Had India been acknowledged as a powerful, cosmopolitan, and sophisticated civilization, what justification could there have been for the British Empire’s “civilizing mission”? How could one claim to bring civilization to a region that had already been highly civilized for thousands of years and had spread its influence across Asia long before the advent of Christianity? Ironically, it was Indian ideas that, in many ways, enabled the West to conquer India.
By the 8th century, Indian numerals had been adopted by the Arabs, facilitated by a Sanskrit-literate dynasty of viziers in Baghdad known as the Barmakids, who were converts from Buddhism. Some members of the Barmakid family had studied Indian mathematics in Kashmir. They dispatched missions to India to obtain scientific texts, resulting in a delegation from Sindh bringing a compilation of Brahmagupta and Aryabhata’s works to Baghdad in 773.
A generation later, Persian polymath Khwarizmi summarized all the Sanskrit mathematical texts stored in Baghdad’s House of Wisdom library. His name gives us the term “algorithm,” and his book “Kitab al-Jabr,” is the root of the word “algebra.” This book became foundational for mathematics across the Arab world. The book’s full title, “The Compendious Book on Calculating by Completion and Balancing, According to Hindu Calculation,” hints at its inspiration.
From Baghdad, these mathematical ideas spread across the Islamic world. Five centuries later, in 1202, Leonardo of Pisa, known as Fibonacci, returned to Italy from Algeria with his father, where he found his fellow citizens still using the Latin numeral system. Fibonacci, fluent in Arabic and familiar with Arab mathematics, wrote the “Liber Abaci” (The Book of Calculation) at the age of 32, after learning about the “nine figures of the Indias” in Algeria. As Fibonacci explained, “With the sign 0, which the Arabs call zephyr (al-sifr), any number whatsoever can be written. Getting to know this pleased me far beyond all else … Therefore I made an effort to compose this book so that in future the Latin race may not be found lacking in mathematical knowledge.”
Fibonacci’s “Liber Abaci” first popularized the use of what would later be known as “Arabic numerals” in Europe, laying the groundwork for the growth of banking and accounting, initially in Italy under families like the Medicis, and subsequently throughout Europe. These innovations played a pivotal role in the commercial and banking revolution that financed the Renaissance, and eventually, as these ideas spread, in the rise of Europe, driving it to look eastward toward India’s riches—the origin of these transformative ideas.
It was arguably European commercial acumen and initiative, just as much as military might, that gave Europe an edge over India. From the mid-18th century, the European East India Company—a corporation headquartered in London’s financial district—used meticulous accounting and corporate strategies to conquer a divided India, marking perhaps the most significant act of corporate aggression in history.
Today, over 75 years after independence, many believe India’s moment has come again. Its economy has grown fourfold in a generation, and its reputation as a hub for mathematics and scientific expertiseremains strong, with Indian software engineers increasingly forming the backbone of the new “Houses of Wisdom” in Silicon Valley. The only questions that remain are whether it will be India, China, or the United States that dominates the world by the end of this century, and what kind of India it will be.
For a millennium, Indian ideas spread along the Golden Road, transforming the world and creating a cultural zone that transcended political boundaries through the sheer power of its ideas. Within this zone, Indian culture and civilization reshaped everything they encountered.
