Hindu (Indian) Mathematics and its Propagation to Europe

Dr Mukul Chandra Bora

(drmukulcbora@gmail.com)

After going through a recent article titled “In Britain, we are still astonishingly ignorant: the hidden story of how ancient India shaped the West,” published in The Guardian on September 1, 2024, as well as numerous books by European and Western scholars on Hindu mathematics, I have come to a compelling conclusion that mathematics and astronomy were the gift of ancient Bharat. There exists a substantial body of research published in the Journal of the Asiatic Society of Bengal that clearly demonstrates how the transmission of knowledge, particularly in mathematics and astronomy, from ancient India to Europe has been largely overlooked by historians both in India and abroad. Despite the work of British scholars such as Henry Thomas Colebrooke (1765-1837) and George Rusby Kaye (1866-1929), the contributions of our ancestors remain largely unrecognized. Ancient India possessed advanced knowledge in mathematics and astronomy, but this wisdom was suppressed during a millennium of foreign and British rule. As a result, we were kept in the dark about the vast intellectual heritage of our past. While many Commonwealth countries have shed their colonial mindsets post-independence, India (Bharat) has struggled to do the same. Successive governments in independent India failed to revive and celebrate this ancient wisdom. Instead, the works of both British and Indian scholars were often neglected, and it took nearly 75 years for this knowledge to be reintroduced into our education system through the National Education Policy (NEP) of 2020.

Our education system was not rooted in the natural heritage of Bharat, making us akin to a bonsai tree, an ornamental plant and perhaps aesthetically pleasing, but lacking the deep roots needed to provide essential benefits like timber, oxygen, and shade. Though a bonsai may add beauty to a garden, it does not offer the substantive value of a tree firmly connected to the earth. A painting of the Indian astronomer Aryabhata (476–550), who calculated the exact length of the solar year to an accuracy of seven decimal places. In AD 628, an Indian sage living on a mountain in Rajasthan made one of the world’s most important mathematical discoveries. The great mathematician Brahmagupta (598–670) explored Indian philosophical ideas about nothingness and the void, and came up with the treatise that more or less invented—and certainly defined—the concept of zero.

Brahmagupta was born near the Rajasthan hill station of Mount Abu. When he was 30 years old, he wrote a 25-chapter treatise on mathematics that was immediately recognised as a work of extraordinary subtlety and genius. He was the first mathematician to treat the circular zero symbol—originally just a dot—as a number just like the others, rather than merely as an absence, and this meant developing rules for doing arithmetic using this additional symbol along with the other nine. These basic rules of mathematics for the first time allowed any number up to infinity to be expressed with just 10 distinct symbols: the nine Indian number symbols devised by earlier generations of Indian mathematicians, plus zero. These rules are still taught in classrooms around the world today.

The Indian mathematician Brahmagupta (598–670) is said to have defined the concept of zero. Brahmagupta also wrote down in Sanskrit verse a set of arithmetic rules for handling positive and negative numbers, another of his innovations. In other writings, he seems to have been the first to describe gravity as an attractive force a full millennium before Isaac Newton. But Brahmagupta was not alone, and he viewed himself as standing on the shoulders of an earlier Indian genius, Aryabhata (476–550). The latter’s work contains a very close approximation of the value of pi is 3.1416 and deals in detail with spherical trigonometry. The ease of making calculations using his system had direct implications for astronomy and allowed him to calculate the movements of the planet, eclipses, the size of the Earth, and, astonishingly, the exact length of the solar year to an accuracy of seven decimal places.

Brahmagupta also correctly proposed a spherical Earth that rotated on its own axis. “By the grace of Brahma,” he wrote, “I dived deep into the ocean of theories, both true and false, and rescued the precious sunken jewel of true knowledge by means of the boat of my own intellect.” The ideas of these two scholars, encapsulating the mathematical wisdom of ancient India, first spread to the Arab world and eventually to the West. Their contributions gave us not only critical mathematical concepts like zero but also the very form of the numbers we use today.

In Britain, the education system still tends to emphasize that the most significant scientific advancements of the ancient world were the result of ancient Greek brilliance. We learn about Pythagoras and Archimedes in primary school, but mathematicians of equal stature from India remain virtually unknown. Names like Brahmagupta and Aryabhata are familiar only to a small circle of scholars. It was these Indian mathematicians who perfected the numeral system now used worldwide—a system that is arguably the closest thing humanity has to a universal language. Yet in the West, we often attribute these numerals to the Arabs, from whom we adopted them, overlooking their true Indian origin.

Though largely unrecognized in the West, Indian scholarship, religious insights, and philosophical ideas have laid some of the crucial foundations for our world. Like ancient Greece, ancient India offered profound answers to fundamental questions about the nature of the world, its workings, the purpose of existence, and how we should lead our lives. What Greece was to Rome and later to the Mediterranean and European world, India was to Southeast and Central Asia, and even to China. It spread its philosophies, political ideas, and architectural styles not through conquest but through sheer cultural allure and sophistication.

For over a millennium, from around 250 BCE to 1200 CE, India was a confident exporter of its diverse civilization, creating an “Indosphere” of cultural influence. During this era, the rest of Asia eagerly received an extensive transfer of Indian soft power—in religion, art, music, dance, technology, astronomy, mathematics, medicine, language, and literature. From India came not just pioneering merchants, astronomers, scientists, and mathematicians, but also the spiritual teachers, monks, and missionaries of various Hindu and Buddhist traditions. These religious philosophies sometimes intertwined, sometimes competed, and occasionally clashed. Yet, together, they came to dominate large parts of South, Central, Southeast, and East Asia. Today, more than half of the world’s population lives in regions where Indian religious and cultural ideas were once, or still are, dominant, with Indian deities capturing the imaginations of millions.

This vast spectrum of early Indian influence is evident everywhere, though often overlooked. It can be seen in the Buddhism of Sri Lanka, Tibet, China, Korea, and Japan; in the place names of Myanmar and Thailand; in the murals and sculptures depicting the Ramayana and Mahabharata in Laos and Cambodia; and in the Hindu temples of Bali.

The Golden Road of monsoon-driven maritime trade routes once connected a vast cultural region—a sweeping Indosphere extending from the Red Sea to the Pacific. Yet, this intricate network, which linked diverse places and ideas, has never been fully recognized or given a unifying name. If India’s transformative impact on surrounding religions and civilizations played such a central role in world history, why is this remarkable diffusion of its influence not more widely acknowledged.

This oversight is likely a lingering legacy of colonialism, particularly Victorian Indology. Colonial narratives often undermined, misrepresented, and devalued Indian history, culture, science, and knowledge. Thomas Babington Macaulay epitomized this attitude when he declared, “A single shelf of a good European library was worth the whole native literature of India and Arabia.” Such views fed into the so-called “civilizing mission” of Victorian Britain, which failed to recognize that Bharat was already a powerful, cosmopolitan, and profoundly sophisticated civilization.

By the 8th century, Indian numerals had been adopted by the Arabs, facilitated by the Barmakids (Barmecides were an influential Iranian family from Balkh)—a family of Sanskrit-literate Buddhist converts who served as viziers in Baghdad. Some members of this dynasty had studied Indian mathematics in Kashmir and actively sought out Indian scientific texts. In 773, a mission from Sindh brought to Baghdad a compilation of works by Indian mathematicians Brahmagupta and Aryabhata. A generation later, these Sanskrit mathematical texts, housed in Baghdad’s House of Wisdom, were summarized by the Persian polymath Khwarizmi. His contributions gave rise to terms like “algorithm” and “algebra.” His book, popularly known as Kitab al-Jabr, was based on Hindu mathematical principles, as suggested by its full title: The Compendious Book on Calculating by Completion and Balancing, According to Hindu Calculation. These Indian mathematical concepts became foundational across the Arab world and later reached Europe, influencing scholars like Leonardo of Pisa, better known as Fibonacci.

From Baghdad, mathematical ideas spread across the Islamic world. In 1202, Leonardo of Pisa, known as Fibonacci, returned to Italy from Algeria, where he had learnt Arabic and Arab mathematics. Noticing that Italians were still using the Latin numeral system, he wrote the Liber Abaci (Book of Calculation) at age 32. In it, he introduced the “nine figures of the Indians,” which later became known in Europe as “Arabic numerals.” This innovation spurred the growth of banking and accounting in Italy and later across Europe, fuelling the Renaissance and Europe’s economic rise. Eventually, Europe, in its pursuit of wealth, turned towards India—the original source of these ideas. In the mid-18th century, the East India Company, a European corporation, exploited fragmented India in what became a monumental act of corporate violence.

Three-quarters of a century after independence, many Indians believe that the country’s moment has arrived again. Its economy has grown fourfold in a generation, and it remains a hub for mathematics and science, with Indian software engineers prominent in Silicon Valley. The question now is whether India, China, or the US will dominate the world by the century’s end and what form India’s influence will take. Historically, India spread its culture and ideas, creating a vast “Indosphere” that transcended borders. It is now time to reclaim global knowledge dominance by exploring the Indian Knowledge System more thoroughly.