Manjul Bhargava, a mathematician of Indian origin who holds dual citizenship in Canada and the United States, and who was awarded the prestigious Fields Medal in 2014, humorously remarked that "the contribution of India to mathematics is zero." However, he quickly clarifies that ancient India was pivotal in a major scientific breakthrough—the formalization of zero. This concept is central to the exhibition "From Shunya to Ananta: From Zero to Infinity. The contribution of Indian civilization to mathematics," which is currently being held at the Swami Vivekananda Indian Cultural Center in Paris. Bhargava, a professor at Princeton University, is highlighting how mathematical ideas have evolved across different cultures and eras, sometimes independently and sometimes through mutual influence.
The concept of zero, or "śūnya" in Sanskrit, meaning "void," has a long and complex history. The earliest documented use of a symbol to represent an empty space in numbers dates back to the third century BC in Mesopotamia, where the Babylonians used two nails to indicate the absence of units. However, this was not yet a number in its own right. Nearly six centuries later, the Mayas developed a symbol resembling an oval or shell to represent zero, primarily used in their calendar and astronomical calculations, but not in algebraic operations. It was in the fifth century that the zero as we know it began to take shape. In 628 AD, the Indian mathematician and astronomer Brahmagupta formally defined zero as a number in his treatise Brāhmasphu ṭasiddhānta. He described it as the result of subtracting a number from itself, a concept that laid the groundwork for modern arithmetic.
The introduction of zero as a number was a revolutionary concept, according to Bhargava. It allowed for the development of positive and negative numbers, which were described in Brahmagupta’s work as "fortune" and "debt." This concept was later adopted by Arab mathematicians, including al-Khwārizmī in the eighth century, and eventually made its way to Europe during the Middle Ages. There, it transformed calculation methods and commerce, replacing the cumbersome Roman numeral system with a more efficient numerical framework.
The exhibition at the Swami Vivekananda Indian Cultural Center explores over two thousand years of mathematical thought in India, drawing on rare palm-leaf manuscripts, historical texts, and interactive displays. It highlights early references to powers of ten in the Yajurveda, the work of Mādhava on infinite series in trigonometry, and the spread of these ideas across civilizations. The exhibition also connects mathematics with Indian cultural expressions, such as music, dance, and poetry. For instance, Bhargava explains that musical harmony can be understood through simple frequency ratios, while dance can be viewed as sequences of motifs that can be rearranged. These connections illustrate how deeply mathematics is embedded in everyday life and how India has played a significant role in its development. The exhibition will remain open until September 24, 2026.
Indian Contributions to Mathematics Highlighted in Paris Exhibition
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