24/09/2026
*** The Indian Context: Trade and Astronomy ***
As civilisations advanced, so did the need for larger numbers. In the
ancient urban centers of the Indus Valley Civilisation, such as Lothal
and Harappa, standardised weights and measures were crucial for
trade. A merchant trading terracotta pottery, lapis lazuli, or cotton
with Mesopotamia needed a robust system of accounting.
During Vedic times, Indian philosophers were fascinated by and
deeply pondered large numbers. In the Vedas, which go back thousands
of years, names were given to all powers of 10 up to 1012 (which was
called parārdha). In the Lalitavistara in the 4th century BCE, Buddha
describes names up to 1053, which is called tallakṣhaṇa.
Expressing quantities in terms of powers of 10 was explicitly used in
the Ṛigveda, thus setting the stage for the number system based on
powers of 10 to be developed in India in the ensuing years, and which
we now use around the world today. The development of the Indian
numeral system in terms of place values and powers of 10 also helped
pave the way for what is perhaps the most important mathematical
invention in human history: the concept of zero.
***The Revolution of Śhūnya: When Nothing
Became Something
For millennia, the number line started at 1. If you had five apples and
gave all five away, you did not have a number to represent your state;
you simply had a void, a lack of apples. Civilisations like the Babylonians
and Mayans used placeholders — symbols to indicate an empty column
in a number — but they did not treat ‘nothing’ as a number that you
could add, subtract, and multiply.
It was in the work of Brahmagupta (628 CE) that the void was formally
transformed into a number, which truly transformed mathematics.
This monumental leap was in turn inspired by Indian philosophical
traditions.
*** From Philosophy to Mathematics: The Concept of Śhūnyatā
In the Upanishads and in the vast Buddhist literature starting well before
the 7th century BCE, the concept of Śhūnyatā (emptiness or nothingness) was a profound state that was the goal of yoga and meditation. The
word śhūnya means zero, and the word śhūnyatā (zeroness) was used
extensively in these works to describe the state that one is trying to
reach during meditation — that of emptying one’s mind of all vṛttis
(fluctuations of the mind) to achieve the state of perfect stillness and
tranquility. Patanjali in the Yoga Sutras around the 3rd century BCE also
describes how śhūnyatā can help lead to control over one’s mind, body,
and senses.
Because Indian thinkers revered this state of ‘emptiness’, they
possessed the conceptual framework necessary to welcome ‘nothingness’
as a concept in philosophy. This concept of zeroness then found its
way into many fields, such as architecture, literature, linguistics, and
eventually made its way into mathematics in the works of Āryabhaṭa and finally Brahmagupta.
Thus, the philosophical concept of emptiness crystallised into the mathematical zero.
*** The Bakhśhālī Manuscript and Brahmagupta’s Rules
In the Hindu Number System that we use today, the physical transition
from a blank space to a symbol can be seen in the Bakhśhālī
Manuscript. Dated to the early centuries CE, it features a bold dot
(bindu) used to represent zero.
However, a symbol is just a mark on a page until it has rules.
The transformation of zero into a fully operational number
occurred in the work of Brahmagupta. In his seminal work, the
Brāhmasphuṭasiddhānta (628 CE), he explicitly defined zero as the
result of subtracting a number from itself (a – a = 0).
Brahmagupta then laid down the fundamental laws of arithmetic
with śhūnya
