In the history of mathematics, the concept of zero is rather new. Humans appeared on the earth approximately 200,000 years ago and only around 3000 BCE, men learned mathematics. Zero was discovered in India around 628 CE.

A thread.

While Sumerian & Babylonian mathematics were quite developed, they did not have 0. Babylonians learned to leave a vacant space between 2 numbers to indicate a place without value. But that was never true 0 because it was never at the end of a number, the way we write 10 or 100.

The Greeks, who contributed vastly in the fields of geometry and number theory, adopted a system based on the additive principle and had no need to introduce zero. They thought of numbers geometrically, where numbers are always represented as lengths of a line.

Greeks didn't have separate symbols for numbers; rather they were drawn from their list of alphabets. They had separate symbols for higher numbers, e.g. 100 = ρ, 200 = σ, 500 = φ etc. The highest number they could write was 10000 = M, or capital μ, also called the "Myriad".

Zero was invented in India. Contribution of India, in the development of mathematics, can be best appreciated from this quote from Pierre-Simon Laplace (1749- 1827), one of the greatest mathematicians from France:

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. (contd.)

But its very simplicity & ease of use has put arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes & Apollonius, two of the greatest men produced by antiquity”

Aryabhatta (476-550 CE), India's most important post-Vedic mathematician & astronomer wrote several mathematical & astronomical treatises, many of which are now lost. His most important work, Aryabhatiya survived up to the modern times. It was written when he was only 23 yrs old.

The first chapter of Aryabhatia is Dasagitika. In Dasagitika, Aryabhatta, possibly under the influence of the Greeks, introduced a numeral system based on the Sanskrit alphabet. To each of the 33 consonants in the Sanskrit, he assigned a numerical value.

In Sanskrit, the first 25 letters are called 'Varga', the rest are called 'Avarga'. Aryabhatta assigned values, 1 to 25 to the Varga letters. The Avarga letters were assigned values of 30, 40, 50, 60, 70, 80, 90 & 100. He also assigned numeric values to the 9 Sanskrit vowels.

Zero originated around 628 CE. Zero had two uses, one as a symbol for nothingness, and the other as a placeholder. Indian mathematician Brahmagupta (598–670 CE) at the age of 30, wrote his treatise, "Brahmasphuṭasiddhanta". THIS IS THE FIRST WORK THAT MENTIONS ZERO AS A NUMBER.

Brahmagupta did not call it zero, rather he called it 'Shunya', to indicate nothingness or vacuum. In the Brahmasphutasiddhanta, Brahmagupta brilliantly defined zero as the result of subtracting a number from itself. He also gave the rules of mathematical operations with zero.

However, Brahmagupta could not define the rule for division of a number by zero. That rule were given by another brilliant Indian mathematician Bhaskara II or Bhaskaracharya (1114-1185 CE), who wrote the famous mathematical treatise 'Lilawati', named after his daughter.

Bhaskaracharya understood infinity as a fraction who's denominator is 0. He did not call it infinity, rather he called it 'Khahar'. In Bijganita 2.20, he wrote:

अस्मिन् विकारः खहरे न
राशावपि प्रविष्टेष्वपि निःसृतेषु।
बहुष्वपि स्यात् लय-सृष्टिकाले
अनन्ते अच्युतेभूतगणेषु यद्वत्॥

"There is no change in the Khahara (infinity) by adding or subtracting, just like infinite immutable (Brahma or Viṣnu)
which does not have any effect by the living beings entering or leaving it at the time of dissolution or creation of the world."

The first, indubitable evidence of the use of zero in India, as early as in 876 CE, was found in a Vishnu temple, at Gwalior Fort, in Gwalior, a city in Madhya Pradesh. The temple has a stone tablet towards the right of Lord Vishnu, with the world's first stone inscribed zero.

The tablet mentions that the people of Gwalior gifted a garden measuring 187 by 280 hastas (One hasta approximately equals to 18 inches), to produce 50 garlands every day for worshipping.

The inscribed 0 on the tablet is exactly similar to today's 0.

End of thread.