When we count from number 1 onwards and beyond number 9... how can we proceed if we don't have a number 10. To have a the number 10 then we must have the number "0". Else how 10 can be written - First writing 1 and followed by a 0. We are not familiar with other method of writing in Decimal system (decimal system origination was Ancient India). If so, then how shall the Vedic rishis could have mentioned such large numbers such as ayuta (अयुत) for ‘ten thousand’, niyuta (नियुत) for ‘hundred thousand’, prayuta (प्रयुत) for ‘million’, arbuda (अर्बुद) for ‘ten million’, nyarbuda for ‘hundred million’ etc. (these are used in Yajur Veda).
Today all encyclopedias are wrongly attributing the invention of "0" to Babylonian mathematics in 7nd century BC, and also giving a passing remark about Acharya Pingala in 3rd Century BC as the one who used "0" in the Chandas shastram. Chandas shastram is a Vedanga - limb of Veda. Acharya Pingala's Chandas shastram like Paninian Grammar was written for both Vedic and Worldly branches of Samskritam. The original Chandas shastram is a part of Veda itself in the earlier Era. Thus it is evident that "0" was there from time of Veda - which is time immemorial
The fact that is evident from the above is that the number "0" as a place value system was there and also "0" as a number was also there from the Vedic times - which in other words means anaadi - time immemorial. So let's not keep repeating the mistake that Sri.Aryabhatta invented "0" etc. Sri.Aryabhatta was a great mathematician and scientist. But saying that Sri.Aryabhatta invented "0" would be an insult our scientific advancements before him. During Mahabharata time - Astra (missile) launch etc. needed calculations which use "0". - Like today how a missile launch can't be done without precise calculations requiring the use of "0".
Maharishi Vyasa write slokas on celestial maps with references to three sequential solar eclipses and to planetary positions. Reference to the first solar eclipse comes in the Sabha Parva (79.29). Second solar eclipse just before Mahabharata war second in the Bhisma Parva (3.29), following a lunar eclipse occurring within the same fortnight. He warns that these successive eclipses are sign of bad times (we can now use these celestial positions to do the detailed astronomical map and also do the dating to precisely estimate Mahabharata war time), all such complex calculations require the useage of "0", thus "0" was in usage in Mahabharata time and even before.
The English word zero came via → French zéro which is from → Venetial zero, which came from (together with Ciper /Cypher) via → Italian zefiro which came from → Arabic صفر, ṣafira = “is empty", ṣifr = "zero", “nothing” This was translation of → the Samskritam word shoonya (शून्य), meaning "empty".
The etymological chain confirms that only the word "Shoonya" (which is used to denote "0" as a valueless number) had travelled and the same word is used for all other purposes of "0" even today. Such as "0" as a valueless number, or place value system, or fraction, etc. Though various mathematical calculations using "0" for other purposes travelled later, but the other Samskritam words didn't travel till 20th century. Later in early 20th century the words such as Void (from Sanskrit word व्योम Vyoma) were starting to be used in computer programming languages.
In Samskritam we have many words for "0" depending on its value. They are below:
पूज्य, /सत् (poojya /sat) = Holy (complete) - from the word Wholly
शून्य, रिक्त, रन्द्र (shunya, rikta, randra) = Valueless
आभु, अव्यक्त (Aabhu, avyakta) = Inexpressible (value can't be determined)
पूर्ण, अनन्त (purna, ananta) = Complete, full, endless (infinite value)
ख, दिब, व्योम, (kha, diba, vyoma) = Infinity
बिन्दु (bindu) = Point /Dot (used in fractions)
अव्यय, (avyaya) = NaN / Indeclinable
साङ्खेय, द्रबिणम् (saankheya, drabinam) = Ordinal (while counting "0" as a number)
Such wide veriety of names used for denoting "0" is found in many places starting from Vedas, Kalpa sutras, Chandas shastra, and many other treatises. Many of the mathematicians of ancient Bharatam were Vaiyakaranaas - as the entire vyakarana sutras of Maharishi Panini by themselves are based on Bija Ganita (Algebra) principles.
The Ganita shaastra (mathematics) has developed into a separate branch of study very long back starting with the Shulba sutras (Sri.Bodhayanacharya) and Jyotisha shastra times. "0" was in wide useage for a very long time even before the development of Ganita as a separate branch of study. Sri. Aryabhatta, Sri.Bhaskara, Sri.Bramhgupta, Sri. Neelakanta Somayaji, etc. these were Ganita Shastragnas after the Period of Sri.Gautama Buddha.
Even before and after the period of Sri.Gautama Buddha, Jain mathematicians were quite popular, and even before Jainism came, Vaiyakaranaas were great mathematicians as well as linguists as the entire Samskritam language is based on mathematics and thus it is most suitable for Computing.
In the ancient times the Ganita shaastra (mathematics) has its branches as - Geometry (Gyamiti) is the study of shapes and their applications; Algebra (Bija Ganita) is the study of operations and their applications; Trignometry (Trikonamiti) is study of Triangles and the relationships between their sides and the angles and Calculus (chalana-kalana Ganita) the study of change.