Pingala
Author
Acharya Pingala was an ancient Indian poet and mathematician, and the author of the Chandaḥśāstra, the earliest known treatise on Sanskrit prosody. The Chandaḥśāstra is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE.
Born: unclear, 3rd or 2nd century BCE
Died: 100 AD
Acharya Pingala was an ancient Indian poet and mathematician, and the author of the Chandaḥśāstra (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.
The Chandaḥśāstra is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE. In the 10th century, Halayudha wrote a commentary elaborating on the Chandaḥśāstra. Pingala Maharshi was also said to be the brother of Panini, the famous sanskrit grammar, and the world’s first linguist.
The Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha’s commentary includes a presentation of Pascal’s triangle (called meruprastāra). Pingala’s work also includes material related to the Fibonacci numbers, called mātrāmeru.
Use of zero is sometimes ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, but Pingala used light (laghu) and heavy (guru) rather than 0 and 1 to describe syllables. As Pingala’s system ranks binary patterns starting at one (four short syllables—binary “0000”—is the first pattern), the nth pattern corresponds to the binary representation of n−1 (with increasing positional values).
Acharya Pingala discovered the immense possibilities of Binary numbers quite by accident. He was working on the meter or Chandah of Vedas. Our Vedas were composed in meters or Chandah. Most Indian Languages have the dheerga or long swar and the laghu or short swar. This combination of long and short sounds is the basis of Sanskrit prosody or meter or chandah. In a work called Chandahsastra was authored by Pingala, the Mathematician. Chandaḥśāstra means the science of meters as used in poetry/ music in which it is recited. While studying chandah, he stumbled on the concept of the Binary number system.

Let us compare decimal numbers with the Pingala, the Mathematician’s Binary system and Modern Binary system.
*Observe that the Pingala’s Binary system is a mirror image of the Binary system
The Chandahsastra, written by Pingala, the Mathematician, has eight chapters, and these mathematical combinations and sequences are mentioned in the 8th chapter.
References to Pingala
‘Vrittaratnakara‘ by Kedara in the 8th century has references to
In the 12th Century AD, Trivikrama referred to Chandahsastra in, ‘Tatparyatika.‘
12th century AD and ‘Mritasanjivani‘ by Halayudha carries a commentary on Commentaries. It was Halayudha who used zero in the place of laghu. By this time, the use of zero was common in India and had travelled to many other parts of the world. Halāyudha’s commentary includes a presentation of the Pascal’s triangle (called meruprastāra)

There is little historical reference available on Pingala; the Mathematician indicates that he was the younger brother of Pāṇini (4th century BCE), or of Patañjali, the author of the Mahabhashya (2nd century BCE).

It took many more centuries for this knowledge to reach Europe. In the town of Pisa in Italy, Leonardo, better known as Fibonacci, learnt the use of Binary numbers from Arabs. He was particular to mention that the Arabs had brought it from India. But his successors chose to call it as Arabic numerals.
Pingala Series
While exploring the number of possibilities of various combinations of the laghu and the guru hit upon a series:

0,1,1,2,5,8,13,21,34,55…………

This was later called the Fibonacci series.
This sequence is seen abundantly in nature: branching in trees, the arrangement of leaves on a stem etc.
The Fibonacci number was initially called mātrāmeru, by Pingala, the Mathematician. Now it is also known as the Gopala–Hemachandra number.,Use of zero is sometimes ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion Pingala Pingala is also credited with the binomial theorem for the index 2, i.e. for (a+b)2, like his contemporary Greek Euclid.
Pingala is credited with using binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), a notation similar to Morse code. Pingala used the Sanskrit word śūnya explicitly to refer to zero.