early use of Boolean logic, of the null operator, and of context free grammars, and includes a precursor of the Backus–Naur form (used in the description programming languages). Pingala (300 BCE – 200 BCE) Among the scholars of the post-Vedic period who contributed to mathematics, the most notable is Pingala () (fl. 300–200 BCE), a music theorist who authored the Chhandas Shastra (, also Chhandas Sutra ), a Sanskrit treatise on prosody. There is evidence that in his work on the enumeration of syllabic combinations, Pingala stumbled upon both Pascal's triangle and binomial coefficients, although he did not have knowledge of the binomial theorem itself. Pingala's work also contains the basic ideas of Fibonacci numbers (called maatraameru). Although the Chandah sutra hasn't survived in its entirety, a 10th-century commentary on it by Halāyudha has. Halāyudha, who refers to the Pascal triangle as Meru-prastāra (literally "the staircase to Mount Meru"), has this to say: The text also indicates that Pingala was aware of the combinatorial identity: Kātyāyana Kātyāyana (c. 3rd century BCE) is notable for being the last of the Vedic mathematicians. He wrote the Katyayana Sulba Sutra, which presented much geometry, including the general Pythagorean theorem and a computation of the square root of 2 correct to five decimal places. Jain mathematics (400 BCE – 200 CE) Although Jainism as a religion and philosophy predates its most famous exponent, the great Mahaviraswami (6th century BCE), most Jain texts on mathematical topics were composed after the 6th century BCE. Jain mathematicians are important historically as crucial links between the mathematics of the Vedic period and that of the "classical period." A significant historical contribution of Jain mathematicians lay in their freeing Indian mathematics from its religious and ritualistic constraints. In particular, their fascination with the enumeration of very large numbers and infinities led them to classify numbers into three classes: enumerable, innumerable and infinite. Not content with a simple notion of infinity, their texts define five different types of infinity: the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually. In addition, Jain mathematicians devised notations for simple powers (and exponents) of numbers like squares and cubes, which enabled them to define simple algebraic equations (beejganita samikaran). Jain mathematicians were apparently also the first to use the word shunya (literally void in Sanskrit) to refer to zero. More than a