Aryabhata, a renowned Indian mathematician and astronomer, is widely regarded as the inventor of the decimal system, which revolutionized the way numbers are represented and calculated.

The symbol 'Shunya' or 'Sunya' was used to represent zero in the Indian numeral system. It played a crucial role in the development of the decimal system and facilitated advanced mathematical calculations.

Brahmagupta, a prominent Indian mathematician and astronomer, introduced the concept of negative numbers and developed rules for their operations. This marked a significant advancement in mathematical thought and enabled the exploration of new mathematical concepts.

The symbol 'Vargamula' was used to represent the square root in Indian mathematics. It is derived from the Sanskrit words 'varga' meaning 'square' and 'mula' meaning 'root'.

Bhaskara II, a renowned Indian mathematician and astronomer, developed the 'chakravala' method, also known as the cyclic method, for solving indeterminate equations. This method involves a series of transformations and substitutions to find integer solutions to Diophantine equations.

The symbol 'Ananta' was used to represent infinity in Indian mathematics. It is derived from the Sanskrit word 'ananta' meaning 'endless' or 'infinite'.

Bhaskara II made significant contributions to the study of permutations and combinations. He developed formulas for calculating the number of ways to arrange objects in different orders and combinations.

The symbol 'Guna' was used to represent the factorial of a number in Indian mathematics. It is derived from the Sanskrit word 'guna' meaning 'multiplication'.

Baudhayana, an ancient Indian mathematician, is credited with developing the 'Sulba Sutras', a collection of mathematical rules and procedures for constructing altars and performing geometric calculations.

The symbol 'Pi' is used to represent the ratio of a circle's circumference to its diameter in Indian mathematics, just as it is in modern mathematics.

Bhaskara II made significant contributions to the study of magic squares. He developed methods for constructing magic squares of various orders and explored their mathematical properties.

The symbol 'Virama' was used to represent the empty set in Indian mathematics. It is derived from the Sanskrit word 'virama' meaning 'cessation' or 'pause'.

Pingala, an ancient Indian mathematician, developed the 'Pingala' system, also known as the binary numeral system, for representing numbers using only two digits, 0 and 1.

The symbol 'Yuta' was used to represent the operation of addition in Indian mathematics. It is derived from the Sanskrit word 'yuta' meaning 'joined' or 'united'.

Bhaskara II studied the Fibonacci sequence and provided a recursive formula for generating its terms. He also explored the mathematical properties of the sequence.