The Sulba Sutras, dating back to the 8th century BCE, contain geometric constructions and rules for ritual altars, demonstrating the early development of mathematical ideas in India.

Brahmagupta, a 7th-century mathematician, introduced the concept of zero as a number and developed rules for its use in arithmetic operations.

Adi Shankara, an 8th-century philosopher, propounded the Advaita Vedanta school of thought, which emphasizes the illusory nature of the world and the ultimate reality of Brahman (the Absolute).

Aryabhatiya, written by Aryabhata in the 5th century CE, includes the first explicit mention of the decimal system, which revolutionized mathematical calculations.

Ramanuja, an 11th-century philosopher, developed the Vishishtadvaita Vedanta school of thought, which emphasizes the individual soul's relationship with Brahman and the concept of Karma and reincarnation.

Bhaskara II, a 12th-century mathematician, discovered the Fibonacci sequence, a series of numbers in which each number is the sum of the two preceding ones.

Vallabhacharya, a 15th-century philosopher, founded the Pushtimarg sect, emphasizing the path of devotion and surrender to Krishna as the supreme deity.

Brahmasphuta Siddhanta, written by Brahmagupta in the 7th century CE, includes solutions to quadratic equations, demonstrating the advanced mathematical knowledge of ancient India.

Madhvacharya, a 13th-century philosopher, founded the Dvaita school of thought, which emphasizes the distinction between Brahman (the Absolute) and the individual soul.

Brahmagupta, in his treatise Brahmasphuta Siddhanta, introduced the concept of negative numbers and developed rules for their use in mathematical operations.

Adi Shankara, an 8th-century philosopher, founded the Advaita Vedanta school of thought, emphasizing the non-dual nature of reality and the identity of the individual soul with Brahman.

Aryabhatiya, written by Aryabhata in the 5th century CE, includes the first explicit mention of the trigonometric sine function, a fundamental concept in trigonometry.

Ramanuja, an 11th-century philosopher, founded the Vishishtadvaita Vedanta school of thought, emphasizing the qualified non-dual nature of reality and the distinction between Brahman (the Absolute) and the individual soul.

Baudhayana, an ancient Indian mathematician, formulated the Pythagorean theorem in his treatise Baudhayana Sulba Sutra, predating Pythagoras' discovery.

Vallabhacharya, a 15th-century philosopher, founded the Pushtimarg sect, emphasizing the path of devotion and surrender to Krishna as the supreme deity.