Pataliputra was the capital of the ancient Indian empire of Magadha, but it was not a major center of mathematical learning.

Brahmagupta was an Indian mathematician and astronomer who lived in the 6th century CE. He is best known for his work on the concept of zero, which he used to develop a system of positional notation.

Ujjain was an ancient Indian city that was known for its work on astronomy. It was home to a number of observatories, and its astronomers made significant contributions to the development of astronomy in India.

Aryabhata was an Indian mathematician and astronomer who lived in the 5th century CE. He is best known for his work on the concept of infinity, which he used to develop a system of calculus.

Takshashila was an ancient Indian city that was known for its work on trigonometry. It was home to a number of mathematicians who made significant contributions to the development of trigonometry in India.

Brahmagupta was an Indian mathematician and astronomer who lived in the 6th century CE. He is best known for his work on the concept of negative numbers, which he used to develop a system of algebra.

Nalanda was an ancient Indian university that was known for its work on geometry. It was home to a number of mathematicians who made significant contributions to the development of geometry in India.

Bhaskara II was an Indian mathematician and astronomer who lived in the 12th century CE. He is best known for his work on the concept of calculus, which he used to develop a system of mathematics that was far more advanced than anything that had been seen before.

Takshashila was an ancient Indian city that was known for its work on algebra. It was home to a number of mathematicians who made significant contributions to the development of algebra in India.

Varahamihira was an Indian mathematician and astronomer who lived in the 6th century CE. He is best known for his work on the concept of probability, which he used to develop a system of gambling.

Nalanda was an ancient Indian university that was known for its work on number theory. It was home to a number of mathematicians who made significant contributions to the development of number theory in India.

Brahmagupta was an Indian mathematician and astronomer who lived in the 6th century CE. He is best known for his work on the concept of matrices, which he used to develop a system of linear algebra.

Takshashila was an ancient Indian city that was known for its work on combinatorics. It was home to a number of mathematicians who made significant contributions to the development of combinatorics in India.

Bhaskara II was an Indian mathematician and astronomer who lived in the 12th century CE. He is best known for his work on the concept of the Fibonacci sequence, which he used to develop a system of mathematics that was far more advanced than anything that had been seen before.

Takshashila was an ancient Indian city that was known for its work on graph theory. It was home to a number of mathematicians who made significant contributions to the development of graph theory in India.