Having discussed Aryabhata's contributions and having furnished a brief introduction to Kerala mathematics in Indian mathematics - I, more light on the latter is thrown here, in addition to accounts on other important mathematicians and contributions of India.

Next to Aryabhata, the figure of major importance was Brahmagupta, who belonged to the Ujjain School in the beginning of the seventh century AD. He made one of the most major contributions to the development of the number system with his remarkable concepts on negative numbers and zero. Who would have realised at that point of time that eight hundred years later European mathematics would be struggling to cope, without the use of negative numbers and zero! These were certainly not Brahmagupta's only contributions to mathematics. Far from it, for he made other major contributions to the understanding of integer solutions to indeterminate equations and to interpolation formulae, invented to aid the computation of sine tables.

A contemporary of Brahmagupta was Bhaskara I, who led the Asmaka School. This school had the study of the works of Aryabhata as its main concern and certainly Bhaskara I was commentator on the mathematics of Aryabhata.

Bhaskara II or Bhaskaracharya, at one point the head of the astronomical observatory at Ujjain, represents the peak of mathematical knowledge in the 12th century. He reached an understanding of the number systems and solving equations which was not to be achieved in Europe for several succeeding centuries. Six works by Bhaskaracharya are known: Lilavati, which is on mathematics; Bijaganita, which is on algebra; the Siddhantasiromani, which is in two parts: the first on mathematical astronomy and the second on the sphere; the Vasanabhasya of Mitaksara, which is Bhaskaracharya's own commentary on the Siddhantasiromani; the Karanakutuhala or Brahmatulya, which is a simplified version of the Siddhantasiromani; and the Vivarana, which is a commentary on the Shishyadhividdhidatantra of Lalla. Given that he was building on the knowledge and understanding of Brahmagupta, it is not surprising that Bhaskaracharya understood zero and negative numbers. However, his understanding went further than that of Brahmagupta. Though the works of other prominent mathematicians such as Varahamihira and Aryabhata II have not been listed here for the want of space, their contributions are far from being trivial.

Let us now focus on the Kerala School. It was a school of mathematics and astronomy founded by Madhava of Sangamagrama, arguably the greatest mathematician-astronomer of medieval India....

Next to Aryabhata, the figure of major importance was Brahmagupta, who belonged to the Ujjain School in the beginning of the seventh century AD. He made one of the most major contributions to the development of the number system with his remarkable concepts on negative numbers and zero. Who would have realised at that point of time that eight hundred years later European mathematics would be struggling to cope, without the use of negative numbers and zero! These were certainly not Brahmagupta's only contributions to mathematics. Far from it, for he made other major contributions to the understanding of integer solutions to indeterminate equations and to interpolation formulae, invented to aid the computation of sine tables.

A contemporary of Brahmagupta was Bhaskara I, who led the Asmaka School. This school had the study of the works of Aryabhata as its main concern and certainly Bhaskara I was commentator on the mathematics of Aryabhata.

Bhaskara II or Bhaskaracharya, at one point the head of the astronomical observatory at Ujjain, represents the peak of mathematical knowledge in the 12th century. He reached an understanding of the number systems and solving equations which was not to be achieved in Europe for several succeeding centuries. Six works by Bhaskaracharya are known: Lilavati, which is on mathematics; Bijaganita, which is on algebra; the Siddhantasiromani, which is in two parts: the first on mathematical astronomy and the second on the sphere; the Vasanabhasya of Mitaksara, which is Bhaskaracharya's own commentary on the Siddhantasiromani; the Karanakutuhala or Brahmatulya, which is a simplified version of the Siddhantasiromani; and the Vivarana, which is a commentary on the Shishyadhividdhidatantra of Lalla. Given that he was building on the knowledge and understanding of Brahmagupta, it is not surprising that Bhaskaracharya understood zero and negative numbers. However, his understanding went further than that of Brahmagupta. Though the works of other prominent mathematicians such as Varahamihira and Aryabhata II have not been listed here for the want of space, their contributions are far from being trivial.

Let us now focus on the Kerala School. It was a school of mathematics and astronomy founded by Madhava of Sangamagrama, arguably the greatest mathematician-astronomer of medieval India....

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