### Post by vkaul1 on Sept 22, 2011 16:34:03 GMT -6

David Mumford (a pretty famous mathematician) en.wikipedia.org/wiki/David_Mumford wrote an excellent review for the book on mathematics in India by Kim Plofer. It shows how Indian mathematics was in fact underestimated by the west and even Arabic scholars. www.ams.org/notices/201003/rtx100300385p.pdf

Some good excerpts from the review.

I think we will do disservice to the thoughtful people of the past to freeze ourselves to a rigid 16 th century medieval Indian view. As the thoughtful people in Indian kept on accommodating new discoveries, we can do the same.

Some good excerpts from the review.

**Another major root of Indian mathematics is the**

work of Paninin.

ini and Pi˙ngala (perhaps in the ﬁfth

century BCE and the third century BCE respectively), described in section 3.3 of Plofker’s book.

Though Panini. is usually described as the great

grammarian of Sanskrit, codifying the rules of the

language that was then being written down for the

ﬁrst time, his ideas have a much wider signiﬁcance

than that. Amazingly, he introduced abstract symbols to denote various subsets of letters and words

that would be treated in some common way in

some rules; and he produced rewrite rules that

were to be applied recursively in a precise order.

One could say without exaggeration that he

anticipated the basic ideas of modern computer

science.work of Paninin.

ini and Pi˙ngala (perhaps in the ﬁfth

century BCE and the third century BCE respectively), described in section 3.3 of Plofker’s book.

Though Panini. is usually described as the great

grammarian of Sanskrit, codifying the rules of the

language that was then being written down for the

ﬁrst time, his ideas have a much wider signiﬁcance

than that. Amazingly, he introduced abstract symbols to denote various subsets of letters and words

that would be treated in some common way in

some rules; and he produced rewrite rules that

were to be applied recursively in a precise order.

One could say without exaggeration that he

anticipated the basic ideas of modern computer

science.

**Chapter 7 of Plofker’s book is devoted to thecrown jewel of Indian mathematics, the work of**

the Kerala school. Kerala is a narrow fertile strip

between the mountains and the Arabian Sea along

the southwest coast of India. Here, in a number

of small villages, supported by the Maharaja of

Calicut, an amazing dynasty

17

of mathematicians

and astronomers lived and thrived. A large proportion of their results were attributed by later

writers to the founder of this school, Madhava of

Sangamagramma, who lived from approximately

1350 to 1425. It seems fair to me to compare him

with Newton and Leibniz. The high points of their

mathematical work were the discoveries of the

power series expansions of arctangent, sine, and

cosine. By a marvelous and unique happenstance,

there survives an informal exposition of these

results with full derivations, written in Malayalam,

the vernacular of Kerala, by Jyes

the Kerala school. Kerala is a narrow fertile strip

between the mountains and the Arabian Sea along

the southwest coast of India. Here, in a number

of small villages, supported by the Maharaja of

Calicut, an amazing dynasty

17

of mathematicians

and astronomers lived and thrived. A large proportion of their results were attributed by later

writers to the founder of this school, Madhava of

Sangamagramma, who lived from approximately

1350 to 1425. It seems fair to me to compare him

with Newton and Leibniz. The high points of their

mathematical work were the discoveries of the

power series expansions of arctangent, sine, and

cosine. By a marvelous and unique happenstance,

there survives an informal exposition of these

results with full derivations, written in Malayalam,

the vernacular of Kerala, by Jyes

I think we will do disservice to the thoughtful people of the past to freeze ourselves to a rigid 16 th century medieval Indian view. As the thoughtful people in Indian kept on accommodating new discoveries, we can do the same.