Died: June 1953 in Mysore, India

**A A Krishnaswami Ayyangar** was born in a traditional Vaishnavaite family. He studied at Pachaiappas College, Chennai (Madras), and was awarded his M.A. in Mathematics in 1911 when he was 18 years old. He was then appointed to teach mathematics at Pachaiappas College and he taught there until 1918.

R S Ridharan, reviewing [1], writes:-

Krishnaswami Ayyangar married Seshammal and they had four sons, A K Srinivasan, A K Ramanujan, A K Rajagopal, A K Vasudevan, and two daughters Mrs Vedavathi Bhogishayana and Mrs Saroja Krishnamurthi. In 1918 Krishnaswami Ayyangar left Chennai and joined the Mysore Educational Service and worked in the Mathematics Department of Maharaja College. He also worked for some time as a Reader in the Department of Statistics, Andhra University at Waltair. During nearly three decades during which he taught and undertook research at Mysore he made many contributions to geometry, statistics, astronomy, the history of Indian mathematics, and other topics.It should be an interesting problem for a socio-psychologist to analyse the effects on the members of a society brought upon by the birth of a genius among them. Such a typical instance was the birth of Srinivasa Ramanujan in the Tamil country. Whatever be the other effects, it certainly led to an increased awareness and appreciation of the rich mathematical heritage of India and a renewal of interest in the study of mathematics. This renaissance in Tamil Nadu showed itself in the coming up of a number of gifted teachers, well versed not only in mathematics, but also in the mathematical legacy of the country. A A Krishnaswami Ayyangar was prominent among them.

His papers include: *Ancient Hindu Mathematics* (1921); *The Hindu sine Table* (1923-24); *The mathematics of Aryabhata* (1926); *The Hindu Arabic numerals* (2 parts) (1928,1929); *Bhaskara and samclishta kuttaka* (1929-30); *New light on Bhaskara's chakravala or cyclic method of solving indeterminate equations of the second degree in two variables* (1929-30); *New proofs of old theorems - Apollonius and Brahmagupta* (1920-30); *Astronomy - past and present* (1930); *Some glimpses of ancient Hindu mathematics* (1933); *Fourteen calendars* (1937); *A new continued fraction* (1937-38); *The Bhakshali manuscript* (1939); *Theory of the nearest square continued fraction* (2 parts) (1940, 1941); *Peeps into India's mathematical past* (1945); and *Remarks on Bhaskara's approximation to the sine of an angle* (1950).

As an example we quote some of A K Srinivasan's comments on Krishnaswami Ayyangar's paper *The Hindu Arabic numerals* [1]:-

As a second example we note thatThis paper traces the history of the Hindu numerals. It establishes that Western writers, who had a bias towards Greek mathematicians, are wrong in saying that Hindus did not have their own system of numerals and that these numerals were spread by Arab merchants to their country. From India these numerals were adapted by others. Leonardo Fibonacci spread the Hindu numerals in Europe and in1202wrote his thesis Liber Abaci.

... traces the ancient Hindu mathematics from800B.C. to1200A.D. It has a brief description of the mathematics and astronomy developed by Indian mathematicians of that era. The following are the topics selected:

- 1
> Vedanga Jyothisha(1200B.C.)

2> The Sulva-Sutras(between800and500B.C.)

3>Surya Siddhanta(through revisions from500A.D. to100A.D.)

4>Aryabhata(Aryabhatiyam:499A.D.)

5>Varahamihira(6th century)

6>Brahmagupta(598A.D.)

7>Sridhara(probably8th century)

8>Mahavira(period between Brahmagupta and Bhaskara)

Krishnaswami Ayyangar retired from the University of Mysore in 1947.In spite of the fact that these articles were written several years ago, they deal with issues which are of current relevance and make interesting reading. One is impressed by the scholarship of the author, his knowledge of the subject as well as of Sanskrit.

Ayyangar joined the Edinburgh Mathematical Society in November 1923. He read the paper *On the Sexi-Sectional Equation* at a meeting of the Society on Friday 7 November 1924. He remained a member of the Society for about 10 years.

**Article by:** *J J O'Connor* and *E F Robertson*

**November 2007**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Ayyangar.html]