The following article was published in Mathrubhumi in March 2011 and is primarily an interview with George conducted by TD Ramakrishnan. The original is, of course, in Malayalam and what appears below is a translation of that interview.

The Crest of the Peacock- A Cultural History of Mathematics

George Gheverghese Joseph/ T. D. Ramakrishnan

Recorded History is all about the story of the winners and their perceptions. The history of science is no exception. All the civilizations in the world had their own path in the pursuit of science and they made valuable contributions in various field of science. In India, mathematics had achieved great heights in ancient times. But the Euro centric view on the development of Mathematics limits the contribution of India and other civilizations to the elementary levels. They have never given any credit, in the development of advanced mathematics, to the Indians or other people. George Gheverghese Joseph challenged this notion in his book, The Crest of the Peacock Non-European Roots of Mathematics. [In relation to India] he had done it by proposing a new school called Kerala School of Mathematics.

In his book, George Gheverghese Joseph made detailed analysis of the works of Samgrama Madhavan, Parameswaran, Jyeshta Devan, Neelakanda Somayaji and Achutha Pisharadi. All of them were believed to be the exponents of the Kerala School of Mathematics. After the release of the book, the Gregory series was renamed as Madhava-Gregory series, which is a clear example of the impact of the book on Western minds.

When I started my novel Francis Ittikkora, I read this book. My journey through the book helped me to shape my novel as it seems now. The protagonist of the novel is a researcher in Mathematics, Hashimotto Morigami. In the novel, there is a comment on George Gheverghese Joseph by Morigami. It reads "the claim put forwarded by the recently published book of George Gheverghese Joseph on the accession of traditional Indian knowledge by the Europeans sounds odd. He claimed that these knowledge reached Europe after the arrival of Jesuit priests in Kerala followed by Vasco de Gama. I have no intention to undervalue the research done by Joseph. I have immense respect for him on his findings that the basics of Calculus were developed much before Newton and Leibnitz in Kerala. Obviously his findings are the driving force behind my research. But he failed to consider the chance of this knowledge transfer through the merchants from Kerala before the arrival of Gama. I thought Joseph became prey to accepted history. So I continue my research beyond the boundaries of the accepted history". In my book, I took the freedom of modifying logic with imagination. I had no intention to underplay the efforts of George Gheverghese Joseph because I have great respect for him and his works. It is believed by some that the genesis of the Kerala School of Mathematics can be traced to Vararuchi in the 4th century AD. There is clear evidence of this School since the time of Samgrama Madhavan. His is believed to have lived between 1340 and 1425. On the basis of this evidence Samgrama Madhavan is considered as the founder of Kerala School of Mathematics. He was lived near the Koodalmanikka temple at Irinjalakkuda in Trissur. *He wrote the book Karanapadhathi in 1375*. He discovered the trigonometric functions like sine, cosine, etc about two hundred years before Leibnitz and Newton. Parameswaran (1370-1460), Damodaran (1410-1510), Neelakanda Somayaji (1443-1544) and Jyeshta Devan (1500-1610) were the torch bearers of Kerala School of Mathematics after Samgrama Madhavan.

The world knew about the Kerala School of Mathematics through an article by Charl Whish, published in Royal Asiatic Society of Great Britain and Ireland in 1835. Kadambathoor Rajagopal and M. S. Rangachari published some articles on the subject in the 1950s. But only after the release of Crest of the Peacock, did Kerala School of Mathematics became a subject for debate. Now there is no doubt about the contributions of Kerala School of Mathematics to modern Mathematics, thanks to George Gheverghese Joseph and his works.

Joseph is attached to the University of Manchester in Britain. His interest in Mathematics [in the past] varies from Applied Mathematics to Computer Programming. He has published a handful of books on various topics. The Crest of the Peacock: Non-European Roots of Mathematics and A Passage to Infinity are the major works among them. Now he is working on a major project on the transfer of Mathematics from medieval Kerala to Europe. He spoke to me about his life and works.

T. D. R: How did you get attracted to the History of Mathematics?

G. G. J: I got interest in the history of Mathematics when I was working as a teacher in Kenya. Kenya then was not free. This was in 1961/ 1962 when Kenya was moving towards independence. Until then there were separate schools for Africans, Asians and Europeans [with quality and availability of education for the three groups being in that ascending scale]. After independence, common schools were started. Unfortunately, African children [with their poor primary school background] found it difficult to cope with the complexities of modern Mathematics. We set out to modify the syllabus so as to provide a level playing field for the three races. It is then I realized the potential and scope of the History of Mathematics in classroom teaching. My interest in Mathematics has been increasing ever since, especially in the existence of mathematical pursuits among marginalized communities across the world. When I started to teach in European Universities, I became aware of the deeply entrenched Eurocentric views on Mathematics. 'They are black and they have done nothing for Mathematics' that was a popular notion then and even used to justify Apartheid in South Africa. That prompted me to take it as a serious problem. Besides I became aware that knowledge of history of mathematics can attract more and more people to mathematics by giving it a 'human' face. It is particularly helpful in motivating an average student studying mathematics.

T. D. R: Were you interested in Mathematics from your school days?

G. G. J: I was transplanted to Mombasa in Kenya, at the age of nine. My parents were teachers there. My father was an English teacher and mother was teaching History. My Grand Father, George Joseph, my mother's father, was a well-known freedom fighter and close associate of Mahatma Gandhi. My parents inculcated in us a living connection with India, which ignited a love of History in me. I began schooling first in Mombasa and later in Nairobi; I chose an interesting combination of subjects: Mathematics, Economics, English and History. My family was not particularly well off. So for University studies, I would have had to return to India. However, I was awarded a Kenya Government Scholarship to study in Britain. That was a big opportunity.

T. D. R: So the expenses for your studies were met by the government?

G. G. J: Not only the living expenses but also special allowances for travel, clothing, books etc. There was a reason for this. Kenya was all set for Africanization. They were planning to select some of us for appointments to top posts in the government service on our return. Before I left I was advised to take up Mathematics and Economics. They probably meant me to work in the Treasury. But on my return they appointed me to the Education Department as a teacher although I could become a Kenyan citizen at any time. I remember the present President of Kenya Mwai Kibaki, who was then in London School of Economics, telling me that being an Asian should not preclude one from rising to the upper echelons of the Civil Service. He described me as a vanainchi. A vanainchi in Swahili means a 'son of the soil. But the job of an Educational Officer was not bad. At the age of 21, I received the same salary as my European counterpart. I had a bungalow and the means to employ two servants if I wanted to. I even became a temporary head of the mathematics /economics department when I was only twenty two. I worked there for six years. Unfortunately at that time my mother was diagnosed with cancer and my father returned to India with her. She died very soon after that. After that I returned to the University of Manchester for further studies. But my stay in Kenya remains a special and cherished experience for me: the Kenyan people, their way of life, the Swahili language and all.

T. D. R: What is your comment on Swahili?

G. G. J: I loved Swahili just as much as my mother tongue, Malayalam. I used to speak Swahili when I was in Mombasa and in Tanzania. But it is not easy to speak Swahili now.

T. D. R: How did you reach Tanzania?

G. G. J: When I was living in Britain as a teacher and a researcher, I retained great affection for both India and Africa. Julius Nyerere was the President of Tanzania. He was a great inspiration for me like Nelson Mandela and Fidel Castro. I went there to teach in the University of Dar-es-salaam. Nyerere included me in what he described as his informal three-member 'think tank' when we occasionally met. Tanzania was experiencing mounting pressure from the IMF. He brilliantly defended his country against the IMF pressures. Our duty as a group was to counter the IMF with the help of statistical analysis. He called us his 'subversives'. Julius Nyerere was a great President. On villages outside Dar-es-Salaam and other cities, much development aid was expended. He initiated a village-centric development model for a balanced development of Tanzania. This did not last long after he left.

T. D. R: What is your personal opinion of IMF?

G. G. J: In the case of Tanzania, IMF had some vested interests. Their policies often led to the helping of the multi-nationals at the expense of the country's welfare. Corruption became rife and in case of some of the African countries, this has lead to the collapse of their economies. At the international level, the IMF often protected the interests of the Western nations only. Before returning from Tanzania I gave a lecture in Swahili to the MA students of the University of Dar-es-Salaam. That was my last lecture in the University.

T. D. R: Why did leave Tanzania?

G. G. J: I could have continued there by accepting the Tanzanian citizenship. That would lead to a sudden fall in my salary since had to accept the salary of a Tanzanian. I feared that it would affect the education of my children. For the future of my kids I decided to return to my university Manchester. I began the research which leads to the Crest of the Peacock after that. At that time, in Britain, there was a lot of concern among teachers regarding teaching Mathematics. We decided to overcome this by developing a multi-cultural perspective. My Indo-African background helped me a lot to achieve this.

T. D. R: Can you describe about the situation which leads to quit your post in Education Department in Kenya and return to University of Manchester?

G. G. J: Sorry, I failed to discuss that. During my last days in Kenya, I had decided to pursue my Post-graduate studies in Britain. But I was not interested in pure mathematics. My intention was to continue my higher studies in applied Mathematics. I wrote letters to friends in Britain expressing my desire. One among them showed the letter to Prof. Jack Johnston. He was the head of the Econometric Department in University of Manchester. He was in search of students who had a mathematical background and were interested in the field of Econometrics and Operations Research. He invited me to study in his Department. So I joined Manchester.

Jack Johnston was not a Mathematician, but an Economist. He asked me to read through the manuscript of the second edition of his well-known textbook, Econometric Methods. Around the time of completion of my post-graduate degree, he met me in the corridors of the Department and told me that there were two vacancies coming up. One was in Econometrics and the other in Social Statistics. Without considering Jack's displeasure, I applied for the post in Social Statistics. I got the job and started my career in University of Manchester. I took my PhD only later. After that, apart from Tanzania, I worked at the University in Papua New Guainía. Because of the security situation I left after six months. I also worked in New Zealand for three months. I lectured at different Indian Universities having been awarded Royal Society Visiting Fellowships on two occasions. I have also given talks at Universities around the world, including Princeton, Chicago, Cornell, New York and Berkeley in the United States.

T. D. R: When did you start serious research?

G. G. J: In Manchester, first three years was a probation period. During that period we had to publish at least two research papers in reputed journals. So I was expected to start research from the very moment I joined. One day the Head of the department told me: "If two research papers are not out in the next six months you will be out". Fortunately my papers were published before the ultimatum. My papers were in Statistics and Mathematical Modeling. Thus I became a member of permanent staff at the University of Manchester. There lecturing students is normally what you do. Promotion is based on your research work. You were free to pursue research in any area you wish. For example, Andrew Wiles, who finally proved Fermat's Last Theorem, was continuously out of office for nine months. If you gave your lectures and worked at your research, nobody bothered you.

T. D. R: When did you start working on the Kerala School of Mathematics?

G. G. J: It started in 1985 as part of developing a multi-cultural perspective in teaching Mathematics. I was given responsibility to look for possibilities of this in history. I started reading in this direction. I was inspired by papers of C. K. Rajagopal. Professor K. V. Sarma rendered me great help. He gave me the manuscript of his translation of Yukthi Bhasha. Another name I should mention as an inspiration was Professor Saraswathi Amma who discussed her work when I visited her in the mid-80's. I also got help from Prof. R. C. Gupta. I discussed the subject with many people and read a number of articles and books. Some of the ideas were then incorporated into The Crest of the Peacock published in 1991. T. D. R: What was the response of the academic community towards the book?

G. G. J: When I gave lectures in Indian Universities, most people in India had not heard of the Kerala School of Mathematics. Some in Europe responded positively. Most of the people from the academic world supported the Eurocentric view. They may acknowledge contributions from India, China and the Arab world but only in elementary mathematics. In the case of advanced mathematics, Greeks were the only people who got a mention. There was a third group. They believe that mathematics developed independently in various parts of the world. They were reluctant to accept the idea of transmission of Kerala Mathematics through the Jesuits. Unfortunately we only have circumstantial evidences to prove this transmission. We have to find out solid documentary evidence to prove this exchange. But the multi-cultural thinking about the history of Mathematics gets good support. Some years ago, in an international seminar, I spoke about the Shang bone (the oldest archeological artifact relating to mathematics dug out from central Africa). After my talk, an African lady, with tears in her eyes, said that it was the first time she had heard of the Bone. It is a hidden part of the great history of Africa. That was the reason for her tears.

T. D. R: Any Criticisms?

G. G. J: Of course. Some people lampooned me by saying that a mathematician should have nothing to do with history. Some alleged that I was trying to glorify Indian and Arabic Mathematics because of my origins. A renowned historian of Indian mathematics, Pingree, was among them. I wrote to him asking how he would react if I suggested that the reason for his attacking my conjectures about the Kerala School of Mathematics was because he was a Jew from the West. Would he accept that? Nevertheless, to establish the transmission of Kerala Mathematics we need to find concrete evidence.

T. D. R: Can we consider research in history of Mathematics as research in Mathematics?

G. G. J: We cannot differentiate research like that.

T. D. R: E. C. G. Sudarshan and you have made the Malayalis proud all around the world. Sudarshan was nominated for the Nobel Prize for six times. But he hasn't got it. In a recent interview he said that he was denied the prize due to the strong opposition from the international level. Have you ever experienced any such opposition?

G. G. J: I haven't ever experienced any such opposition. It might be because of there is no Nobel Prize in Mathematics! There is a joke about not including mathematics among the subjects for Nobel Prize. The wife of Alfred Nobel eloped with a mathematician, so he didn't include mathematics for Nobel Prize.

T. D. R: But there is Field Medal and Crawford Prize

G. G. J: Yes. But there are no such pressures behind these prizes. I don't know what really happened in the case of Sudarshan. The opposition I have faced is purely political and ideological. The historians of mathematics criticized me by saying that I was wrongly interpreting history. In academic circles, I have faced more criticism from the Indians than foreigners. Especially from the exponents of the so-called 'Vedic Mathematics'. The others are pure mathematicians. They are not ready to indulge in anything beyond mathematics. To them history of their subject is only two or three research papers deep. Most of the well-known Indian mathematicians living are in their fifties or sixties. Recently a number of books have been published on the mathematical history of various countries - Babylonian Mathematics and Chinese Mathematics are good examples. There have been some major works on Islamic Mathematics also. I thought it worthwhile to discuss these in the third edition of the Crest of the Peacock which Princeton University Press brought out last year.

T. D. R: In 'The Crest of Mathematics', you had discussed the mathematical history of various parts of the world. But in your book 'A Passage to Infinity', you focused on Kerala School of Mathematics, why?

G. G. J: There is a popular belief that the non-European roots of mathematics are elementary. And that Indian mathematics stagnated after Bhaskaracharya. But the contributions of the Kerala School of Mathematics are enough to disprove this. Work on the infinite series which form the basis of modern calculus was introduced by the Kerala School of Mathematics.

T. D. R: Can you describe the functioning of the Kerala School of Mathematics?

G. G. J: The members of the School were mainly based in the houses of Brahmins. Except for the eldest son, others were free to cohabit with females from the Nair community which was matriarchal. So the younger sons in the family had less responsibility in running the family. It gave them immense opportunities to work in their fields of interest. Literature, Astronomy, Astrology and Mathematics were drew a number of people. They found people with similar interests and made them disciples. At that time literature and science were complementary. So they wrote mathematics and astronomy in verses and practiced them by chanting. Because of the caste system, the other communities in the society had little access to this knowledge. That is the reason why this knowledge remained confined of the darkness of the Illams. After the arrival of the Jesuits, the knowledge may have spread to the Western world.

T. D. R: Can you say how was it happened?

G. G. J: Kerala is a part of the Indian sub-continent which had trade ties with Africa and Arabs from the ancient times. The arrival of Vasco de Gama opened the doors to the Iberian Peninsula and further north and west. After that the mathematics of Kerala may have been transmitted through the Jesuits or Arab merchants or Jews to the West. There are lots of documents in the European archives which prove indirectly the involvement of Jesuit priests in this exchange. More evidences may have lost in the earth quake that happened in Lisbon in 1755 and the setting ablaze of the Jesuit library in Kochi.

T. D. R: Can you explain why a book like Yukthi BhashaI was written in Malayalam. I am asking this because it was written in the sixteenth century?

G. G. J: The Yukthi Bhasha written by Jyeshta Deva is not like the other books of that period. In this book he gave importance to logic. He provided all the theorems with adequate proof. Being written in Malayalam presupposes that the book was aimed at a wider audience. The great importance of the contributions of the Kerala School of Mathematics can be understood from this work. Prof. K. V. Sarma has translated it into English under the title Ganitha Yukthi Bhasha.

T. D. R: Morigami, the protagonist in my novel Francis Ittikkora, strongly opposes your convictions. The main reason for this was you didn't consider the chances of Keralites went abroad for trade. It was said that Vasco da Gama set out for Kozhikode from Malindi accompanied by a Gujarati guide. If there is no route, how is a guide possible?

G. G. J: Such a conduit is also possible, although unlikely. In fiction you have the poetic licence to think like that. Anyway, you have popularized Crest of the Peacock and the Kerala School of Mathematics among the people of Kerala through your novel. I am also interesting in 'subverting' the accepted history like you.

T. D. R: Is there a Vasco da Gama memorial in Malindi? What is the response of the Kenyans to Gama?

G. G. J: Yes, in Malindi at a prominent spot there is a memorial. It doesn't attract much interest ordinarily, but a protest was staged to mark the 500th anniversary of Gama's arrival.

T. D. R: Your childhood memories about India?

G. G. J: I was born in my grandmother's house in Chengannur. But Madurai immediately pops up in my mind when I think about my childhood. My mother was a teacher there. I enrolled in the same school. We lived very close to the Meenakshi temple. I used to walk around the sacred pond inside the temple. In those days there would be musical concerts in the temple almost daily. So I got the opportunity to listen to good music from my early childhood. At the age of nine we went to Mombasa.

T. D. R: Marriage?

G. G. J: Leela is a doctor. We were neighbors in Kenya. Her mother was also a teacher there. She studied in Vellore Medical College. Later we met in England. Between us we have three children and eight grandchildren. Our children are settled in England and Canada.

T. D. R: There is a common thinking that mathematicians are eccentrics like John Nash and Paul Erdos. What is your comment on this?

G. G. J: There are bound to be eccentrics among mathematicians also. The film 'The Beautiful Mind' based on the life of Nash made such belief widespread. John Nash was a genius. Paul Erdos was also of the same breed. I first met him at a conference in Budapest. He carried his worldly possessions in a suitcase of his own. He travelled from conference hall to conference hall. His colleagues arranged everything for him. He was one of the finest mathematicians of his generation. It was difficult to understand him at times because of his heavy Hungarian accent. He was known as the most brilliant problem solver in the field of mathematics.