India, as a country, has contributed to the world of mathematics in an unparalleled way. It is a well known fact that the most fundamental contribution of ancient India in mathematics is the invention of decimal system of numeration, including the invention of zero. The Vedas and Valmiki Ramayana are also believed to have used this system. Ancient civilizations like MohanjoDaro and Harappa excavations around 3000 B.C. old also give specimens of writing in India.

The soil of India has given birth to great mathematicians such as, Aryabhata (475 A.D. -550 A.D.) the first well known Indian mathematician, Brahmagupta (598 A.D. -665 A.D.) renowned for introduction of negative numbers and operations on zero into arithmetic and Bhaskara (1114 A.D. -1185 A.D.) Bhaskaracharaya - the most well known ancient Indian mathematician.

This month, we are introducing to you yet another great Indian contemporary mathematician who has been highly acclaimed by the gurus of mathematics in the western world.  Dr Jagannath Mazumdar, our column guest for this month – has a list of degrees and awards up his sleeves. He is a double PhD (Moscow State University, Russia) and PhD (Hony)  (University of Adelaide, Australia), M.Sc in Applied Mathematics, First Class and First Rank (Patna University, India) and a member of New York Academy of Sciences, USA.

Dr Mazumdar has been holding various prestigious positions throughout his careers starting from being a Lecturer in Mathematics, Patna University,India, to Research Scholar, Moscow State University to  Lecturer, senior Lecturer, Reader, A/Professor  in Applied Mathematics, the University of Adelaide, Director and Emeritus Director, Centre for  Biomedical Engineering, Adelaide University, Adjunct  Professor, School of Electrical and Electronics Engineering , and School of Applied Mathematics, the University of Adelaide and also Adjunct  Professor of Electrical and Information Engineering, University of South Australia , Mawson Lakes.

Dr Mazumdar has been awarded various times by different prestigious organizations. He has been a recipient (three times) of prestigious Ken Clarke Prize for the best papers published in the journal ACPSEM in 1989, 1991, 1994, Supervisor of the year (Hony. Mention) Award 1995, EMG National Award of Engineering Mathematics 1998, Institution of Engineers, Australia Engineeing Mathematics Award 2000, Man of the Year 2000 Award from the American Biographical Institute 2000 Millenium Medal of ABI and best of all 2002 Noble Prize by the United Cultural Convention, USA

Dr Mazumdar came to Australia at the end of 1966 after completing his Ph.D. from Moscow University. Over the past thirty five years or so, he has been involved in two main areas of research and has made original contributions in both of them. These are Solid Mechanics and Biomechanics /Biomedical Engineering, the former being his area of research in continuation of his PhD work, and the later a more recent area of research which he has established single-handedly at the Adelaide University as a multidisciplinary research area with groups in Engineering and Medicine.

For more information on his credentials, please visit
http://www.maths.adelaide.edu.au/Applied/staff/jmazumdar/

We requested Dr Mazumdar to enlighten us on the great world of mathematics from his treasure of knowledge:

Q1) Tell us about your Indian background. Which part of India did you grow up in?
I was born in a small town called Purulia in West Bengal in 1937. I had my University education in Patna, Bihar. My wife also came from Patna, her father was at that time Vice-Chancellor of Patna University. After my B.Sc(Hons) and M.Sc in Applied Mathematics from Patna University, I worked as a Lecturer and Assistant Professor at the Bihar Institute of Technology. Subsequently, I received

Govt. of India’s Scholarship  for my Ph.D. study in Moscow under Indo-Soviet Cultural Exchange Programme. When I was about to complete my Ph.D. from Moscow State University in 1966, I received an offer of a lecturer, from the University of Adelaide, South Australia which I accepted and came to Australia at the end of 1966. This was the time when “White Australia” policy was gradually disappearing politically.

Q2) How do you think India has contributed to the world in the area of mathematical science. Do you believe India has to work a little harder to inform the world about her ancient contributions to mathematics, such as, the invention of decimal system and symbol of zero.
Firstly, let me give you a brief account of India’s contribution in early mathematics. Of the great civilization of antiquity- Babylon, Greece and later on India were prolific contributors to the development of mathematics.

All arithmetical operations- addition, subtraction,etc were carried out in Babylonian mathematics from the second millennium BC and the beginning around the 5^th century BC by the astronomers of India. When Hindu astronomy was developed about the 5^th century, the zero symbol was transferred to a decimal place-value notation. In the 6^th century the House of Wisdom was established in Baghdad and Indian  astronomy reached Baghdad, thus creating the first school of Islamic astronomy.. However, the most significant contribution of India to ancient mathematics was in the field of trigonometry. The progress due to Hindu mathematicians and astronomers for investigations related to the periodicity of planetary movement is well documented. Accurate tables for trigonometric functions were computed.

In the field of algebra, India’s contribution is immense. Among Hindu algebraists, Brahmagupta whose work in 630AD deserves special mention. Somewhat later, about  1150 AD, are the outstanding works of  Bhaskara- the Vija-Ganita “Algebra” and  the Lilavati “Arithmatic” named after his daughter. These works for the first time gave rules for dealing with negative numbers. It was mentioned by Bhaskara for the first time that positive numbers have two square roots and there are no roots for negative numbers.

It was during the fall of Roman Empire that  Aryabhata  another of the oldest Indian mathematicians was born.. His best known work ,written in 499AD known as  “Aryabhatiya”, convey astronomy and mathematics. This is indeed a monumental volume of ancient Hindu mathematical masterpiece derived from  Vedas, the oldest embodiment of scientific knowledge.

It should be remarked that the earliest undoubted occurrence of a  zero in India is in an inscription of 876. It is quite possible that zero originated in Alexandria, and that it was transmitted to India after the decimal system had been established there. With the introduction, in the Hindu notation , of the tenth numeral for zero, the modern system of numeration for integers was completed.

On the other hand, not many people know about the origin of  Infinity. Bhaskara’s Vija-Ganita mentions the first statement that division of a number other than zero by the number zero is infinity. Hindu definition of Infinity unfortunately has not received much well-deserved recognition in the history.of ancient mathematics.

We have known from  Upanishads which are intended to awaken cosmic consciousness in the aspirant one significant revelation:  What is beyond the universe is infinity, what has apparently become the universe is infinity. Infinity alone is in the manifested and unmanifested states.”   Upanishad

says:

   “Purnamadah purnamidam

     Purnet purnamudacyate;

     Purnasya purnamadaya,

     Purnamevavasisyate”

The Invisible is Full , the Visible is Full. From the Full (Invisible) , the Full (Visible) has come. The Full (invisible) remains the same, even after the Full (visible) has come out of the Full. This the basis of  Infinity in Mathematics- Infinity minus Infinity also is Infinity.

So you can see, India’s contribution in the field of mathematics is indeed immense. The Indian Mathematical Society not long ago has set up a committee to compile a “History of Hindu Mathematics”, divided into three periods- Ancient, Medieval and Modern. However, the compilation has not been much advertised outside India and not many overseas mathematicians know about the existence of such important document.. I believe you are right that India has to work harder to inform the world of her mathemathical heritage.

Q3) Is there a real connection between the study of mathematics and astrology as believed by most of the Indians?
Astrology as you know is the science of predicting the influence of planets and stars on earthly affairs in order to predict the destinies of individuals. Astrology originated in Mesopotamia, perhaps in 3^rd millennium BC and spread to India in its older Mesopotamian form. The techniques of Indian astrology are thus not surprisingly similar to those of its Mesopotamian’s counterpart.

Astrology studies the relationship of the significant celestial moments ( e.g. the times of the occurrences of eclipses. planetary conjunctions,etc) to social groups and nations. It determines whether or not a chosen moment is astrologically conducive to the success of a course of action. The main purpose of astrology is to forecast to an individual on the basis of the positions of the planets and of the zodiacal signs at the moment of his birth or conception. Hence, a very accurate mathematical calculations are involved.

For some , however, astrology is not an exact science like astronomy but merely indictes trends and directions that can be altered either by divine or by human will. The Indians also found it useful to make more elaborate complex methodology. They added as significant elements : the naksatras (lunar mansions), an elaborate system of three categories of  yogas, dozens of different varieties of dasas and antardasas and based on horoscopy a complex theory of  astakavarya. All of these complications serve, among other purposes, to provide the astrologer with convenient excuses for his inevitable errors. However, with the advent of modern mathematical and computing methodology, the errors these days are minimized and astrological findings are accepted as accurate findings.

Hence I do believe that there is a connection between mathematics and astrology.

Q4) Which country, in your opinion, has had the best mathematical practices so far?
It is difficult to mention any one country which can be regarded as the best in mathematics. However, amongst earliest pioneers in mathematical research the names of Russian, French, Hungarian and Chinese mathematicians  deserve special mention. They all belong to more or less in the same category. These days, American mathematicians are regarded as the best in the world of mathematics.

Q5) How do you define the level of mathematics taught in Indian institutes today compared to US or Australia?
Although I have left India quite a few years ago, I have been visiting India quite frequently. I have visited India on invitations from Indian Science Congress, on invitations as Visiting Professor from Indian Institute of Science, Bangalore, IIT, Delhi, etc. Hence I have a  first hand knowledge of the current standard of Mathematics taught at Indian Institutes .I can categorically say that the standard of mathematics at IIT s and IISc, Bangalore is exceptionally high. But then, of course, these are the best Institutes in India. However, from my personal experience I can say that the standard of mathematics in general is a mixture of good and bad. Some of the good is superlatively good and some of the bads need proper attention !! These comments are made comparing the standards in Australia and the USA

Q6) How would you describe to a layman the close connection between mathematics and human body functions, such as the use of Casson's equation to approximate blood flow through arteries.
As is well-known, coronary artery disease (CAD) is the largest single cause of mortality in developed nations. Recently, it was estimated that CAD is responsible for 24.13% of deaths in Australia , and 21.34 in the USA. It occurs when the coronary arteries narrow to such an extent that they are unable to transport sufficient blood to the heart muscle for it to function efficiently. The two main causes of death from CAD are rupture of the plaque causing sudden occlusion of the artery and the slow build up of a narrowing of the artery (stenosis) due to accumulation of fatty substance. Therefore, there is a considerable interest in models of blood flow through  arteries.

In recent years, researchers  have turned to hemodynamics, the study of fluid  dynamics of blood flow, in an attempt to understand the significance in the genesis and proliferation of arterial disease.

Mathematical modeling provides an economical and non-invasive method of studying blood flow through arteries. However, blood flow through small arteries have revealed that it exhibits non-Newtonian characterstics in vessels with a diamater less than 0.8 mm. Although the major coronary arteries can be as wide as 4mm in diamater, this is rarely the case in an atheriosclerotic region when the diamater of the artery is reduced to 85% or more. To study such a situation, Casson model seems to best fit the results under these circumstances. Thus in order to address blood flow through a small artery containing a partial blockage, this model has proved to be very appropriate.

This mathematical model is seen as a means of assisting cardiologists in understanding the progression of arterial diseases and more importantly the causes of the disease.

Q7) What aspirations did you have while growing up. Did you always want to be a mathematician?
Although I had a mathematical aptitude from my childhood which was evident from my Primary School teachers reports to my parents, I had never aspired to have a career in Mathematics or Engineering. I come from a Doctor’s family, my late father was a Medical Practitioner and out of my eight brothers four are medical doctors. My  father also wanted me to be a Doctor, but because of my University results and being recipients of University merit scholarship for study in Mathematics, my luck brought me in this field. However, I have no regrets for this.

Q8) Any message you would like to convey to growing mathematicians.
My message would be always remember “Mathematics is the Queen of all sciences.”. You can do a lot of rewarding things with the help of mathematics if you seriously think so. Applied Mathematics is a field where you can do research in the fields  of Engineering, Medicine, Agriculture, Economics, and virtually any field you name. So work hard and always think of  real problems where your knowledge of mathematics can be applied. Don’t be afraid of working with people of other disciplines.  They will eventually understand what a mathematician can do for them.