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 singlehandedly
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 ViceChancellor 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 IndoSoviet 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 placevalue 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 VijaGanita “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 VijaGanita 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 welldeserved 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 wellknown, 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 noninvasive method of studying blood flow
through arteries. However,
blood flow through small arteries have revealed that it exhibits nonNewtonian
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.
