28-09-2012, 11:03 AM
A perspective on the status of mathematics in India
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ABSTRACT
My intention here is to comment briefly on the present status of mathematics in India. I approach
the task with some diffidence because my own mathematical knowledge is limited and I have lived for
some thirty-three years outside India. Thus, the perspective can at best be partial. Please bear with
me if you see flagrant errors of detail or substance.
A few historical remarks
I am no expert on the history of mathematics in India and
am aware of the intrinsic difficulties in being precise. My
brief remarks, such as they are, have been culled entirely
from secondary though serious sources, and are meant to
set the stage for comments to follow.
It appears even to a casual observer that India has good
reasons to be proud of its heritage in mathematics. It can
even be said that the sustained efforts in India led, through
the Arabs, to the revival of mathematics in Europe. Scholars
have noted that the decimal system was already in place
in the Harappan period, though a few centuries had to
lapse for its importance to be appreciated fully. Arithmetic
operations and sequences, fractions and certain geometric
rules were known some one thousand years before
Christ, including results such as the Pythagoras theorem.
Jains were fascinated by large numbers and had an advanced
knowledge of infinity (though it fell far short of our present
understanding), and maintained the tradition of
mathematics for centuries. Buddhists knew infinite and
indeterminate numbers. Important developments came
through astronomy. Because the tradition of scholarship in
ancient India was to reduce everything to aphorisms and
mnemonics while obliterating intermediate steps, it is hard
to ascertain the reliability of modern-day assessments of
the past. The best I can do is to refer to some source material1
where lively discussion can be found; there is, in fact, a
well-articulated view, even in India, that the claims of its
mathematical past have been exaggerated. There is, however,
no controversy to my knowledge about the legendary
contributions of the mathematician–astronomers, Aryabhata
(476–550), Varahamihira (505–587), Brahmagupta
(598–670), Bhaskara (600–680) and Bhaskaracharya
(1114–1185).
Indian mathematics in recent centuries
For the past four or so centuries, most major developments
have come from Europe and, lately, also from the US.
Descartes, Newton, Euler, Gauss, Riemann, Hilbert and
Poincaré are some names that come to mind immediately.
In that class belongs Ramanujan, who represents the transition
between the traditional and the modern mathematics
in India. For instance, Hardy7 remarks that the concept of
mathematical proof was somewhat alien to Ramanujan,
yet one can argue that his work was more influenced by
the Western tradition than by his Indian background. Ramanujan’s
story8 is known too well to need recounting here,
but I wish to call attention to Narasimha’s analysis9 of
Ramanujan’s way of doing mathematics. It suffices here to
say that while Ramanujan was singular in most respects –
and the first Indian mathematician to gain recognition
from the West in his lifetime – the country did have several
other less well-known mathematicians in his time10. All
of them explicitly followed the traditions of the West11.
The status of mathematics in modern India
After independence, many new universities were created,
as were several National Laboratories and five Indian Institutes
of Technology (IIT). There already was the Indian
Institute of Science (IISc) in Bangalore – which, by the
way, will be celebrating its 100th anniversary soon, and
about which I will say more later on. A particular mention
must be made of the Tata Institute of Fundamental
Research (TIFR), Mumbai, which has been a centre of
sustained excellence in mathematics, rejuvenating the
tradition, though perhaps inadvertently, of the mathematics
schools of the last fifteen centuries which thrived along
the western coast of India. Let me first comment on these
special institutions before returning to the universities.
The languishing university system
In the 1980s, the University Grants Commission (UGC),
New Delhi tried to build centres of excellence in Pune,
Bangalore, Coimbatore, as well as other places. I cite two
examples merely for specificity: the UGC Centre Advanced
Fluid Mechanics in the Central College, Bangalore,
built around N. Rudraiah, and the Centre for Nonlinear
Dynamics in the Bharathidasan Universrity, Tiruchirapalli,
built around M. Lakshmanan. These and other existing
groups are generally centred on a single leader, and work
against many odds. There are active researchers elsewhere,
but few schools engaged in adjacent or overlapping
activities at a high level, over a sustained period of time.
broad-brush assessment
It is clear that the lifting up of the entire mathematics system
will be difficult, and so one will have to be selective by
singling out some universities or centres for specific actions.
This choice should be guided by the internal drive
from the institutions themselves, accompanied by proper
evaluation and funding mechanisms. Here, the intellectual
leadership of the leading institutions in the country,
such as the TIFR, has a large role to play, but at least a
few universities have to be brought on-board.
A great department in any branch of science always
consists of some stars and a number of up-and-coming
young people. Star departments or centres, are essential
for upholding the excitement of the field. Such schools have
been few in India, and TIFR has been an exception in
mathematics.