Prof. P.V. Subrahmanyam in conversation with Prof. Vetrivel
It’s my pleasure to invite Professor P. V. Subrahmanyam. He is a
retired…from IIT…Department of Mathematics, IIT Madras
to this Oral History Interview, on behalf of Heritage Centre IIT Madras.
And I…Professor P. V. Subrahmanyam
been here for more than 3 decades here in IIT Madras,
and I am…I am so happy to interview him on behalf of the Heritage Centre.
Sir, welcome, sir,
Thank you.
to the Heritage Centre, and
I know…I don’t know whether you remember,
I have been associated with you for more than 30 years.
In fact How can I forget that you were a student here initially,
Yes sir, yes sir, yes sir. And then you were my colleague.
Yes, yes sir, as a student Even a fortnight back you conducted a symposium
for which I was an invited speaker.
Yes, sir. So, how can I forget?
Yes, yes, yes, sir.
Still I…I remember those days, when I came here for…as a Ph.D. student,
you were in the interview committee,
and, afterwards, you were…in…for my core course,
you were the teacher for my course on functional analysis.
Ok. Still I can remember, whatever I know in function analysis, is mainly
what you have taught during that period for our batch.
Especially, I still remember the…what you taught about
reflexive spaces and their properties,
still I remember what you taught from G. F. Simmons topology.
Well, I don’t know all the details…and
thank you for your kind words about my course.
That is what I can tell at this moment.
I cannot recall whatever details you are conveying.
Of course, functional analysis has become one of the
most important branches of mathematics,
both from a theory point of view, as well as applications.
Yeah, and sir, I just want to know I…I know when I
joined here, you were Associate Professor or something
and afterwards I…I…I don’t know much about your previous…I
I know that you have done Ph.D. here, IIT Madras
under Professor P. V. Subbarao.
And then before…I…I just want to know about your
education background before you joined IIT Madras.
Well, I did my…I was born and brought up in Chennai only.
My father lived for a couple of years in the CLRI quarters,
he was a scientist from Central Leather Research Institute.
And I studied in a school in Adyar
called at that time called Rani Meyyammai High School,
later on it had become into Kumara Raja Muthiah Chetti School or something.
Prof. Vetrivel: Yes sir, yes sir.
Muthiah Chettiar was the patron of the school.
When we studied, it was a co-educational school and
though the infrastructure was not very impressive, we had fine teachers.
Mention must be made of one Ms. L. K. Ganga Bai,
who taught us English as well as geography.
She used to live just opposite to the school, and
took great interest in educating us.
She used to bring issues of National Geographic,
encyclopaedia and teach us various subjects.
She was herself a women’s champion in chess
Prof. Subrahmanyam: in the city for several years. Prof. Vetrivel: Okay.
And all that gave a good academic background for many of us.
Prof. Vetrivel: I see.
Later on, I joined the Vivekananda College in Mylapore,
which had a an excellent tradition in mathematics.
Prof. Vetrivel: Yes.
I did my Pre-University, and then moved on to do B.Sc.,
Prof. Subrahmanyam: although many of my uncles on the paternal side were chemists. Prof. Vetrivel: Okay.
And on my maternal side, they were into humanities.
Prof. Vetrivel: Okay.
So I was the first deviant opting for mathematics.
Prof. Vetrivel: Okay.
I thought, if you learn mathematics,
Prof. Subrahmanyam: you will know…most of the sciences you can understand. Prof. Vetrivel: Okay.
That's how I ventured into mathematics.
Prof. Vetrivel: Okay.
I must confess, mathematics is not my cup of tea how…
however, over the years, I cultivated a special liking for mathematics,
despite my…my handicaps.
Prof. Vetrivel: Okay.
And, in Vivekananda College we had excellent teachers,
and after finishing my B.Sc. there,
I didn’t join the engineering courses, etc.
My father also encouraged me to pursue my own,
I mean my line of thinking.
After finishing my B.Sc., I could have joined the MIT,
Madras Institute of Technology.
Yes, there used to be a programme.
At that time, they had a 3 year programme in engineering. Yes.
I also join…I mean could have joined the M.Sc. programme
in Vivekananda College in Mathematics Department.
But then, one of our family friends from my maternal side,
one Professor K. N. Venkataraman, who was later
the Head of the Department of Statistics in Madras University.
He said, “IIT Madras Mathematics Department is rated
the best in South India, why don’t you join there?”
And then I joined, after I took the entrance exam,
they conducted an entrance exam, it was
Okay.
locally done at that time, unlike the JAM and other exam.
Which year it was sir?
I think it was in the year 1969.
’69, okay.
’69. I did M.Sc. here during ’69-‘71.
’71, okay.
Prof. Subrahmanyam: So, at that time Professor Nigam was the Head of the Department. Prof. Vetrivel: Okay.
Professor S. K. Srinivasan was another Professor, the…
but there were no more Professors in the department,
we had a…a young Assistant Professor by the name Dr. K. M. Das,
Prof. Vetrivel: Das, yes sir.
who was a student of Zeev Nehari from the Carnegie Institute of Technology,
and then we had other Assistant Professors like Dr. K. R. Parthasarathy,
well known graph theoretician,
Dr. R Subramaniam who was into operations research.
Prof. Vetrivel: Yes sir.
Then Dr. K. N….U. N. Srivastava who was at that time, an Associate Lecturer
or Lecturer or something, and they had at that time,
when I joined, revised the syllabi.
Prof. Subrahmanyam: So, every semester we used to have 4 subjects. Prof. Vetrivel: Okay.
The lectures were from 8 to 12 in the morning,
Prof. Subrahmanyam: and after 12, after our lunch in the hostel, Prof. Vetrivel: Okay.
We are…we were let free to spend the rest of the day in the library.
Prof. Vetrivel: Library, okay.
Working out problems, looking up books and so on.
Prof. Vetrivel: Okay, okay.
So, at that time the syllabi were equipoise between
pure mathematics and applied mathematics.
So in the first semester we had real analysis, complex analysis,
Prof. Subrahmanyam: then tensor analysis and then linear algebra. Prof. Vetrivel: Okay.
In the second semester, one Dr. Jyoti Chaudhuri at that time,
Prof. Vetrivel: Okay, we don’t know.
subsequently she was…she became Jyoti Das.
Prof. Subrahmanyam: She was a student of Titchmarsh? Prof. Vetrivel: Okay.
And then she worked in differential equation,
but then later on she moved to University of Calcutta.
I also met her couple of years back.
She was teaching…she taught us differential equation,
ordinary differential equations.
Prof. Vetrivel: Okay.
So in the second semester we had ordinary differential equations,
then measure theory, algebraic structures and
Prof. Subrahmanyam: then Hamiltonian mechanics. Prof. Vetrivel: Okay.
Prof. Subrahmanyam: So we had the book by Goldstein, Prof. Vetrivel: Yeah.
which used to be rated very highly by physicists
and others, and in the third semester we had topology,
Prof. Subrahmanyam: then continuum mechanics. Prof. Vetrivel: Yeah okay.
And then…continuum mechanics,
Prof. Subrahmanyam: partial differential equations, Prof. Vetrivel: Okay.
Prof. Subrahmanyam: and numerical analysis. Prof. Vetrivel: Okay.
And in the fourth semester, fluid mechanics,
Prof. Subrahmanyam: then one elective we…I was again guided by Professor… Prof. Vetrivel: Professor Das.
Professor Venkataraman of Madras University, he said, “Take stochastic processes.”
And then I took stochastic processes and then electromagnetic theory.
Prof. Subrahmanyam: And then functional analysis. Prof. Vetrivel: Okay.
So, at that time, the teachers; most of them were
not specialists in pure mathematics
like the topics in topology, functional analysis, algebra et cetera.
Most of them were Applied Mathematicians.
Like fluid mechanics, operations research and so on.
But they read on their own and then delivered the goods
so and the process was a little difficult
for both the teacher and the student, nevertheless,
they rose up to the occasion,
we also hopefully did justice by satisfying their tough questions
Prof. Subrahmanyam: In the exams and so on. Prof. Vetri: Examination.
About the stochastic process,
Professor Srinivasan who was deemed an authority on applied
Prof. Vetrivel: Stochastic. Prof. Subrahmanyam: stochastic processes and probability theory,
originally did not want to give that course.
Prof. Subrahmanyam: Although, many research scholars were eager to take that course. Prof. Vetrivel: Okay.
And then, I went and represented to him, because there are only 3 students
Prof. Subrahmanyam: who would opt for stochastic. Prof. Vetri: Stochastic processes.
Prof. Subrahmanyam: So he agreed and they gave that course. Prof. Vetrivel: Okay okay.
See at that time, the department approach was different.
So, they used to set up…set a question paper
Prof. Subrahmanyam: and it was all absolute grading, you have to get 50 marks Prof. Vetrivel: Oh.
Prof. Subrahmanyam: to pass the course. Prof. Vetrivel: Ok.
Otherwise, you will be finished,
Prof. Subrahmanyam: you will have to repeat the course. Prof. Vetrivel: Okay.
I mean, you have to rewrite the course,
if you fail in that you will have to repeat the course.
Repeat.
It was so tough. And then, there were a number of elective subjects
offered in the fourth semester, including graph theory,
topological dynamics, a specialization of Professor Das, and so on.
Here, I must mention about the method of teaching
or lecturing in the department at that time.
See, there was no…what should I say…we don’t…
we didn’t expect the kind of teaching we were exposed to in the colleges.
There, the approach was different.
They used to describe a theorem and go on working out riders and problems,
a number of problems to illustrate the point.
Here, we were all bombarded with concepts and so many theorems.
You imagine, the whole of Bartle, real analysis
Prof. Subrahmanyam: was covered in one semester. Prof. Vetrivel: Okay.
Plus, Fourier series from Rudin’s Principles
Prof. Subrahmanyam: of Mathematical Analysis. Prof. Vetrivel: Mathematical Analysis.
It was really tough, and we do not know how we could
understand the intricacies of various proofs.
Because, they were all classical theorems
proved by eminent mathematicians like Heine, Borel , Cantor and so on.
Anyway, we have managed to survive,
that is what I would put it, and the teachers,
they used to refer to several books.
So, for…for instance, let Professor K. R. Parthasarathy,
when he taught measure theory,
Prof. Subrahmanyam: he initially started with Berberian, then from Halmos. Prof. Vetrivel: Halmos.
Then from Taylor, then from Kingman and so on,
it was really very difficult for us to cope with the development of the subject
because their notations, their approaches were all different anyway,
that's how probably that is the reason why we were asked
to spend the rest of the day in the library.
In the library okay, okay. And I…I am sure, I mean you have a great memories and…
So it was an…I mean unforgettable programme in my life.
Okay, okay, okay.
Because I…I…as I told you, I am not really a mathematically oriented person.
Okay, okay.
And in order to understand the abstract ideas of topology and all that,
Prof. Subrahmanyam: I had to work throughout the day after my lunch. Prof. Vetrivel: Okay.
In my own way, and I avoided going to various…
yeah, I mean I didn’t go…go for entertainments,
say, films and all that, of course,
Prof. Vetrivel: So it was a drastic difference from the B.Sc. time to. Prof. Subrahmanyam: Yeah, B.Sc. to
Prof. Vetrivel: M.Sc. Prof. Subrahmanyam: M.Sc. was. Prof. Vetrivel: Okay, okay.
Total…I mean it’s a kind of cataclysmic change, I should say.
I see, okay, okay. How about now nowadays for our
M.Sc. programme, we have a project at the fourth year…
at the second year, fourth semester.
No, at that time what happened was,
every semester, we had to appear for a viva voce.
Viva voce, oh okay.
And, they used to ask questions from all the topics we had studied.
It was really nightmarish, so…so to say.
Okay, okay.
But fortunately, the teachers were also considerate,
they understood our limitations,
and didn’t inflict the pain which was more…
Prof. Subrahmanyam: more unbearable than we could take. Prof. Vetrivel: Okay.
So, after your M.Sc., in 1971 you…
Yeah, what I did was, I thought this type of mathematics
which I got exposed to, was
too much for me, and I thought of going for other places to do Ph.D. and so on.
I was selected for an M.Phil. programme in Madurai University.
I didn’t want to go for M.Phil.,
at that time, Matscience which…which was a
a neighbouring institute, they were entertaining Ph.D. students.
So, nearly 12 of us, not all from IIT,
from various places joined.
Unfortunately, the Matscience was funded on a
quarterly basis by the state government
and the Department of Atomic Energy.
So, they didn’t expect the…
they were expecting a huge chunk of funds,
which unfortunately didn’t materialize.
So, most of us except one girl in pure mathematics,
Prof. Vetrivel: They got in.
they were all…I mean turned down.
We had to go…and unfortunately,
that was the end of August, and in no other place you would be…
they would be calling for application and so on.
For Ph.D. position and so…
anyway, I was studying at home for some time.
And then, in the meanwhile, I used to…
I cultivated some people in the Ramanujan Institute
which was the University of Madras, Mathematics Department
and I used to discuss with some people
and, even while at Matscience,
I had got some ideas about fixed point theorems I developed,
and in the December of ‘71,
I…’72 I should say,
I presented a paper in the Indian Mathematical Society Conference at Bhopal.
Prof. Vetrivel: Bhopal, okay.
And then, I…there I came into contact with
the well-known probabilist Professor K. R. Parthasarathy,
who was at that time in University of Bombay.
Prof. Vetrivel: Oh okay.
So he asked me to come to Bombay and join him,
but then, it was the time of Telangana agitation and so on.
I had narrowly escaped being stranded in the
Bhopal station while travelling to
To Chennai.
Chennai…and then somehow came back,
and meanwhile, after encouraging me to apply
to University of Bombay and all that,
Professor K. R. Parthasarathy had moved to IIT Delhi.
IIT Delhi.
So I looked at all these things,
I thought my alma mater should be the better place and I applied here.
Prof. Vetrivel: Your IIT Madras. Prof. Subrahmanyam: And I was entertained here.
At that time also,
it was not cakewalk…there were many
Prof. Vetrivel: Many candidates. Prof. Subrahmanyam: Competitors, there we had to be interviewed, and I was selected.
Okay.
Though I was not placed in the top rank,
I got the 4th rank or 5th rank, something like that.
Kesavan was also selected at that time.
Oh, okay.
He was 2 years junior to me in…
Okay.
IIT Madras.
Okay, okay and…
And then, I…I was assigned Professor U. Subb…V. Subbarao,
who wanted me to work in numerical analysis
Prof. Vetrivel: Yeah.
and so on. But he gave me a book to present lectures from,
that was a nice book by Ortega and Rheinboldt
on non-linear equations and iterative methods or something like that.
Other members in the group were one
Dr. Jain who then left for IIT Delhi, numerical analysis man,
Dr. R. P. Agarwal who was a post-doc at that time,
He later on moved to Italy,
from there he moved to…
Prof. Vetrivel: UK.
US.
Prof. Vetrivel: Yeah.
He is active still.
So, we started discussing on these topics,
every alternate day, I used to present from that book.
It was going on for a couple of weeks,
then, the great strike took place here.
Prof. Vetrivel: I see. Prof. Subrahmanyam: The hostel staff and the
Prof. Vetrivel: Okay. Prof. Subrahmanyam: administrative staff had lot of grievances,
and every day they were shouting slogans,
and, one day it happened that they even broke the
water mains and water was stopped in the hostel until a crisis
blew over and we had to stop the classes, lectures.
Finally, it all…it was all sorted out.
So, in the meanwhile, I was discuss…considering
some more aspects of my own problem
and Subbarao was a nice gentleman.
He encouraged me to pursue my own line of
Prof. Vetrivel: Okay.
thinking and research, but all the time,
he was insisting on…look for applications.
I was also happy that I could get a paper
published in the Journal of Approximation Theory and so on.
At that time, the concept of Ph.D. courses was different.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: We had one or two courses from the department.
One was done by Professor Nigam,
it was from Stakgold’s book on Boundary Value Problems.
That was the…a monograph which discussed weak solutions,
Prof. Vetrivel: Okay. distributional solutions of differential equations.
Prof. Vetrivel: Okay.
And then another course; it was a specialized course
for M.Sc., which some teacher used to give.
Then we were also asked to do one course from a sister department.
Prof. Vetrivel: Okay.
So, they were even at that time thinking of interdisciplinarity.
So I took a course on singular perturbations from Aeronautics Department.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: One Professor Rajappa gave that course,
they were talking about Poincaré series and all that.
Somehow I also scraped through that course and
submitted my…my thesis in November ‘76
and then got the degree in ‘77.
’77, okay.
So…so with a couple of paper publications.
Prof. Vetrivel: Okay.
And then, at that time, the…the…the concept was either to go for
Prof. Vetrivel: Post-doctoral. Prof. Subrahmanyam: post-doctoral fellow or to seek a job.
I didn’t want to go for a post-doctoral fellow
because I feared that it might be a kind of a…a
postponing your career, and so on.
I…at that time, I also had an offer of a research associateship
or something like that from TIFR,
but I thought taking a lectureship was far better,
because you gain teaching experience,
everywhere they are asking for teaching experience.
At that time, in the Madras University and other places,
senior teachers in the colleges were encouraged to do Ph.D.,
so under that scheme, some lecturers were sent to IIT,
some to the Ramanujan Institute.
So there…there were leave vacancies as they were called.
So, I applied for that and then joined the Loyola College of
Prof. Vetrivel: Okay.
at Nungambakkam.
It was a very interesting experience,
I taught the undergraduate students, large classes,
I also taught the M.Sc. students functional analysis
Prof. Vetrivel: Okay.
from Sobolev and Lusternik.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: That was a different textbook. Prof. Vetrivel: Lusternik.
Different from…the Simmons, and
then, meanwhile, I had applied to various places,
I got selected in the Madras University postgraduate centre at Tiruchi.
Probably, I was the first person to have been
appointed to a Madras University Maths Department,
because, Madras University Maths Department
was considered a citadel of pure mathematics.
Prof. Vetrivel: Okay.
And then from there, I moved over to Hyderabad Central University,
which was expected to become…like become
a great centre for sciences, humanities and so on.
And you know, that university was created to appease the Telangana
agitationists and so on,
somehow it also didn’t…it…it had lot of problems in the beginning.
Prof. Subrahmanyam: So again I felt, my alma mater is the best place. Prof. Vetrivel: Correct, correct.
And so, so I applied and got back here.
Okay, which…which year you joined here?
I remember the date 21 5 1981.
Prof. Vetrivel: Okay, fine, fine, fine.
So I joined and then I taught B.Tech., M.Sc.
And, just want to ask you, when you joined…
so the dominating subjects were like…as you said,
fluid dynamics and stochastic process.
And of course, Professor B. V. Subbarao in numerical analysis…
how you found yourself in that community, like?
Prof. Subrahmanyam: You see. Prof. Vetrivel: If you are totally a pure mathematics person.
Although the research of the department was focused on two streams,
Prof. Vetrivel: Yes sir. Prof. Subrahmanyam: Mainly
Fluid.
Fluid mechanics and stochastic process,
Prof. Subrahmanyam: already Bhattacharya had joined the department. Prof. Vetrivel: Okay.
Prof. Subrahmanyam: He was a complex analyst, and already Professor Das was there. Prof. Vetrivel: Das okay, Das was there.
Though he was a concerned with differential equations,
he was handling the bulk of the pure subjects like
Prof. Vetrivel: Okay. Prof. Subrahmanyam: Topology, functional analysis and so on.
So, they had need for people to do
teaching at the M.Sc. level and so on,
so, I won’t say it was…yeah it was not a very,
what should I say, it was not a very nice situation.
You…you see in the department,
the…you were all left to…I mean people were left to themselves.
Prof. Vetrivel: Yeah independence, independence. Prof. Subrahmanyam: You evolve on your own
Prof. Vetrivel: Yeah, that independence. Prof. Subrahmanyam: and they don’t interfere and they gave you lot of freedom.
I…I could I in fact,
I mean formulated two courses which were accepted.
Okay.
And, it was an elective on fixed point theory, probably
Prof. Subrahmanyam: that was the first course on fixed point theory which must have been Prof. Vetrivel: Yes sir, still continuing.
Prof. Vetrivel: Still continuing. Prof. Subrahmanyam: formulated in the M.Sc. syllabus anywhere in India.
Correct.
So we had formulated and when I joined, already
graph theory was being taught,
already probability theory was being taught as a core course.
Prof. Vetrivel: Okay, so many subjects were there. Prof. Subrahmanyam: So, some such
developments have taken place and I was, I mean
nobody stood in the way of my proposing other courses
in non-linear analysis and so on.
Already, Professor Subbarao has given a course on approximation theory.
So the concept at that time was, you do pure mathematics
so that the develo…it could help the development
in applied mathematics, fluid mechanics,
Prof. Vetrivel: Correct. Prof. Subrahmanyam: stochastics and so on.
In fact, I remember, Professor S. K. Srinivasan had invited Professor Athreya
an expert in probability and stochastic process for…as a visiting professor;
so that they could interact, and so on.
So, it I mean it was not as if the department
was only pursuing applied mathematics in an exclusive way,
they were open to suggestions and you know, developments.
But, there the initial period, the developments
were in fluid mechanics and
Prof. Vetrivel: Okay. Prof. Subrahmanyam: stochastic process.
How was the selection procedure, sir, those times?
Now we…you know that
since you were head of the department in the recent times,
our selection procedure is like one interview,
one presentation, then oral interview…all that.
So that…
Prof. Subrahmanyam: For the faculty or the student? Prof. Vetrivel: For a faculty…faculty.
No no it had by then, become stabilized, I should say.
Prof. Vetrivel: Okay, okay.
Because when I joined,
Prof. Subrahmanyam: I was asked to give a presentation for Prof. Vetrivel: Presentation.
10 or 15 minutes on my research topic.
Prof. Vetrivel: Okay. And then, I was interviewed in the Director’s Office.
The same…same procedure.
So, same procedure.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: And, probably later on
they have added the faculty giving marks this and that,
maybe at that time also it was there,
but I didn’t know, because I was not a faculty member at that time.
Prof. Vetrivel: Okay.
I was giving the presentation and all the…all were sitting in that presentation.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: All the faculty members, and maybe even other participants
other interview…persons who had
been invited for the interview.
Okay, okay. And regarding…I have heard of your…
after you joined here, I have heard of your
your conference, what you organized in the department,
which is a mega conference, I would say…
Prof. Vetrivel: on non-linear analysis, on analysis…non-linear analysis. Prof. Subrahmanyam: Yeah.
So, you see, my thinking was that,
already there was interview…the…there was interaction with
Matscience, especially Professor Vasudevan,
Professor Ranganathan and others
were interacting with Professor Srinivasan and so on.
There was also a cosmologist
at that time, by name Prasanna and so on.
So on the applied mathematics side, there was interaction.
So, analysis side, I thought I would initiate some symposium
Prof. Subrahmanyam: and Professor Unni at that time, a professor in the Matscience. Prof. Vetrivel: K. R. Unni, K. R. Unni.
He…I invited him, gave a talk and the venue was in one of the
Prof. Subrahmanyam: seminar halls of the Chemistry Lecture Theatre. Prof. Vetrivel: Okay, okay.
Prof. Subrahmanyam: I think it was in ‘83 or ‘84 Prof. Vetrivel: 4…’84.
And the proceedings were published in our journal,
at that time the department was running a journal:
Prof. Vetrivel: Journal of Mathematical Physical Sciences, yes sir. Prof. Subrahmanyam: The Journal of Mathematical and Physical Sciences.
It had a very illustrious editorial board.
Prof. Vetrivel: Okay.
Professor Lakshmikantham, Kichenassamy…many others.
Somehow, it has faded over the years.
Okay. And…I just want to know about your Ph.D. guidance, sir.
Like, your students.
One paper…you…you one of your students Dr. Chitra,
when you have done something on
a non-linear complementarity problem,
but I don’t see many papers on this direction,
though linear complementarity problem has
been well studied in the last 4-5 decades.
But this something…still people are referring whoever works on this.
I have seen this…and also your recent work with your…
your later students…like on functional equations.
See, I was specializing in fixed point theorems;
fixed point theory, you cannot say is a branch…
I mean, it is an independent branch of mathematics,
Prof. Subrahmanyam: in…in the sense that it has…it borrows techniques and tools from Prof. Vetrivel: Tools, yes.
several areas of mathematics.
So, since its applications are vast,
I naturally took interest in functional equations and optimization.
One part of optimization theory heavily
relies on fixed point theorems of the Kakutani type,
Brouwer’s fixed point theory theorem and so on.
So in that sense I entered
a non-linear complementarity problem.
In fact, what I feel is, the department should offer a…a course,
core course on optimization which is an important
Prof. Vetrivel: Yes sir, yes sir.
subject.
Now it is being considered,
Prof. Vetrivel: now we have even proposed that. Prof. Subrahmanyam: I think this is a must.
Prof. Vetrivel: Yes. Prof. Subrahmanyam: And you have to also look at the current trends
and accordingly reorient the syllabi.
In fact, Professor Subbarao conducted a seminar,
involving all the other departments, asking them to present
their views on mathematics and application,
if you have such a seminar, then.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: There will be brainstorming
and new ideas may emerge,
and also you should look at the trends in top universities of the world,
for example: Oxford, Cambridge,
they are thinking of mathematical engineering…
Stanford for example, is thinking of mathematical
engineering course and so on.
So, there are also courses on mathematics education.
See, IIT is a premier institute and mathematics education programme
helps people learn how to teach mathematics
even at the school level and so on.
Now our country is facing a dearth of good teachers,
even at the school level.
So, if we can think of such a programme, it will help
our basic education in the country,
Prof. Vetrivel: Okay. Prof. Subrahmanyam: in the long run.
Prof. Subrahmanyam: So, your collegium of Professors should think along these lines Prof. Vetrivel: Sure, sure.
and come up with such novel ideas.
Of course, we have a nice programme on
Prof. Subrahmanyam: industrial mathematics. Prof. Vetrivel: Mathematics sciences, yeah.
But then the syllabi have to be revised
and see the…get the feedback of the students and reorient and so on.
Prof. Vetrivel: Okay.
If I…whole thing depends on the initiative of the faculty members and so on.
See, I would also like to add that
I had conducted a number of conferences,
when I joined in ’81, Professor Das himself organized
a big international conference on non-linear analysis,
Prof. Subrahmanyam: for which eminent mathematicians like [indistinct], Ambrosetti had come. Prof. Vetrivel: Ambrosetti, yes.
And then I organized a national symposium on analysis.
Subsequently in 2007 or so, I organized…2005
I think, I don’t remember, I organized a conference on
Prof. Vetrivel: Optimization [indistinct]
FIA…FIM IIT conference.
Prof. Vetrivel: Yes sir. Prof. Subrahmanyam: Then I tried to have a collaborative conference
with University of Madras on fuzzy sets.
So I tried to involve other departments, other institutions also.
In fact, when some Professors like Avudainayagam
others were heading the department,
I told them that I would like to have a one day workshop
on calculus for our school teachers.
And it was readily agreed, and
when I was the Executive Chairman of Association
of Mathematics Teachers in India, I conducted it here.
Prof. Vetrivel: Okay, okay.
So, such programmes you have to do and
already IIT has given you great
opportunity to organize teacher training programmes.
I organized 3 teacher training programmes:
one on non non-linear analysis, another on fuzzy sets
and another on Fourier analysis.
Prof. Subrahmanyam: I think you were also associated with Fourier analysis. Prof. Vetrivel: Yes sir, yes sir, yes sir, yes.
So these are all important
Prof. Vetrivel: Yes sir.
aspects. And see, mathematics being a very tough subject,
often repulsive for the student,
you should encourage all kinds of students to take to mathematics,
and you should not have very harshly evaluate students
Prof. Subrahmanyam: and allow them to grow Prof. Vetrivel: Okay.
in their own way,
so that their interest and enthusiasm for mathematics is not stifled.
See, what is more important now is
that people should have a liking for mathematics,
they should not abhor mathematics.
So, that being the approach, you should be able to attract
many students at several levels.
Several…I understand, sir.
Sir, and one…one I just ask you one difficult question, sir,
like, you have served in IIT Madras for more than 35-36 years,
and in that if you divide the whole service period into three parts,
which you are…how do you compare your…the growth of the department
and your experience, for example, 12 years, 12 years, the next 12 years.
How do you compare?
See, when I joined as a research scholar,
at that…at that time we had a a big conference,
national conference, they called it ISTAM, Indian Society for
Prof. Subrahmanyam: Theoretical and Applied Mechanics it was huge conference. Prof. Vetrivel: Theoretical and Applied Mechanics,
Yes, sir.
Prof. Subrahmanyam: A kind of Kumbha Mela type conference. Prof. Vetrivel: Yes, yes, yes.
So, we were all asked to bring the…we were all asked to
volunteer; get the delegates from the railway station, airport and so on.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: So we are trained that way.
Prof. Vetrivel: Okay.
So, that kind of thing, whether it is being done,
and we enjoyed it actually, we didn’t resent such responsibilities,
and at that time, the Head of the Department was powerful.
And, I mean over the years, the…due to the
the trickling of democratization process,
people have become more demanding at the lower level,
and you have to take everybody together,
Prof. Subrahmanyam: otherwise growth will not be possible. Prof. Vetrivel: Correct, correct.
So, you cannot do it in a very a brusque way and put down opposition.
If it is a good suggestion, you have to take it. And a
lot of…I mean…afterwards, what…what should I say,
I mean the first 12 years, the
domination of the Head of the Department,
Professors was more, and then the power was
trickling down and so on, but at the…at no stage,
I mean, you were blocked to
Prof. Vetrivel: For anything. Yeah, so Prof. Subrahmanyam: pursue your research.
That independence is something.
Prof. Subrahmanyam: Yes, yes. See, you were not, Prof. Vetrivel: Yeah.
Prof. Subrahmanyam: I mean troubled to do this type of research or that type. Prof. Vetrivel: Correct, correct.
There were suggestions, because
IIT being an institute of technology,
it is natural to expect that what you do
has some relevance for engineering and technology; nothing wrong in that,
but they never imposed such views, only… I mean implicit…
I mean…only made indirect suggestions.
Prof. Vetrivel: Fine.
Which will act, in due course, in your subconscious.
Actually, I…Professor Subbarao
was asking me to concentrate on numerical method.
Now, I mean my…one of the…my latest students Vijaya,
she was working on Newton methods.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: It was a very…
it was in the heart of numerical method, so to say.
So, that suggestion was in my subconscious
for quite some time, and it bloomed.
Okay, fine.
So, it’s a good suggestion, I should say.
Sir, and myself and my other colleagues,
we really enjoyed your headship time, that period…
what is your experience about
Well…
that period especially? I should say it was not a…
What are the new things you brought…something?
Okay, at that time, I also had to head the IIT Hyderabad…
As a mentor.
Prof. Subrahmanyam: Mathematics Department. Prof. Vetrivel: Yes, yes.
I was not living in the campus,
Prof. Vetrivel: Okay. Prof. Subrahmanyam: which would have been convenient,
but due to personal problems, I had to stay outside the campus.
So I had to avoid going outside Chennai too many times.
So what I did was, thanks to our studio,
I arranged lot of seminars for those students.
Prof. Vetrivel: Okay.
In fact, when Pro…Dr. Sivakumar from Texas
A&M University gave a course here,
Prof. Subrahmanyam: I had it telecast over there. Prof. Vetrivel: Yeah, yeah, telecasted there yes, yes.
They attended those courses and they also
Prof. Vetrivel: Okay.
I mean, took the exam.
Prof. Vetrivel: Okay, okay exam was… Prof. Subrahmanyam: When the exam was going on here simultaneously
it was conducted there, and they enjoyed it,
lot of mathematicians who were in the city
were invited to give lectures; not only here, and the lecture
Prof. Subrahmanyam: was immediately telecast there. Prof. Vetrivel: Telecasted there.
So all these things were the…done and
see, we have to take uh suggestions from all the colleagues,
whether he is a junior colleague or a senior colleague.
See that the mathematics is promoted
in the best possible way. And regarding students,
You see, you cannot experiment with the undergraduate students.
That is my thinking. You see, if somebody is
teaching a particular topic, let us say probability
and statistics in the best possible way,
do not unnecessarily disturb that arrangement and
put a raw hand to do that course
Prof. Subrahmanyam: and make a miserable situation of a nice…nicely going programme. Prof. Vetrivel: Correct.
Of course, people also have to be trained.
So, how to do that?
So, what I did was, I associated with each teacher,
a senior teacher who has taught the
subject several times, a young faculty
Prof. Vetrivel: Faculty. Prof. Subrahmanyam: who has not taught it.
So that he gains confidence, and there is interaction,
so that subsequently he can take over.
But, I am not sure whether that worked out all that…
because it was becoming like this; you split the course into two halves,
Prof. Vetrivel: Okay.
the easier half was given to the raw faculty,
Prof. Subrahmanyam: while the tougher one was. Prof. Vetrivel: Tougher one.
taken care of by the more experienced faculty.
But unfortunately, people thought half plus half plus half is more than 2,
and this kind of problem led naturally to the
collapse of the programme.
So that experiment didn’t succeed.
Okay. Sir, and one more thing
I just wanted to ask you…you…you
you were the last person who used to consider something like
the classical analysis like summability theory
and all the…used to refer the books of Blumenthal and all that,
now nobody is using or talking about those topics.
See, like every subject, mathematics also has its fashions and so on.
Prof. Vetrivel: Fine, fine.
So, if people are interested in such topics,
Prof. Vetrivel: Welcome.
there must be journals to publish,
if there are no journals, what to do?
In my time, it all clicked,
now I cannot say that you study distance geometry or some other topic.
Prof. Vetrivel: Correct. Prof. Subrahmanyam: Of course, you can pursue it as a…a passion and so on,
but we cannot inflict it on others.
Prof. Vetrivel: Okay.
who are especially
Prof. Vetrivel: Correct. Prof. Subrahmanyam: growing up in a career and all that.
Prof. Vetrivel: Okay.
So, it all changes.
See, nowadays, even departments like…I mean institutes like Oxford,
they are thinking of industrial mathematics, mathematical engineering
Prof. Vetrivel: Correct. Prof. Subrahmanyam: and things like that,
they are thinking of a programme in which actuarial mathematics,
a bit of statistics; all these things are clubbed together…data analytics,
all those things.
So, you have to be alive to the changes
in the academic world and also, I mean
train our students accordingly.
After all, globalization cannot be wished away now.
So, you have to train the students not only for the local consumption,
but also for the global requirement.
So, it’s a tough problem,
I don’t think the problems have become easy now,
it…they have become more complex.
Thank God that I have come out of it.
Prof. Vetrivel: Okay.
And you are facing all these complicated things.
Prof. C. S. Swamy: I have one question to both of you,
Prof. Swamy: you mentioned about the journal
Prof. Swamy: which was started by the Mathematics Department,
Prof. Swamy: is it continuing now?
It is with Aerospace Department,
Prof. Vetrivel: it went to Aerospace Department. Prof. Swamy: Pardon.
It is…went to Aerospace Department.
Prof. Swamy: Oh that journal is there
Yeah, yeah, yeah.
Prof. Swamy: I see.
Now, there is a committee which is managing that…
Prof. Vetrivel: not regular…like what used to be. Prof. Swamy: I know that Professor Subramaniam
Prof. Swamy: of Aeronautics. Prof. Vetrivel: Yes, yes and Swaminathan was
Prof. Subrahmanyam: Yeah that… Prof. Swamy: I see. Now Subramaniam
Prof. Subrahmanyam: Yes, yes, yeah…that was Prof. Vetrivel: Oh DS.
Prof. Subrahmanyam: 20 years back or something like that. Prof. Swamy: Yeah, yeah.
Yes, yes.
Prof. Swamy: Now the…is the journal still coming?
It’s not…yeah it is still there,
Prof. Vetrivel: but not on the regular issues. Prof. Subrahmanyam: Sir
Prof. Swamy: Mathematics [indistinct]. Prof. Subrahmanyam: No no, we do…I do not know because
I am no longer associated.
Prof. Swamy: I know, you know, I am asking
Yes, yes sir, it is…the journal is still there.
But not the regular issues, like in
the number of issues per year is reduced.
Prof. Swamy: I see.
Prof. Vetrivel: And, it is managed by the Engineering Departments. yes. Prof. Swamy: Committee, committee.
There is a committee managing that.
Prof. Swamy: Another thing is, since you have joined very early,
Prof. Swamy: you know, in the initial stages
Prof. Swamy: when those who were working in differential equation all that,
Prof. Swamy: they used to say they had to manage all the calculations.
Facet machines.
Prof. Swamy: Facet calculator,
Prof. Swamy: do you have any facet calculators in your department?
No, we don’t have, you know…
Prof. Swamy: Can you find out? Because,
Prof. Vetrivel: Yes, yes. Prof. Swamy: We wanted this as…its being a Heritage Centre.
Prof. Vetrivel: Heritage Centre okay, okay, okay. Prof. Swamy: We want to have
Prof. Swamy: one model of facet calculator. Prof. Vetrivel: Okay.
Prof. Swamy: We have asked various departments.
I…I don’t think
Prof. Swamy: Engineering Department also we have to use this. Pof. Vetrivel: even in your period also there was no such.
Prof. Swamy: before the computers came in, you know.
In fact, for our numerical analysis course,
Prof. Swamy: Yeah.
We were use…we were taught how to use a slide rule
Prof. Swamy: Okay, okay Prof. Subrahmanyam: and, also a facet
Prof. Subrahmanyam: calculator yes. Prof. Swamy: Facet calculator.
Prof. Swamy: Slide rule, maybe somebody might be having,
Prof. Swamy: but facet calculator is what we were interested in.
I am told that the facet calculator company itself
Prof. Subrahmanyam: modified it into a typewriter. Prof. Swamy: I know, I know. That is the reason
Prof. Swamy: why we are looking for Prof. Vetrivel: That one, okay.
Prof. Swamy: looking for any model
Prof. Swamy: somewhere in. Prof. Vetrivel: Oh, that okay, for Heritage Centre.
Even in my tenure here,
maybe even by early ‘90s,
the machine was completely…
Prof. Swamy: Yeah, I know. Prof. Subrahmanyam: I mean it was not there in the department,
they must have condemned it;
Prof. Subrahmanyam: you have a condemnation committee in the department. Prof. Swamy: Yeah, yeah, yeah.
So it is all gone.
Prof. Swamy: Another thing you said that,
Prof. Swamy: you worked or you applied for the Institute of
Prof. Swamy: Advanced Mathematics, Madras University.
Ramanujan Institute, no no, I used to interact.
Prof. Swamy: Who was the Director then?
At that time,
Prof. Swamy: Bhanumurthy?
Prof. Subrahmanyam: Yeah, Bhanumurthy was the Director. Prof. Swamy: Okay, now, Bhanumurthy’s brother is working
Prof. Subrahmanyam: Yeah, he was in Shankara, Dr. Shankara. Prof. Swamy: Shankara.
Prof. Swamy: Okay, how many years did he serve here?
I think he was…I should say, when I joined, he was there
when I was a research scholar.
Prof. Swamy: I see.
So…
Prof. Swamy: What was…what was his field?
He was doing relativity.
Prof. Swamy: I see…I see. And of course, later he took science and all that Prof. Subrahmanyam: Yeah, right.
Prof. Swamy: Yeah I know about that one.
Prof. Swamy: So…and, another thing I wanted to ask.
In 5 minutes.
Prof. Swamy: You wrote
Prof. Swamy: an article or something about Subbarao in… Prof. Vetrivel: 5 minutes
Prof. Swamy: that actor is demised.
Yeah, yeah I mailed.
Prof. Swamy: Yeah, the…I saw it in our retirees…[indistinct]
Mail.
Prof. Swamy: So, you please… Prof. Subrahmanyam: Yeah.
No, if you want, I can show…
I had collected some photographs.
Prof. Swamy: Yeah, it looked very interesting.
So, I conducted…see, the on the…I mean
I am not trying to advertise myself.
Prof. Swamy: No, no, no. Prof. Subrahmanyam: I wanted to give some aspects of our activity.
So…as I told, I was interested in organizing many
conferences, workshops and so on.
Prof. Swamy: Definitely.
So, I organized an analysis worksh…I mean…con…
symposium on the teaching of analysis, because
it should be interesting not only for students,
but also for teachers who may not be
analysts themselves, but may be teaching.
So I invited people from Ramanujan Institute,
Matscience and they all gave the
Prof. Swamy: Professor.
talks, and I even brought out the proceedings,
and I had got some snaps.
Prof. Subrahmanyam: So these are the…some snaps.
Prof. Swamy: Oh wonderful.
Some our…our…we have…
I organized a symposium,
Prof. Vetrivel: Yeah. Prof. Subrahmanyam: on teaching of analysis.
I had even brought out the
Off screen voice: Dates on…[indistinct]
I think it was the time when Avudainayagam
was the Head of the Department.
I think…it should have been around 2006,
7 or 8 or something like that.
So you also have a photograph of Professor Nigam,
Parthasarthy and others.
Prof. Swamy: Yeah, yeah that also [indistinct].
So that's how I…maybe you can keep them.
Prof. Swamy: Oh oh, thank you.
And, these are the books.
See…for the QAP short term,
(softly) I don’t know it’s some…
This was in the year,
I think it was in 1997.
Prof. Swamy: Yeah.
So, we conducted a short term course.
Prof. Vetrivel: (reads) Non-linear.
Prof. Swamy: [Indistinct]
This is the collaborative conference.
Prof. Subrahmanyam: Inter-departmental, I collaborated with
Prof. Subrahmanyam: Dr. Mohan of Civil Engineering on fuzzy sets.
Prof. Subrahmanyam: Along with Madras University.
Prof. Vetrivel: Okay.
Ande this is the first mathematical symposium
which was brought out by…our…that journal.
Prof. Vetrivel: [Indistinct]
Yeah, 1984.
Prof. Vetrivel: Yeah, this is what you were talking about.
Prof. Subrahmanyam: And then this was about 2008 something.
Prof. Subrahmanyam: I organized the Ramanujan Mathematical Society,
Prof. Subrahmanyam: I mean Ramanujan Day celebrations were already going on.
Prof. Subrahmanyam: So, we brought out the lectures
as a booklet after referring and so on.
Prof. Swamy: I want to ask one more
This is an international conference
Prof. Swamy: Yeah.
held in IIT Madras with the forum
Prof. Subrahmanyam: for inter-disciplinary mathematics Prof. Vetrivel: Yeah.
at Stella Maris College.
Prof. Vetrivel: Okay. Sir, I wanted to… Prof. Swamy: I wanted to know whether the Nobel laureate
Prof. Swamy: Professor Chandrasekhar; astrophysicist have visited your department?
Yes yes.
Prof. Swamy: Here visited.
Prof. Swamy: When was it?
‘87.
Prof. Swamy: Do you have photographs of that?
We have to ask Professor Majhi.
Prof. Swamy: Oh Majhi, is it?
Yeah, yeah, Majhi must be having…
Prof. Swamy: Oh, we will find out.
He was the organizer.
No, no we had the centenary celebrations
Prof. Subrahmanyam: of Srinivasa Ramanujan. Prof. Vetrivel: Srinivasa Ramanujan.
Prof. Vetrivel: So, he visited at that time. Prof. Swamy: Yeah. Prof. Subrahmanyam: So at that time he had come.
Prof. Swamy: Professor Chandrasekhar.
Prof. Vetrivel: Yes, yes. Prof. Subrahmanyam: Chandrasekhar had come and given a talk in the
Prof. Vetrivel: In the CLT.
auditorium of Madras University,
I do not know whether he had come here.
Prof. Vetrivel: He had come here. Prof. Subrahmanyam: Many eminent mathematicians had come.
Prof. Swamy: I was told he came only to Mathematics Department.
Prof. Vetrivel: Yes yes. Prof. Swamy: He
Prof. Swamy: didn’t gave any lecture in CLT.
Yeah.
Prof. Swamy: And, much…very much like before
Prof. Swamy: became, got a Nobel Prize, I had heard in AC College, that was in ‘60s. Prof. Vetrivel: Okay, correct.
Prof. Swamy: So, he never visited.
Prof. Swamy: So, I came to know that he used to visit Mathematics Department,
Prof. Swamy: that's why I asked you.
Prof. Swamy: And, another thing I want to know was
Prof. Swamy: number of monographs were produced from
Prof. Swamy: your department, say published by
Different.
famous…the German publishers [indistinct]
Springer.
Yes sir.
Prof. Swamy: Do you have copies of that?
Yes sir, every faculty they have copies
Prof. Swamy: So, if anything,
Yes sir.
Prof. Swamy: before it is lost,
Yes, yes.
Prof. Swamy: So we very much wish that you send it to the Heritage Centre
Prof. Vetrivel: Sure, sure, sure, sure, I will. Prof. Swamy: We would like to preserve it.
Okay, yeah.
Prof. Swamy: Okay?
Sure sure.
Prof. Swamy: Thank you very much. Prof. Vetrivel: Yeah.
Prof. Swamy: [Indistinct] So, you can carry on.
I just…finally, I end this with a couple of questions that I wanted to ask.
What is your interaction with this forum
that is interdisciplinary Forum for…you are active still I think
you are still active, you are
Prof. Vetrivel: you were a President of that society? Prof. Subrahmanyam: Yeah, I was president for two terms.
Okay.
See, Forum for Interdisciplinary Mathematics is a…
an organization which is registered at Delhi,
it was started by a couple of Delhi University Professors.
And, many eminent mathematicians
had been associated with it,
including the great statistician Professor C. R. Rao.
In fact, some IIT Directors had also been Presidents,
especially in Electrical Engineering, I don’t remember.
We have recently started a series;
Springer FIM Series for promoting publications
approved by Forum for Interdisciplinary Mathematics and so on.
So, 3 volumes have come.
In fact, one volume just arrived today at my home address,
because I am the chief editor.
Prof. Vetrivel: Okay. Prof. Subrahmanyam: They are sending copies to me.
Prof. Swamy: Okay.
So I just received a copy on game theory proceedings
conducted by one Dr. Lalita and somebody.
So, we have brought out about 4 monographs,
and 2 or 3 more are in the pipeline.
And, this forum is doing…promoting interdisciplinary mathematics;
it is concentrating on operations research,
graph theory, combinatorics, decision sciences and so on.
The only problem is mathematics has developed so vast,
any…any beginning student will be…I mean, will be puzzled
how to get into research level mathematics
in the least time, this is a big problem.
Because, methods are…so many methods have developed,
which method he has to concentrate on
so that the problem can be tackled and so on.
So, forming the right syllabi and
taking him to the research level in the shortest possible time,
these are all challenging problems.
I am told that in the US, it just takes 3 or 4 years
for a student to gain his Ph.D., but whether we can do it here,
so that that this Ph.D. student…thesis is of a decent level, these are all questions.
Of course, basic mathematical education
must be strengthened, otherwise you will not be able to attract people
for this subject which has become invasively persuasive.
Sir, and finally I just ask you one question:
You said you have lived very short period in the campus.
Yes.
What is your experience about IIT campus?
We, as faculty, we are enjoying the present B-type quarters all that.
Well, campus life was excellent, no doubt about it.
Prof. Vetrivel: Okay.
But I had built a house in the outskirts of the
city, and the tenants will not pay me the rent,
and there became a situation when I would lose the house itself.
So I had to frantically get out and stay there.
Another problem is, the campus…you have…the people here are prone
to…more prone to bronchial infections,
because of the pollen in the air and so on.
One of the Chief Medical Officers has told me that
the bronchial infection rate here is 100 percent more than in the city.
I think a couple of years or months back,
I saw some research from a Biotechnology Department
Professor saying that certain type of fungi
are present in the atmosphere due to trees or something like that,
I don’t…don’t remember the details.
So, my daughter developed wheezing problems and so on.
So, I thought that was another reason for me
to get out from the campus, and
so on. Campus life is excellent, no doubt about it because,
any time you can go to the department and work, and so on.
But of course, with the availability of laptop and so on,
it…it should not be a problem for…for a mathematician
to live outside and pursue his research.
So with this, I say I will…once again
I thank you for your visit here, sir.
And…I thank the organizer of Heritage Centre
for giving me this opportunity to interview Professor P. V. Subrahmanyam.
Thank you very much, sir.
Prof. Subrahmanyam: You’re welcome, and it’s my pleasure to have participated here. Prof. Vetrivel: Okay.
Thank you, sir.
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