PROF.S.MINAKSHISUNDARAM
A SKETCH
BY
PROF. A.SATYANARAYANA RAO WRITTEN IN 1968.
Subramiah Minakshisundaram was born on 12th. October 1913 in Trichur, Kerala State , of India. He studied in C.R.C.High School, Perambur, Madras State from 3rd Class to Sixth Form during 1919 to 1929 when he passed S.S.L.C. He had constantly Topped in Mathematics having shown a marked aptitude for it. Collegiate Education : Studied Intermediate in Pachiyappa's College, Madras from 1929 to 1931.
Higher Education : Studied B.A. Hons. Mathematics from Loyola College, Madras from 1931 to 1934 and secured First Class First. Got his M.A. Degree in Mathematics of the Madras University on payment of a token sum as was the custom in some universities in India those days.
Research Work after M.A. : His teachers were the well known Prof.K.Anand Rau and Prof. R. Vaidyanathaswamy . For a few years he worked under R.Vaidyanathaswamy. After studying the books " Mathoden der Mathematics Physik " of Prof. Richard Courant and Prof.Lichtenstein, then Prof.Razaiuddin Siddiqui author of Lectures on Quantum Mechanics and former Professor of Osmania University and who worked under Prof. Werner Heisenberg of Germany he published a few papers in Non-Linear Parabolic Equations. His thesis was entitled "Fourier Ansatz and Non- Linear Parabolic Equations ." Some of his papers were published in the Proceedings of the Indian Academy of Sciences while most of them appeared in the Journal of the Indian Mathematical Society . The thesis as a whole was published by the Madras University in their Journal. In the year 1940 he was awarded the D.Sc. in Mathematics of the Madras University , its distinguished alumnus, the much coveted degree of those days of a reputed university.
For some time he was Research Fellow , Department of Mathematics of the Madras University on a meagre sum. For a long time he was without any financial assistance and during that period he eked out his livelihood by private tuitions .
I heard Dr.P.K.Menon, Director , Joint Cipher Bureau, New Delhi mention that the active Mathematician of Madras that he was in those days and the name he made for himself in mathematical circles of Madras. He was and active member and was primarily responsible for organising a mainature Mathematics Club at Madras , of which Prof.C.T.Rajagopal, Prof.K.Chandrasekharan, Prof.K.G.Ramanathan and few others were active participants.
His work attracted the attention of stalwarts in the field of Partial Differential Equations at that time, one of them being Dr.Richard Courant , Professor Emeritus , Courant Institute of Mathematical Sciences, New York University. The report on his thesis was excellent and it was praised very much. His thesis was adjudged to be one of the best thesis for the year 1940 and awarded the Narsinga Rao Medal and also he was awarded the Ramanujam Medal.
Prof.Minakshisundaram could not secure a job in those difficult days in spite of his academic distinctions. Late Prof.Narsinga Rao promised him the job of a Tutor in Mathematics at the Annamalia University, Annamalainagar when he was the Head of the Department of Mathematics there. But in 1943 , when the Department of Mathematical Physics was started by the University at the initiative of late Dr. C.R.Reddy, an eminent educationist, and under the Headship of Prof.Nagendra Nath, Minakshisundaram was offered the post of Lecturer in the Department of Mathematical Physics by Dr.. C.R.Reddy who was very much impressed with his academic achievements.Thus he joined the Andhra University Department of Mathematical Physics as lecturer in the year 1943.
From 1943 to 1946 he worked as Lecturer in the Department of Mathematical Physics in the Andhra University. In 1946 he was invited by the Director , Dr.Aydelotte, to be a Member of the School of Mathematics of the Institute of Advanced Study, Princeton, New Jersey, USA. He was there from 1946 to 1948. Meanwhile the Andhra University Authorities promoted him to Readership in the Department of Mathematical Physics. He worked as Reader in the Department from 1946 to 1950.
Late Prof.A.Narsinga Rao was then Head of the Department of Mathematical Physics having come over from Annamalai University at the invitation of late Dr.C.R.Reddy, Vice Chancellor. In those days Andhra University could boast of having eminent Mathematicians of the country as members of its staff, namely: Prof.Vijayaraghavan, Head of the Departmentof Pure Mathematics, Prof.A.Narsinga Rao, Head of Mathematical Physics, Dr.V.Ramaswamy,Dr.S.Minakshisundaram, and Dr.T.Venkatarayudu, all eminent in their respective fields.People used to remark that the backbone of the Indian Mathematics was at Waltair.on account of heavy concentration of mathematical talent at that time.
While at Princeton , Prof.Minakshisundaram had shown his mettle as a Mathematician of the front rank. If one refers to the Bulletin of the American Mathematical Society 1950, Volume 3, one finds complimentary tributes about him from Prof.Herman Weyl, who was very much pleased with Prof. Minakshisundaram's contributions to Mathematics. Late Prof.Jon Ven Neuman too was impressed with Prof.Minakshisundaram and we were told that he spared no pains in presenting Prof. Minakshisundaram with a complete set of his own books and reprints on Rings of Operators and Continuous Geometry. Later, from accounts , the Princeton School of Mathematics treated Minakshisundaram with very great respect and those who visited the Institute for Advanced Study later had to face a series of affectionate inquiries from the galaxy of topmost mathematicians and mathematical physicists of the world about Prof.Minakshisundaram. This was disclosed to us by Prof.K.Satchidananda Murthy , Professor of Philosophy and at present Principal of the Post Graduate Centre of the Andhra University, Guntur. It was a pleasure for him to meet his old friend at Madras former Prof.K.Chandrasekharan of the Tata Institute of Fundamental Research, Bombay, now residing in Zurich, who got his Ph.D. degree of Princeston University, and who later collaborated with Prof.Solomen Bechner of the Princeton University and institute for Advanced Study, Princeton, in writing the well known book on "Fourier Transforms" Volume 4.
It was Madras again at Princeton when Minakshisundaram and Chandrasekharan developed intimate friendship with each other for the cause of Indian Mathematics. Both of them impressed topmost American Mathematicians such as to earn their high esteem. Not only this even non American Mathematicians , came forward to collaborate with Prof.Minakshisundaram as we can easily see his joint paper with Prof. A.Pleijel now Professor of Mathematics at the University of Uppasala, Sweden (5). I have known Prof.Minakshisundaram mention that this was in his opinion, one of the very best papers he produced.
Returning from the Institute of Advanced Study, Princeton, in 1948, he rejoined duty as Reader in the Department of Mathematical Physics, Andhra University and continued in the post till he became Professor and Head of the Department of Mathematical Physics in the year 1951, after the post became vacant due dto the retirement of Prof.A.Narsinga Rao in the year 1950. A significant event in Prof.Minakshisundaram"s career as a Mathematician during 1950 was the invitation to the International Symposium on Differential Equations, Stillwater, Oaklahoma, USA. His participation in the deliberations of the International Congress of Mathematics held at Cambridge, Massachussets, USA , at invitation of the congress.
He was the Head of the Department of Mathematical Physics from 1951 to 1962.During this period he worked hard in bringing the reputation of the Department of Mathematical Physics to limelight and a measure of respectability for the students of the department elsewhere in learned Institutions of the world. In 1958 He was invited on an Educational Tour to USA. as a member of the General Education Team. He was also invited to the International Congress of Mathematicians, Edinburgh, to deliver lecture. This lecture was well received and praised. Dr.M.H.Stone visited the Department of Mathematical Physics and was the guest of honor at a valedictory function of the Departmental Association. It was all due to the personality of Prof.S.Minakshisundaram as a reputed Mathematician. A couple of his students misunderstood him as the path to modern research is difficult. He used to point out his achievemnts as coming from his own hard work and in this none was his guide. In a sense late Prof.K.Ananda Rau and Prof.R.Vaidanathaswamy appeared to be his guides in disguise when he was confronted with difficulties in his mathematical labors.
In the year 1951, he participated in a summer seminar organized at the Tata Institute of Fundamental Research,Bombay along with his students, now Prof.P.Sambasiva Rao of the Department of Engineering Mathematics of the Andhra University, at the invitation of Prof.K.Chandrasekharan.During that period there was close collaboration between the two eminent Mathematicians which resulted in their book " Typical Means " seeing the light of day. It was very well received by Mathematicians the world over. It is a source book for further work which the authors have taken pains to compose.
The period 1951 to 1962, as Professor and Head of the Department of Mathematical Physics was a period of intense activity academically and otherwise for Prof. Minakshisundaram. There was not a single day when he was not pestered by some visitor or other for advice on problem mathematical or otherwise. He was not only a mentor of his students but also a trusted, and highly dependable friend, guide and philosopher, to his colleagues. He was the well wisher of many a person. He was a source of attraction and inspiration to many in all respects. Late Dr.V.S.Krishna, former Vice-Chancellor of the Andhra University and an eminent educationist, was his intimate friend who held him in high esteem and used to seek his advice on many day to day problem pertaining to the university, academics,and administrative as well.
Mathematics was his first love and his unabated zeal for the propagation of mathematical knowledge to all interested was unquestionable.He was responsible for starting a separate Library exclusively for the use of the students of the Department of Mathematical Physics and he gave several mathematics books of his own for it. Not only this , he initiated the Seminar movement in the Department and he actively participated in several of them.In 1958 he participated in the International Congress of Mathematicians held at Edinburgh. He was invited by the Organizing Committee to deliver a one hour Lecture on " Hilbert Algebras" 6. He met several of his old friend and experts in various fields of study in Mathematics there. Notably he met late Prof.E.C.Titehmarsh of the Oxford University, for whose contributions in " Eigenfunctions Expansions ," he had great respect.
He was elected Fellow of the National Institute of Sciences, India during the Silver Jublee year of the Institute 1960, for his significant contributions to barious branches of pure mathematics.
In the year 1962 , due to the sudden demise of Prof.V.Ramaswamy, the chair in Mathematics at the Andhra University fell vacant and Prof.Minakshisundaram became Head of the Department of Mathematics the same year, a fulfillment of his long cherished desire to become a Head of the Pure Mathematics Department , his proper place as a Top Ranking Mathematician of the world.Soon he made his mark even here, and what was a loss to the Department of Mathematical physics was a gain to the Department of Mathematics of the Andhra University . A new look was brought into the syllabii which was matde attractive in keeping place with the rapidly expanding scene of mathematical knowledge. The same year he took elaborate pains to invite the Indian Mathematical Society to hold its Annaul Conference at Waltair. It was a labor of love for him and almost every Delegate who attended the Conference applauded his efforts and paid tributes to his zeal and the band of dedicated workers around him.
He was thus a very important person of the Andhra University and his many sided personality was fully utilized by the University. He was Honorary Librarian of the Andhra University Library during 1958 to 1959. He also officiated as the Warden of the Andhra University Hostels twice.He was in charge Register of the University for a short period. Whatever position of responsibility he occupied he brought forth a significant color to it and distinguished himself.
With missionary zeal he set before himself the noble task of spreading whatever he knew in mathematics to his fellowmen even rejecting lucrative offers of more money and facilities for creatice work elsewhere. He was offered Professorship at reputed American University while he was at Princeton and he rejected the offer in view of his desire to be of service to his country and his countrymen . To be useful to play his part to put them on the road to progress and enlightenment.
During the year 1966 to 1967 he was deputed as Research Professor of Mathematics at the " Indian Institute for Advance Studies ," Simla. At a function organized under the auspices of the Faculty club of Andhra University bidding him farewell , Prof.K.Satchidananda Murthy , professor of philosophy and at present principal of the Post Graduate Center of the Andhra University, Guntur, congratulating him on his appointment, mentioned that his knowledge of contemporary philosophy was such to entitle him without the usual rigmarole, a Master's Degree of any standard university of repute in philosophy.This speaks of his great interest in philosophy too.
He was very social and had many friends in all ranks of the University Staff and elsewhere. There was none who did not know Prof.Minakshisundaram for generations and generations of students , colleagues and administrative personnel. In a sense he was an idealist, and often at times used to live in a world of his own, always dreamy and always thoughtful,thinking over some some problem mathematical or otherwise. Mrs.Minakshisundaram had to take a lot of pains to remind him of his food and other small human requirements of daily life.
He had an eye for talent and ability and wherever it was found he used to enslave himself for them. Most of the young talented students were his great friends and he used to derive aesthetic pleasure in their company. He trained a number of students for various examinations and many of them now occupy positions of responsibility in various walks of life.
During the year 1967, while he was at Simla, he was once again invited by the then Vice Chancellor Prof. K.R.Srinivasa Iyengar to be the first Director and later Principal of the Post Graduate Center of the Andhra university at Guntur. As Prof.S.Minakshisundaram had a soft corner for Andhra University he relinquished his post at Simla and rejoined the University.He occupied himself both day and night in organising the Center in various ways which shortened his life as is seen from his premature death through heart disease due to overwork. He had a severe heart attack at Guntur and had to retire prmaturely from service of the University much to his regret and those of his admirers.
While at Guntur he was offered a Research Professorship in Mathematics at the Institute for Fluid Dynamics and Applied Mathematics, College Park, University of Maryland, USA. on a very high salary and attractive terms in recognition of his unusual talents and abilities . Unfortunately , he could not avail himself of the opportunity because of his bad health at that time. His name was proposed for the post of President of the Indian Mathematical Society , a unique academic honor , but we could not see him function as President of the Society. He was also selected as Research professor in Mathematics under the U.G.C. scheme for Retired Professors in India. But even this opportunity was denied by cruel Fate which took away his precious life quite unexpectedly. He had a panoramic plan of publishing a number of books on advanced mathematics and it should be mentioned that his premature death was a great loss to Indian Mathematics.
He belonged to a respectable family devoted to the spirit of higher learning. His two daughters were married while he was alive and his son was married recently.
His very close academic friends, among others , include:
1.Prof.K.Chandrasekharan, now at Zurich.2.Prof.K.G.Ramanadham,Professor of Mathematics at the Tata Institute of Fundamental Research.
3.Prof.C.T.Rajagopal,Retired Director of the Ramanujam Institute of Mathematics,Madras.
4.Rev.Fr.R.P.Racine,Professor of Mathematics of the Loyola College, Madras.
His research students in all were the following persons occupying responsible positions in various universities within the country and abroad. They were:
1.Prof.B.Sambasiva Rao, Professor and Head of the Department of Engineering Mathematics, Andhra University.
2.Prof.T.V.Avdhani, Professor and Head of the Department of Statistics, Andhra University.
3.Prof.V.Viswanadham, Professor and Head of the Department of Mathematics at the Post Graduate Centre of Osmania University, Warangal.
4.Prof.M.Rajagopalan, Professor of Mathematics, Madurai University, Madurai.
5.Dr.D.R.K.Sangameswara Rao, Reader, Applied Mathematics Department, Andhra University.
6.Dr.A.Satynarayana Rao, Lecturer, Applied Mathematics Department, Andhra University.
7.Miss.V.Syamala Devi, Lecturer, Applied Mathematics Department, Andhra University.
8.Mr.G.V.Kameswara Rao, Research Fellow, Department of Mathematics at the University of Maryland.
9.Mr.V.Ch.V.Rao, Research Fellow , Department of Mathematics at the University of Maryland, besides a few others.
PAPERS PUBLISHED.
S.Minakshisundaram.
1. Tauberian Theorems on Dirichlst's Series.
Journal of the Indian Mathematical Society, 1936.
2. On the extension of a Theorem of Caratheodary in the Theory of Fourier Series.
Journal of the Indian Mathematical Society, 1937.
3. The Fourier Series of a Sequence of Functions.
Journal of the Indian Mathematical Society, 1937.
4. A Tauberian Theoremon Process of Summation.
Journal of the Indian Mathematical Society, 1938.
5. On V.Ramaswamy's Tauberian Theorem on Oscillation.
Journal of the Indian Mathematical Society, 1938.
6. On an Infinite System of Non-Linear Integral Equations.
Proceedings of the Indian Academy of Sciences , 1938.
7. On an Infinite System of Non-Linear Integral -Differential Equations.
Proceedings of the Indian Academy of Sciences, 1939.
8. On Non-Linear Partial Differential Equations of Hyperbolic type.
Proceedings of the Indian Academy of Sciences , 1939.
9. On Non-Linear Partial Differential Equations of Parabolic type.
Proceedings of the Indian Academy of Sciences, 1939.
10. On the Theory of Non-Linear Partial Differential Equations of the Parabolic type.
Journal of the Indian Mathematical Society, 1939.
11. On the Roots of a Continuous Non-Differential Function .
Journal of the Indian Mathematical Society, 1939.
12. On the Expansion of an arbitrary function in a series of Eigen Functions of Boundary Value Problems.
Proceedings of the Indian Academy of Sciences, 1940.
13. On the Expansion of an Arbitrary Function in Series of Eigenfunctions of Boundary Value Problems II.
Journal of the Indian Mathematical Society,1941.
14. A Note on the Theory of Infinite Series.
Mathematics Student, 1941.
15. On the Expansion of an Arbitrary Functions in a Series of Eigen-Functions of Boundary Value Problems. III.
Journal of the Indian Mathematical Society,1942.
16. Studies in Fourier Ansatz and Parabolic Equtions.
Journal of the Indian Mathematical Society , 1942.
17. Studies in Fourier Ansatz and Parabolic Equations.
Journal of the Madras University, 1942.
18. Fourier Ansatz and Non-Linear Parabolic Equations.
Journal of the Indian Mathematical Society,1943.
19. On Expansion in Eigen-Functions of Boundary Value Problems, IV and V.
Journal of the Indian Mathematical Society, 1943.
20. On Expansion in Eigen -Functions of Boundary Value Problems-VI.
Bulletin of the Calcutta Mathematical Society, 1943.
21. A Note on the Theory of Fourier Series.
Proceedings of Indian Academy of Sciences, 1944.
22. On the Differential Series of Eigen-Functions.
Journal of the Indian Mathematical Society, 1944.
23. Fourier Expansions I.
Journal of the London Mathematical Society, 1945.
With Dr.C.T.Rajagopal:
24. Tauberian Theorems of Ananda Rau.
Quarterly Journal of Mathematics, 1946.
25. Uniqueness Theorem for Eigen-Function Expansions.
Proceedings of National Academy of Sciences, U.S.A., 1947.
26. Fourier Expansions II.
Journal of the London Mathematical Society , 1947.
27. Postscript to a Tauberian Theorem.
Quarterly Journal of Mathematics , 1947.
With Dr. Otto Szasz :
28. Absolute Convergence of Multiple Fourier Series.
Transactions of American Mathematical Society, 1947.
With Dr.Chandrasekharan :
29. Some results on Double Fourier Series.
Duke Mathematical Journal , 1947.
With Dr.C.T.Rajagopal :
30. Tauberian Theorem of Mordell.
Proceedings of the London Mathematical Society, 1948.
S.Minakshisundaram :
31. Zeta Functions on the Sphere.
Journal of the Indian Mathematical Society, 1949.
32. Fourier Expansions III.
American Journal of Mathematics, 1949.
33. Epstein Zeta Functions.
Canadian Journal of Mathematics, 1949.
With Dr.Ake Pleijel :
34. Eigen-Functions of the Laplace Operator on Riemannian Manifolds.
Canadian Journal of Mathematics, 1949.
S.Minakshisundaram:
35. Expansions in Eigen-Functions of the Membrane Problem.
Proceedings of the Symposium of Spectral Theory and Differential Problems, Oaklahoma Agricultural and Mechanical College, Stillwater, Oaklahoma, U.S.A., 1951.
36. Lattice Point and Eigen Value Problems.
Proceedings of the Symposium on Spectral Theory and Differential Problems, Oaklahoma , Agricultural and Mechanical College, Stillwater,Oaklahoma, U.S.A., 1951.
37. Zeta Functions on the Unitary Sphere.
Canadian Journal of Mathematics, 1952.
With Dr.K.Chandrasekharan:
38. A Note on Typical Means. Journal of the Indian Mathematical Society, 1954.
S.Minakshisundaram :
39. Eigen-Functions on Riemannian, Manifolds.
Journal of the Indian Mathematical Society, 1955.
40. On the Structure of Unitary Symplection Groups.
Journal of the Indian Mathematical Society, 1955.
41. Hilbert Algebras:
Proceedings of the International Congress of Mathematicians, 1958, pg 407-411.
Cambridge University Press, New York, 1960.
42. On the Product of Dirichlet Series.
Journal of the London Mathematical Society, 37, 1962, pg 90-102.
43. On the Multiplication of Dirichlet Series.
Mathematical Zeitschrift 79, 1962, pg 44-52.
44. Summability of Eigen_Function Expansions.
Mathematics Zeitschrift 83, 1964, pg 321-335.
BOOKS PUBLISHED.
1. TYPICAL MEANS
S.Minakshisundaram and K.Chandrasekharan .
Oxford University Press- Bombay 1952-Fundamental Research Monograms.
2. Lectures on Functional Analysis and Applications.
Lectures delivered in I.I.T. Madras, 1965.
3. Composite Mathematics Text in Telugu for students of the VIII Class , Government of Andhra Pradesh Publication and Editor, 1968.
4. SPECTRAL THEORY OF DIFFERENTIAL OPERATORS-HEAT EQUATION.
Under Security for possible publication in the Higher Mathematics Series of the Von Nostrand Company, U.S.A.
REFERENCES.
1. Metheden der Mathematiechen Physik- Vols. I and II.
Springer Verlag, Berlin, 1937.
2. Lectures on Quantum Mechanics- Raziuddin Siddiqui- published by Osmania University, Hyderabad, 1933- Osmania University Publication.
3. Ramifications, old and now of the Eigen Value Problem by Prof.Hermann Weyl, Bulletin of the American Mathematical Society, 1960.
4. Fourier Transforms by S.Bochner and K.Chandrasekharan, Princeton University Press, Princeton, 1948.
5. Eigen Functions of the Laplace Operator on Riecamannian Manifolds- S.Minakshisundaram and A.Pleijel. Canadian Journal of Mathematics, 1949.
6. Hilbert Algebras - One hour address by S.Minakshisundaram . Proceedings of the International Congress of Mathematicians, Edinburg, 1958, pp-407-411, Cambridge University Press, New York, 1960.
**********
Positions held in Andhra University.
1. Joined the Faculty as Lecturer in 1943 of the Mathematical Physics Department.
2. Reader in the Mathematical Physics Department from 1946 to 1950.
3. Professor and Head of Mathematical Physics Department from 1951 to 1961.
4. Warden of the University Hostels in 1957 and again 1962.
5. Librarian of the University Library from 1960 to 1961.
6. In Charge Registrar of the Andhra University in 1961.
7. Research Professor in Indian Institute of Advanced Studies, Simla 1966 to 1967.
8. First Special Officer , Post Graduate Center, Guntur, 1967 to 1968.
9. He organized the Indian Mathematical Society Conference at Andhra University in 1961.
10. He gave Special Lectures Seminars during his distinguished career at Andhra University
from 1948 to 1966.
from 1948 to 1966.
