S.MINAKSHISINDARAM
By
G.S.R.Sarma
Gottingen, Germany.
Some Personal Reminiscences.
S.Minakshisundaram was for us simply ' Babai ' meaning in Telugu, father's younger brother. He was first my mother's second cousin who later married my mother's younger sister and thus our maternal relationship was doubly strengthened. He and my father addressed each other in their frequent correspondences ' My Dear Brother.' Despite genealogical clan connections dating back generations when their ancestors moved from coastal Andhra to coastal Kerala, Malabar, a thousand kilometers away, there were many similarities of family tradition preserved through all the migrations. For instance, my father' s name was Somasundaram and his eldest brother was Balasundaram, also epithets for Shiva. It may be mentioned that Babai's family surname , KOTRA, is rather well known in Andhra linguistic circles through the Telugu lexical works: Andhra Vachaspatyam by Kotra Symalakama Sastry and Lakshminarayaneeyam by Kotra Lakshminarayana Sastry. Kotra means 'short' ( according to Sabdartha Chandrika )' perhaps descriptive of a well known progenitor personage of the family.However, living in the Malayalam/Tamil speaking areas of then Madras Presidency,they adopted the local convention of prefixing the father's name to their given names. Hence he was officially registered as Subbaramaiah Minakshisundaram. They spoke Telugu at home but otherwise used proficiently the regional lingua franca Malayalam and afterwards Tamil as they moved later towards Madras.
Although quite a few other uncles had the technically equivalent relationship to us, this dear one was just Babai without any qualifying prefixes. He was not outwardly sentimental in general but was very close and affectionate to our entire family. This closeness and understanding were further fostered after he got his first full academic position as lecturer in Mathematical Physics at the Andhra University (AU) in 1943 during its world war sojourn at Guntur about 100km from our place. This town was already a focus of our family affections for decades through our eldest paternal aunt and her family there. That proximity promoted our occasional visits mutual assistance and appreciation over the years.
I still recall inquiring , as a small school kid, of my father about his doctoral title. The word doctor had only a medical connotation for most people. My father told me it is a special degree awarded for a new and important discovery. My father, despite his quite good standing in high school mathematics, was MA Economics. He has great admiration and actually awe for mathematicians but could not have gone any further about Babai's doctoral discovery. Maybe, my own further education has now finally enabled me to figure it out somewhat. At least , I can recognize many of the technical terms in Babai's publications and follow his general ideas,especially the classical ones on 'eigenfunction expansions,' boundary value problems, and divergent series and summability. I also had the opportunity to listen to some of his discussions with his doctoral hopefuls during 1958-60, he considered himself a pure mathematician even while heading the Mathematical Physics Department and always taught a course on Numbery Theory in the Pure Mathematics Department but his work found plethora of applications in physics, it turns out. He used to tell us that at the higher levels mathematics and physics are interwoven inextricably . That was indeed the running theme of ot 20th century physics, especially the quantum and field theories in both of which his own results found applications and ramifications. The monographs cited at the end amply corroborate his views.
He used to visit our hometown Machlipatnam (Bandar) as a member of an AU Commission to inspect the progress on plans to upgrade BSc courses at the affiliated Hindu College. The visits were once in autumn and again the following spring. He had a standard quip on me: How come you are in the same class were you in last year also! He used to laugh and play with us kids during such visits. I had the privilege of washing his pair of dhothis he used to have as his wardrobe on these visits. He was appreciative of the occasional chores I used to do to help my mother. Apparently he did so himself in his boyhood to help his own mother. A spin-off benefit for me on these visits was that he used to take me to the cinema. Not so much for the running film he cared, it turned out, but the chance the outing gave him to smoke and think in peace, as I construed later. Smoking was common in the cinema halls then and was tolerated even in the 1960's. Confirme non stop smoker though he was after return from USA, he would not however smoke inside our house. Such was his respect for traditional values of the times. I recall once my father pleading with him on our outside terrace literally to wean him off from smoking. I could sense their's was a pure and direct kinship.
He used to travel by train from our town to Vijayawada to catch the Howrah Mail or the Grand Trunk Express back to Waltair. The train journey of about 60km Vijayawada , with about a dozen (scheduled) stops en route would take three hours normally but he used to say, it won't matter even if it's delayed since he'd sleep off any way on the night train which often took an hour longer with all the morning milk vendors getting their wares on board. There used to be four classes on the trains in those days and he used to travel first or second class on these trips just to have exclusive privacy for undisturbed sleep. He read a lot on such trips and also wherever he had spare time.
He was the magnet that aligned us to the University which in fact he symbolized for us. When I was considering in 1955 different courses of higher study his casual remark was that a cultural degree is better than a mere professional degree. He cited Dr.V.S.Krishna, the then Vice Chancellor an his close friend, to that effect. He never of course imposed his will or opinion on others. Relatives and friends were quite surprised when I chose to take up the B.Sc. (Honors in the Mathematics Physics Department although I was admitted to the much coveted engineering course started that year at the AU.
I lived for the first academic year with my uncle and aunt and only next year moved to the hostels. The room I stayed was midway in their vestibule like quarters a spin-off from WW II , served as a drawing room and a temporary accommodation for stranded students.
The only course I took from him was on co-ordinate geometry. When he dealt with the conic sections I was asking for some proof for the ellipse case and he answered it follows the same line as for the parabola. He used to say , at the university we have to learn to learn things by ourselves and should not expect spoon-feeding. When I was in the second and final year I even offered to give free tutorials for the juniors. He liked the audacious idea but it could only be done informally, given the structural constraints of the system. When we were struggling to solve differential equations he used to tell us about new electronic machines doing such problems. He was aware of the work of John Von Neumann on ENIAC (Electronic Numerical Integrator and Automatic Calculator) in Philadelphia used , by the way, first to tackle gas dynamic shock wave problems in ballistics and later for other problems on JONIAC at the Advanced Study in Princeton. Developments towards today 's IT revolution were just incipient then . Computers were meant only for scientific and big business data problems.
The years at the AU, 1955-1958 as a student, 1958-1964 on the staff, were among the most impressionable of my formative period both in terms of formal education as well as cultural and social development in a very unique campus life amidst a gorgeous natural scenery: the deep blue Bay of Bengal down below on the east , the hills on the west, wooded greenery on a red soil all around, a mild sea breeze and a clear blue sky most of the time.
There was an honor code at the AU that if a next of kin is an examinee, the related faculty member may not be an examiner for that academic year. Since we had full-fledged university examinations in Mathematical Physics in pre final and final years, my uncle who was Chief Examiner ex officio as Head of the Department, gave up his examinership for both the years. Those days it meant a nontrivial financial sacrifice since that was the only extra bonus senior faculty could claim.
In 1964 I moved on to USA for my doctoral studies, by the way, with his intact suitcase from Princeton in my luggage. I kept in touch with him while he went through various taxing assignments and health crises as he wrote to me . The last I heard from him was in 1968 while he was convalescing from those cardiac crises. My younger sister Sarvamangala , of whom he was also especially fond, recounted her visit to him then in the Guntur hospital. His gentle simplicity even under those stressful circumstances was evident when he asked her to read for him stories from the Andhra Prabha weekly. While listening to them he enjoyed the Bandar Chegodies brought by her from our native place.
All that he ever wanted to do, I felt, was just mathematics but he allowed himself to be caught up in enervating routines out of his sense of duty and loyalty to the AU that gave him his first paid job after a frustrating unemployed 'D.Sc.' status of the early 1940's in Madras.
His modesty and simple humour were enticing . He used to joke that his first class in B.A.(Honours) with a high rank on the Madras University graduation list was due to someone else below who had to be given a First as well. Another quip was about his job that he was glad he narrowly escaped becoming a Professor at the Annamalai university which had then apparently even lower salaries than faculty positions at the AU. My own salary scale as a lecturer at AU in 1959 was 210-15/2-300 Rupees p.m. which had the benevolent biennial increment of Rs.15 to reach a ceiling of 300 after 12 years of continuous service. University Grant Commission changed all that later on for the better.
About money he was quite unconcerned and was generally detached to many material matters. His unfailing humour even under otherwise trying circumstances is illustrated by an incident on the eve of his departure from their residence in Mambalam , Madras, to start his month long voyage to USA from Colombo in 1946. Dressing up for departure he checked his pockets but couldn't find the money purse he put in there earlier. It had a rather large amount to cover travel expenses, a friendly loan extended by a well wisher . After some perplexed and desperate search for the purse here and there he just went to the open terrace upstairs and broke out laughing it seems when he found the currency strewn all over the floor by his little playful son.Fortunately , the wind was graciously calm at the time.
He was almost childlike in his simplicity and honesty in his approach without ever being pontifical. His eyes used to sparkle as he listened attentively to for instance, what I, a mere youngster, was affirming or hypothesize. He agreed to it by just blinking acquiescence.With him I somehow had unreserved access and freedom of expression , to many people's surprise. Generally he left me or others to try things on one's own and become independent. He never sought or expected favors and he tried to encourage the same attitude in others. He helped in a direct matter-of-fact way when one genuinely needed help , e.g. like signing a formal guarantee statement while I was applying in 1964 for a passport to go abroad.
He never dreamt of dropping names for dramatic effect of indirect association. This was remarkable considering the galaxy of superstars he lived and worked alongside at the Institute for Advanced Study Princeton during 1946--1948. His principle and practice were always : you do your work well and it speaks for itself. No need for salesmanship! He really practised the Gita dictum of diligent duty in a spirit of detachment from the fruits of action. He was a man of positive expression and action. He used to say, don't about things past you, you can't change. Take care of things you can do something about now or next.
He was of small stature, keenly observant, a mercurial and magnetic but also unostentatious presence, neat and simple in attire , never flamboyant, felt most comfortable in dhothi and shirtsleeves, peacefully thinking and smoking while seated on his reclining cane chair on the veranda at home. Apropos stature, his shirts were my size as a teen. I got two of his nice white combed-cotton US long sleeves , 'full-hand shirts' we used to call them, as hand-me-downs. He was very sociable talking to guests ,playing bridge and ping-pong at the faculty club but never went to town, , shopping or movies etc. His personal outfit, like all other household matters, was my aunt's responsibility. She even used to take his foot prints on a paper and get his sandals made in town. The only time I ever saw him go out was to the new book shop that opened near the campus. He advised the shop owner on the browsing privilege and attraction of book shops. There was no open access system at any store those days. He loved the Ashram life on the AU campus in Waltair which used to be a salubrious peaceful refuge far from the humdrum crowded life of Vizag, the Dolphin's nose harbour town down below.
Although Mathematics was his main passion, he was not an ivory tower mathematician--the absent-minded, spaced-out stereotype image usually depicted and even cultivated by some. He liked and lived fully the campus life to which he of course gladly dedicated himself. On campus he enjoyed and encouraged sports, music and drama programs and my own participation in such organisations and extracurricular events, rather rare then among students of physics and mathematics . I recall his asking me at a relative's marriage dinner to render a musical verse from a classical drama we had enacted a few months earlier on AU stage.
Apart from his heavy academic duties he served the university in various capacities. e.g. as a Librarian - in - charge and Chief Warden of the hostels. In the latter capacity he encouraged us, young staff members , to run our own Kirlampudi Hostel and mess which turned out to be a nice model experiment at the time and even attracted paying guests from the staff quarters.
Deeply spiritual without being overtly religious let alone ritualistic but he left others to go about their own beliefs and practices. He was fully versed in the Bhagavad Gita, and an avid reader in general. I recall the big book on the Life of Sri.Ramakrishna he read through in a couple of days during a stay at our place while on AU deputation work. He Never went to temples or participated in religious festivals but quietly understood others who did so. At Princeton, Oppenheimer and Weyl in particular used to engage him in discussions on Indian philosophy. Weyl recited the Rig Veda in some of his work and Oppenheimer recited from the Bhagavad Gita when he witnessed the first atomic test in Los Alamos. There was a greater communion between these kindred spirits beyond mathematics and physics.
His chain smoking habit , his nemesis unfortunately, he acquired at middle age while on the long ship journey back from U.S.A. He was never seen on without a cigarette except in the class room.Even so, he used to say that the students have a right to smoke only on their own money and not on their parent's. In the last years , he used to confide that this habit controlled him like a Pisacham ( devil ) which he tried occasionally but in vain to exorcise. He said he could be off smoking for some days but then he just couldn't think or do Mathematics. Withdrawal symptoms from Mathematics were more painful to him than those from smoking. I think the addictive habit was particularly harmful in his case due to his slight basic build and light eating, like a bird, as I often observed.
As my own specialisation went eventually towards fluid dynamics and related aerospace application,I thought it'd be wiser to request a few leading experts active in areas drawing on the fundamental contributions of S.Minakshisundaram(SMS) to kindly contribute brief sketches in appreciation of his work and its impact on current research in Mathematical Physics. We are immensely grateful for their contributions that are very illuminating for us in the present context.
Let me just add a few observations of personal admiration on my uncle's remarkable work and accomplishments. He started off on classical lines during and after his doctoral thesis devising new ideas and techniques on Fourier series, summability methods for classically divergent series, Tauberian theorems and eigenvalue problems which were all adjudged to be among the best of the times and are still cited and used. They also laid the foundations for hes even greater accomplishments at Princeton.His work eventually fertilized fields like Spectral Geometry and Quantum Gravity, frontier areas of research areas even today [ cf.Avramidi (2000) and his article in this Special Issue.]
Mark Kac raised the intriguing question : Can one hear the shape of a drum ? This is a take-off on the problem of relating the boundary inversely to the spectrum of eigenvalues generated by the corresponding boundary value problem, related also to the work of SMS which indeed paved the way for Inverse Spectral Geometry [ of Fulling (1989) and his article in this Special Issue.] It turns out that the inverse relationship is non unique but the eigenvalue spectrum imposes restrictions on the classes of related boundaries. For instance, area and perimeter of the drum is determinable from the asymptotic spectrum but not its exact shape. A bit more about this later in my Note : ' Musings.
Weyl took the first step in 1912 on the above Inverses Spectral Geometry problem by connecting the area to the asymptotic eigenvalue spectrum of the memorable problem. the work of SMS and later that of Pleijel, Kac ,Mckean Jr. Singer, Patodi,... accompleished further difficult steps to identify the asymptotic spectrum also with the perimeter and curvature of the boundary.The Collected Papers of Vijay Kumar Patodi (1996) give details on several contributions to the related work as also on the fundamental work of Atiyah,Bott&Patodi on the famous Atiyah-Bott-Singer Index theorem. Sir.Michael Atiyah, FRS, Field Medalist 1966 (regarded as a Nobel Laureate in Mathematics ), kindly responded to me in an e-mail regarding SMS saying " I never met him but I studied his paper with Pleijel and it was an important influence on my research." The Minakshisundaram-Pleijel coefficients have in particular become a cornucopia for many physical applications including the continuing efforts towards a merger of quantum mechanics and general relativity in Quantum Gravity.
Similarly,his work on Zeta functions and Heat Kernels have led in applications in Quantum Gravity and Field theories along with other mathematical investigations [ of.Elizalde et al.(1995), Elizalde (1994), Estrada & Kanwal (2002) , Williams (1992) ].
One of his most quoted papers [Can.J.Math, Vol.1, pp. 242-256, 1949] appears, maybe as an interesting coincidence, right after the paper by Einstein & Infield: ' One the motion of particles in general relativity theory' SMS was of course known to them while working at the Institute for Advanced Study. That was during its heyday when i.a.,Bochner, Harald Bohr, Dirac, Einstein, Godel, Halmos, Harishchandra (who started out, by the way, as a Physicist getting his doctorate in Cambridge under Dirac's supervision and then metamorphosed into an eminent mathematician0, Morse, Oppenheimer, Sieggel, VonNeumann, Weyl,...worked there forming an amazing joint forum for mathematics and physics. No wonder SMS had his energies and talents focused laser-like in that stimulating ambience.
As mentioned earlier, SMS taught regularly a graduate course on classical Number Theory. He included this interest also into his research repertoire on eigenvalue problems of Mathematical Physics by connecting it naturally to lattice point problems of Analytic Number Theory , such as for instance the issue of expressing positive integers in different ways as sums of squares. This led further to several interesting and valuable overlapping contributions to both fields which he presented briefly at the Symposium on Spectral Theory & Differential Problems in 1950 at Stillwater, Oklahoma . He had fruitful contacts with Carl.L.Seigel (Gottingen ) and Hel Braun (Hamburg) from his Princeton years leading to his work on symplectic groups. I used to see they had frequent correspondence.
Despite heavy odds and lack of group support at AU he pursued his interests even 1960's. He made one last heroic effort to rejuvenate his natural mathematical gifts by accepting the Research Professorship at the Institute for Advance Studies in Simla and later at the University of Maryland. But his services were again requisitioned for starting a Post Graduate Center of the AU in Guntur, the origin of his career and he returned there dutifully, may be even nostalgically. The Center he founded and supervised became later the Acharya Nagarjuna University, named after the Great Mahayana Buddhist Master of the early years AD who directed a school of higher learning in the region up the river Krishna. Then, alas,SMS was cut off too soon before he could return to his cherished dream of doing just mathematics.
Nevertheless, he lives on in our fond memories and more so in the continuing seminal vitality of his ideas and work, as can be seen clearly in the Bibliography below and which will motivate young talent to explore further frontiers. I found , in a quick random search, more than a hundred recent papers drawing inspiration and basic ideas from his work in close connection to current research. I'd like to believe he's now enjoying a discerning, relaxed , panoramic view over all these developments from a higher dimension.
Our ancient Seers realized that form is finite and ephemeral, subject to limitations of space-time and spirit is the eternal essence. It is the spiritual connection that transcends all bounds. Thus it is no mere coincidence, it seems to me , these Reminiscences of SMS have been composed from the Gottingen precincts wherin H.Bohr, Caratheodory, Courant , Dirichlet, Gauss, Hilbert, Klein,E.Landau, Oppenheimer, Riemann, Siegel, and Weyl worked and left their legacy in areas that fruitfully engaged the interests of SMS along his professional path.
Select Bibliography.
1. I.G.Avramidi (2000) , Heat Kernel & Quantum Gravity, Springer Verlag, Berlin.
2. P.B.Gilkey (2004), Asymptotic Formulae in Spectral Geometry, Chapman & Hall / CRC Press Boca Raton, Fl.
3. P.B.Gilkey (1995 ), Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem , CRC Press, Boca Raton, FL.
4. E.Elizaide (1994 ) , Then Physical Applications of Spectral Zeta Functions, Springer Verlag, Berlin.
5. Elizaide, E.,et al (1995) , Zeta Regularization Technique with Applications , World Scientific, Singapore.
6. Estrada . R. & Kanwal .R.P. (2002), A Distributional Approach to Asymptotics: Theory and Applications, Birkhauser Verlag, Basel.
7. Fulling S.A. (1989), Aspects of Quantum Field Theory in Curved Space-Time, Cambridge University Press , Cambridge, UK.
8. The Collected Papers of V.K.Patodi, Editors. M.F.Atiyah & M.Narasimhan, World Scientific, Singapore (1996).
9. E.C.Titchmarsh (1958) , Eigenfunction Expansions Associated with Second -order Differential Equations, Part II, Clarendon Press, Oxford.
10. Williams,F.L.(1992), Some Zeta functions attached t a /G / K, Pages 163-177, in "New Developments in Lie Theory and Applications " (Editors J.Tirao & N.Walch), Birkhauser Verlag, Basel.
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