Some memories of Chandra

I first met Subrahmanyan Chandrasekhar in December 1972, but did not get to know him well until early 1976, more than a year after I arrived at the University of Chicago as a postdoc in the relativity group. For nearly 20 years after that, until his death in 1995, we interacted on an almost daily basis. My memories of those conversations and interactions have faded considerably over the past 15 years—I simply do not have Chandra’s remarkable ability to recall all details of events that occurred long ago. However, the overall impression that Chandra left on me and many other scientists is something that will never fade away.

To many who met him but did not get to know him well, Chandra must have seemed an exceptionally austere and formidable figure—an impression with a great deal of validity. Of all the scientists I have met, Chandra had the highest standards for both intellectual rigor and personal integrity. He applied those standards most uncompromisingly to himself, but he also did not tolerate failings by others in such matters. He was particularly intolerant of scientists motivated primarily by the hope of receiving recognition from others rather than by a deep, inner conviction that their work was of importance and interest, whatever anyone else might think. He was equally intolerant of scientists who rested on their laurels or were otherwise lazy or sloppy, rather than applying their full intellectual efforts toward their work. It was not unusual for Chandra to ask questions of a seminar speaker that were aimed at discerning the speaker’s convictions or at probing how carefully the speaker had thought through the relevant issues. Often those were uncomfortable moments for the speaker.

To get to know Chandra well, a barrier first had to be crossed, a barrier undoubtedly enhanced by the man’s impeccable dress—a suit and tie on all occasions—and by his impeccable speech and manners. It is unfortunate that this barrier had the effect of isolating him from a portion of the scientific community. I believe all that was needed to cross the barrier was some expression to him of the depth of one’s passion for research or other intellectual endeavors. With the barrier crossed, the very sensitive, caring, and above all loyal nature of Chandra’s personality would become readily apparent. The combination of those very human qualities with Chandra’s almost superhuman discipline, self-sacrifice, and dedication to science had a profound and lasting effect on all who knew him.

In his scientific career of more than 65 years, Chandra’s enthusiasm for the pursuit of science never declined, nor did his fortitude in carrying out major projects. I do not recall a single instance in which he appeared to be motivated by personal gain, nor a single occasion when he made an excuse for not doing something he felt should be done. If he thought a visit to a collaborator or other scientist would help advance his research, he would make the visit without seeking reimbursement for his travel expenses. Similarly, he never requested summer salary from his NSF grant. It appears that the free pursuit of his own scientific research was so important to Chandra that he did not want it tainted or encumbered with issues involving personal gain or accountability.

Chandra will be remembered for the next hundred years and beyond primarily for his truly major contributions to a remarkably broad range of areas in physics and astronomy. He ensured that his scientific legacy will pass on to future generations in unadulterated form by writing a definitive monograph on each of the topics on which he worked. It is highly appropriate that Chandra be remembered primarily for his scientific work. But it also is important that he be remembered for his personal qualities.

To convey a more complete picture of what Chandra was like as a person, I present four reminiscences from scientists who knew him well. John Friedman, professor of physics at the University of Wisconsin-Milwaukee, was one of Chandra’s last students and closely collaborated with him in the early 1970s. Abhay Ashtekar, Eberly Professor of Physics at the Pennsylvania State University, was a student in the Chicago relativity group in the early 1970s, a postdoc in the group in the late 1970s, and a close friend of Chandra’s thereafter. Valeria Ferrari, professor of physics at the University of Rome I (“La Sapienza”), was Chandra’s closest collaborator during the last 10 years of his life. Roger Penrose, emeritus Rouse Ball Professor of Mathematics at Oxford University, was someone whose research Chandra particularly admired and whose scientific advice Chandra sought when he encountered particularly challenging problems. The excerpts below were written about a year after Chandra’s death and are taken from S. Chandrasekhar: The Man Behind the Legend, edited by Kameshwar C. Wali (Imperial College Press, 1997). They are reprinted here with the permission of the publisher and the authors.

John Friedman

Despite the fact that he was still sole editor of The Astrophysical Journal, Chandra spent as much time on research as did his most dedicated students. Beginning his work by 5 am, he finished each 13-hour workday late in the evening. As part of his moral instruction to us, Chandra did not hesitate to point out that by the time his colleagues arrived in the morning, he had already put in half as many hours as they would work in a day. He described a visit to Caltech mainly by noting that the physicists had spent several evenings during the week at cocktail parties. How, he asked, could they get anything done if this was the way they lived? If a few supremely talented physicists could afford such lapses, Chandra placed himself (and, of course, us) among that vast majority for whom success in science was a matter of character.…

In my last year of graduate work, Chandra and [his wife] Lalitha were scheduled to spend six months at Oxford, and Chandra asked me to come with him to finish up my thesis work, a collaboration with him on the stability of rapidly rotating “configurations,” none of which had, at that time, been observed. [My wife] Paula, Mack (our six-month old son), and I traveled to Oxford in time for the great blackout of ′72, one of the miners’ strikes.

In the darkness of that winter, when Chandra went home to his apartment with Lalitha and I to the row house we rented from the Rev. Gauntlett of Maid Marion Way in Nottingham, we worked by candlelight.… It was dim and as damp as England’s winters have always been. I might have been feeling a little down myself, tired from our son’s cries and straining to check equations in the dark. But when I came in to work, Chandra’s meticulous script was as elegant as ever, lengthy error-free art, ink on bond. He smiled with mischievous pleasure that I had also been working by candle. Amid 13th century stone walls, built to sequester from the town a secular clergy that once comprised Oxford, he was obviously proud that we each had again spent a day and an evening showing our devotion. It was, he said, as if we were medieval scribes.

The beautiful hand in which his equations were written mirrored Chandra’s understanding of the equations themselves. For most physicists on the mathematical side, equations are viewed abstractly in a way that highlights the properties their expressions share as operators on a Hilbert space, while astrophysicists usually take from mathematics only what is needed for the problem at hand. Chandra, however, fell in neither camp. For his time, Chandra was, to my knowledge, unique in the way he treated the equations of relativistic astrophysics seriously as objects in themselves, their structure clear in the manner he displayed them, their meaning to be found in this structure. That mathematics was the language of nature he never doubted, and he served nature all his life.

Chandra was also unique in the way he combined a deep understanding of classical mathematics, of astrophysics and of the history of science, particularly the history of classical physics and astronomy. [Andrzej] Trautman and Roger Penrose were then the physicists to whom Chandra seemed closest in temperament and perspective, while his interests were closest to those of the astrophysical relativists, Kip Thorne and James Bardeen. The understanding that grew from Chandra’s history distinguished the problems he worked on, and the unmatched artistry with which he handled his language of equations distinguished their solutions. He was as devoted to science as anyone I have ever met.

Abhay Ashtekar

I first met Chandra when I arrived at the University of Chicago as a green graduate student in ′71. He had just turned sixty. I had done my undergraduate work in India and to me—as to most other Indian students in science—Chandra’s stature was god-like. We had heard of the innumerable discoveries he had made whose meaning and scope we understood only in the vaguest terms. But there was a feeling of awe and admiration and a conviction that for a single person to accomplish all this, he had to be superhuman. And so, I was very surprised when I first met him. Yes, he did have that pristine air about him, and yes, everything he did—the way he dressed, the way he sat in seminars, even the hard-backed chairs he chose to sit on—everything had an aura about it that set him apart. One immediately sensed a refined, dignified and austere personality, just of the type one would expect of a legendary figure like him. Yet, when it came to science, there was unexpected openness. He treated us, students in the newly formed relativity group at Chicago, as if we were his colleagues, his equals. He would come to all seminars, including the ones given by students. He would ask us technical questions with genuine interest. When discussions began, he seemed to become genuinely young, almost one of us. I still remember the smile that would light up his face in the middle of a talk when he heard a beautiful result. Sometimes, when he had cracked a hard problem, something that he found truly satisfying, he would tell us about it. The joy he experienced was so manifest and so contagious!…

Chandra was a master storyteller; I have yet to encounter his equal. He had such a fantastic memory for dates and details that, in the anecdotes he recounted, everything became alive. And his anecdotes ranged from incidents that took place in the lofty halls of the Trinity College in Cambridge to his small cabin in the ship he took across the North Sea when he went to Russia. He would recount the events as if they had happened yesterday. We would later shake our heads in astonishment. For, here was Chandra telling about a storm he encountered during the North Sea passage in 1934, or his interesting meetings with the then President of the University of Chicago in 1946, with such clarity and in such detail that we could not have matched in describing events that took place in our own lives just a year before!

I still vividly recall the first time that I heard him tell a story. The students and post-docs in the relativity group had organized a potluck dinner. Chandra and his wife Lalitha came with a delicious vegetarian casserole. When it came to coffee time, there was some unease about how the event was going to end. Do we just say good-bye and leave? Students had planned the menu well but hadn’t thought of anything specific as an after-dinner activity. So, there was some unease. Chandra got up spontaneously and told us some wonderful ghost stories—one told to him by Dirac! They were short, dry and crisp and we all gasped when the punch line came and then laughed. Then other people got up to tell other stories and the evening ended in a relaxed and friendly mood.

Valeria Ferrari

My collaboration with S. Chandrasekhar started in October of 1983. We had met in Rome after the X International Conference on General Relativity, held in Padova in the summer of 1983, and he had invited me to work with him on some relations existing between the mathematical theory of black holes and exact solutions of Einstein’s equations possessing two spacelike Killing vectors.

I arrived in Chicago a few days after he had been awarded the Nobel Prize. I was afraid that the commitments associated with such an important event would prevent Chandra from working with me. But my fears were unwarranted, because he was more interested in the work we were doing than in giving interviews to the press. Our first paper was completed in two weeks.

For me, this first interaction with Chandra was surprising in many respects. Knowing the breadth and wide range of his scientific accomplishments and having listened to his lectures at conferences, I had nurtured the idea that he was very strict and rigorous, a man totally and exclusively dedicated to science, and so overwhelming that it would be difficult for me even to talk to him. But Chandra turned out to be entirely different from my preconceptions. In our work, for example, he never used his authority to impose his view on a subject; we always discussed and confronted our ideas as if we were on the same footing. At the same time he was an extraordinary teacher, and shared with me his knowledge and the secrets of his technical ability.

I had to change my views also about Chandra’s personality. In spite of his strict appearance, he was a very warm person, to whom friendship was of great importance. Although I came to know him only during the last twelve years of his life, from many episodes that he narrated to me I think that this had always been the case. For example, in remembering [Arthur] Eddington, with whom he had had the famous scientific dispute that strongly affected his life and his career, he never expressed feelings of resentment or disrespect. I was surprised to learn that while Eddington attacked Chandra’s work in international conferences (he characterized the theory of the limiting mass for the white dwarfs [as] “a stellar buffoonery”), in private they remained on good terms, joining for tea or for a bicycle ride. Chandra was convinced that Eddington’s opposition to his theory was motivated by honest scientific disagreement, and his enormous respect, admiration and affection for him were unharmed by these events. At that time Chandra was in his mid-twenties. Chandra told me that when he used to see Eddington walking the streets of Cambridge with an umbrella under his arm, he thought that this was the picture of a man who had dedicated his life to the pursuit of science and finally had reached a sense of harmony and contentment. Thinking of his own future, he would think that he would also experience a similar sense of harmony, peace and contentment in his old age. “But,” he would add, “it hasn’t turned out that way.” He had a feeling of disappointment because the hope for contentment and a peaceful outlook on life as a result of single-minded pursuit of science had remained unfulfilled. I used to wonder, how could a man like Chandra have this feeling of discontentment about his life? Chandra did not exactly know the reason himself. However, I used to feel a sense of relief in seeing that the excitation for a new result, or the occurrence of a problem difficult to solve, was always able to divert his mind from these sad thoughts.

Roger Penrose

This world has seen some scientists of extraordinary ability—some who are quick and often arrogant, others cautious and possessing genuine humility. Among that small proportion who are of real and rare distinction are the very few who are truly great. It has been my considerable good fortune to have made the acquaintance of some four or five of those that fall into this final category, but only one of them could I claim to have known at all well—Subrahmanyan Chandrasekhar.…

My acquaintance with Chandra dates back to 1962, when I first encountered him at the Warsaw International Conference on General Relativity and Gravitation. That occasion had a particular significance for Chandra with regard to general relativity, as it marked his entry into the world of general relativists. In fact, he attended that meeting as a “student,” as his way to acquaint himself best with the current activity in that subject.

Why did Chandra have such determination, at the age of 51, to break entirely into a new field, demanding the learning of many new concepts and techniques, where much of the vast expertise that he had built up over many decades would have little direct relevance? It would be natural to suppose, and as I would strongly suspect myself, that it was his desire finally to address the profound conundrum that his early work had thrown up, dating back to his calculations in 1930 on the boat from India to England—that white dwarf stars of more than about one and one-half solar masses cannot sustain themselves against gravitational collapse. It seems clear that even at that time, Chandra was basically aware of the awesome implications of this conclusion, namely that the collapse of the star must eventually take it out of the realm of known physics and into an area shrouded in puzzlement and mystery. But he was by nature an extremely cautious individual, as is made manifest in the modest way he stated his conclusion:

The life-history of a star of small mass must be essentially different from the life-history of a star with large mass. For a star of small mass the natural white-dwarf stage is an initial step towards complete extinction. A star of large mass cannot pass into the white-dwarf stage and one is left speculating on other possibilities.

He was not the sort who would attempt, without due preparation, to make “authoritative” assessments of the likely fate of the material of a body indulging in gravitational collapse. There are, indeed, still many possible loopholes in the arguments which lead to the final conclusion that has now become an accepted implication of present-day theory—that, at least in some cases, the fate of a body in gravitational collapse must be to encounter a space-time singularity, representing, for the constituents of that body, an end to time!

The issue had been at the root of his difficulties with Eddington, when Eddington had so unfairly attacked his work at a meeting of the Royal Astronomical Society in 1935. Eddington, also, was aware of the implications of Chandra’s findings, but regarded this as a reductio ad absurdum and preferred to move along his own highly speculative route towards a fundamental theory, thereby rejecting the sound reasoning within the accepted tenets of procedure that had characterized what Chandra had achieved. Chandra appears to have been deeply hurt by Eddington’s reaction—the reaction of a man whom Chandra had previously so admired and looked up to. In response, Chandra turned his back on Cambridge and on the immediate problems thrown up by the structure of white dwarfs, apparently devoting his attention entirely to other problems. Yet the question of the ultimate fate of a gravitationally collapsing body must have continued to nag at his physical understandings for many intervening years—even while he was engaging in thorough studies of matters pertaining to quite other astrophysical questions. It is almost as though he had made a tactical retreat, circling around and exploring the details of the surrounding terrain—stellar dynamics, radiative transfer, and the stability of various types of astrophysical structures—before he felt ready for an assault on the profound issue that his early work had uncovered.

His assault was carefully prepared, and required many years of study of the intricacies of Einstein’s general relativity. Not only did he familiarize himself with the standard mathematical techniques and conceptual notions that had been developed for that subject over the years, but he engaged the assistance of certain relativists, such as Andrzej Trautman (and even myself), who had specialist knowledge of some of the less familiar modern mathematical procedures, to give a series of lectures in Chicago to him, his co-workers, and students.

Chandra’s first contributions in which he was able to bring general relativity to bear on astrophysical questions showed that there were additional instabilities, beyond those of Newtonian theory, making their mark earlier than had been expected, and leading even more surely to the ultimate situation of a black-hole fate for a collapsing star. He then moved to the study of black holes themselves, and became fascinated by the beauty of these structures—particularly the Kerr geometry that pertains to a stationary rotating black hole, the ultimate configuration of gravitational collapse. He eventually referred to black holes, in the prologue to his epic book on the subject, The Mathematical Theory of Black Holes , as “the most perfect macroscopic objects that there are in the universe.” …

His fascination with black holes gained as much from aesthetics as from a desire to push forward the frontiers of scientific knowledge. In his later years Chandra became quite explicit as to the importance of aesthetic qualities in science and in his own work in particular.

This brings out what must surely be one of Chandra’s very special qualities: his profound appreciation of the beauty of mathematical formulae. This appreciation extended into pure mathematics as well as applied, and he had an especial admiration for the work of Srinivasa Ramanujan. (He often expressed to me his delight in the fact that the only known photograph of Ramanujan was one that he had himself retrieved. Ramanujan had served as an important inspiration for Chandra in his early aspirations to become a scientist.) Chandra’s wonderful way with mathematical formulae must have been a quality that benefited him also through his earlier work—and provided a thread of continuity throughout his scientific researches in various disparate fields of endeavour. However, this quality is particularly apparent in his work in relativity theory. No doubt he was struck by the fact that the closer his researches took him to fundamental issues in physics—in the analysis of the very nature of space-time—the greater was the mathematical elegance that he encountered in the equations.…

What are the qualities that stand out in my memories of Chandra? That he was a great and prolific scientist, there is no doubt, and a deeply individual original thinker. He was enormously systematic and well organized, and he worked incredibly hard. He was a rigorous and somewhat autocratic taskmaster, but he had a genuine appreciation of quality in others. He was a loyal friend, reliable, and totally honest. He was deeply sensitive, but proud. He was a difficult man to criticize, and on occasion his pride might get the better of him—but he would be scrupulously generous with his critics if he could be found to be in error. He was polite and enormously dignified: a greatly cultured individual with a feeling for what is valuable in humanity wherever it might be found. He respected life in all forms (he was a strict vegetarian) and had deep appreciation of the works of Nature. He particularly valued the arts and took great pleasure in them, perceiving profound links between artistic and scientific values. [See the article on page 57.]

How did he view the status of his own scientific contributions in relation to his initial aspirations? One recalls Chandra’s distinctive way of working—reminiscent of the great mathematician David Hilbert—whereby (in essence) Chandra would devote different decades of his life to different topics, culminating each with a definitive book, and leaving each topic behind when he embarked on the next. What does one conclude from this? It might seem that these decades must have represented, to him, completed work that would be neatly wrapped up in the final book. Perhaps so; yet I detected a restlessness in him indicative of a dissatisfaction with what he had ever been able to achieve.

I suspect that his work in relativity theory was what brought him closest to the ultimate goals that he was striving for. He must have derived great satisfaction from his study of black holes, but there were always profound questions left open—and the more that were resolved, the more new ones would appear. Moreover, in his black-hole work, it was the vicinity of the horizon that was being studied, and this lay far outside the central region where the matter of the collapsing star would meet its fate. To gain insights into the nature of this region one must study the space-time singularities—where space and time themselves reach their final termination. Chandra’s work on colliding plane waves must surely have been directed towards gaining an understanding of these singularities, for they provide specific models where one can examine the generation of singularities explicitly.

It is inevitable that the results of this work must remain inconclusive, despite the power and insights that Chandra and his associates were able to provide. If the problem of the ultimate fate of a collapsing star—or a collapsing universe—remains unresolved, it is no discredit to him. He opened our eyes to this profound and deeply important problem and he made great strides towards resolving it. Quite apart from all his other achievements, that in itself might be thought to be enough for any man.