Rough PassagesHeresy and the Editing of Mathematical KnowledgeGauri Viswanathan » ISHS: International Society for Heresy Studies



Rough Passages
Heresy and the Editing of Mathematical Knowledge

Gauri Viswanathan

NB: This essay is available in PDF format.

Srinivas Ramanujan (1887-1920) is acclaimed to be one of the greatest mathematicians of the twentieth century, memorable not only for his brilliant solutions to thorny mathematical problems, but also for having surmounted obstacles of an intensely personal nature that threatened to leave his talents neglected and abused. Languishing as a clerk in a backwater office in Madras, India, he came to the attention of some of the top mathematicians of the time who, upon examining his notebooks written furtively on the side, recognized him “to be a mathematician of a new and high, if not transcendental, order of genius.”[1] G. H. Hardy (1877-1947), a leading mathematician at Cambridge University, needed no persuasion to facilitate Ramanujan’s travel to England so that the young Indian could pursue mathematical study in an environment where his talents would prosper. Hardy’s complicated, if not fraught, relationship with Ramanujan from that point onwards has been retold in various formats, including biography (among which the most widely read is Robert Kanigel’s The Man Who Knew Infinity), documentary (the PBS Nova series “The Man Who Loved Numbers,” among others), off-Broadway play (A First Class Man by David Freeman, roughly based on Kanigel’s biography), novel (The Indian Clerk by David Leavitt), and most recently, feature film (The Man Who Knew Infinity, taking its title and narrative arc from Kanigel’s biography and starring Jeremy Irons as Hardy and Dev Patel as Ramanujan).

What remains constant in these different retellings is an unremitting focus on the anomaly of Ramanujan’s genius: How could one possibly account for Ramanujan’s breathtaking mathematical theorems when he offered no proofs to indicate the method by which he arrived at them? In the absence of discernible method, could it be concluded that his mathematics was indeed born of mystical insight and occult intuition? Ramanujan’s fascination for modern readers lies in the perception that he broke every conceivable mold, defying the norms of disciplined thought. The fact that his intellectual work did not emerge from preexisting paradigms pushed skeptics, on the other hand, to view his mathematics as unorthodox and thus an illegitimate form of knowledge. And yet there was no denying that he had unlocked problems that had long baffled mathematicians. The frustration of his British interlocutors in their inability to reverse engineer Ramanujan’s method from his solutions was matched only by their condescension towards the mysticism that guided his thinking, confirming them in their view that Ramanujan’s insights were purely fortuitous—an accident upon which he stumbled after years of being steeped in Hindu numerology and other non-scientific practices.

Who was Srinivas Ramanujan, a man about whom much has been written but who still remains a shadowy figure even within those accounts?[2] Though Ramanujan’s letters are a rich treasure trove for those seeking a window into his personality, they cast little light on the issues that appeared most problematic to his fellows both in India and Britain: namely, how he reached his mathematical insights and whether he saw his training at Cambridge as being at odds with his creative mind. The following letter from Ramanujan to Hardy vividly captures the cross-purposes of their communication:

I find in many a place in your letter rigorous proofs are required and so on and you ask me to communicate the methods of proof. If I had given you my methods of proof I am sure you will follow the London Professor [who urged him to study Bromwich’s Infinite Series and not pursue divergent series]. . . . [Y]ou will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. . . . Verify the results I give and if they agree with your results. . . you should at least grant that there may be some truths in my fundamental basis. So what I want at this stage is for eminent professors like you to recognize that there is some worth in me. I am already a half starving man. To preserve my brains I want food and this is now my first consideration.[3]

Ramanujan’s alacrity in sharing his solutions to mathematical theorems was at odds with his unwillingness to declare how he arrived at them, leaving his letters a source of frustration to those at the receiving end. Because of the inadequacy of his letters, other people sought to fill in the gaps in his thought and personality, which makes Ramanujan a person more written about than writing himself. Indeed, his letters from England showed his preoccupation with two major topics: his solutions to mathematical problems and his complaints about the lack of vegetarian fare for a strict Hindu Brahmin like himself and the consequent effects on his failing health.

The letters are perhaps most useful for revealing the importance of his orthodox religious background in his worldview. Born on December 22, 1887, to an uppercaste Iyengar (Vaishnavite) family, Ramanujan grew up with the traditional devotionalism of his Brahmin caste. Following Hindu custom, he was married off to a child bride, Janaki, who moved to his home only after she attained puberty. Although he won a scholarship to a college in his home town of Kumbakonam, his indifference to all subjects except mathematics caused him to lose his scholarship. A similar story dogged him in his academic pursuits in other institutions. The study of mathematics was, and remained, his lasting passion. Notwithstanding a checkered academic career, he managed to secure a clerkship in the accounts section of the Madras Port Trust, where, in his leisure time, he cultivated his love of mathematics. His job placement was enabled by a family friend; a widening circle of support was to play an increasingly important role in his recognition by others.

Indeed, one of the remarkable aspects of Ramanujan’s story is the extent to which his upward mobility was facilitated by his acquaintances, most of whom wished to see his unusual mathematical ability properly nurtured in a more conducive environment. If a great deal of Ramanujan’s story is told not so much by him but from the perspective of his well-wishers and social circle, as well as later by the British academics who brought him to Cambridge, it is largely because the governing trope of their narratives is that Ramanujan’s mathematical gift was too valuable to be left alone, and that social and academic networks had to expend efforts on his behalf since he was unable to do so on his own. Ramanujan’s voice did not disappear so much as it was amplified by those for whom he had become an object of concern, lest his mathematical genius atrophied.

Read as a story unfolding in the period of British rule in India and the growing tide of nationalist movements, Ramanujan’s “discovery” by Hardy plays out the complex dynamics of colonizer-colonized relationships in a deeply contested area: education.[4] With the establishment of the university system in 1857 in the three presidencies of Madras, Calcutta, and Bombay, on the model of London University, British India came under a more centralized form of education. The universities were set up primarily as a way of eliminating the cumbersome lists the government had hitherto relied on to recruit meritorious students for public employment.[5] Under a centralized system that required all students to take a common examination, the acquisition of a university degree and academic distinctions automatically brought the most capable young men to the government’s notice.

Given this context, Ramanujan’s life story would appear to contradict every goal of British education. He failed to equip himself with the necessary credentials to secure employment; he lacked the discipline and training to be socialized into the world of institutional study or produce work that met the standards of established methodology. More seriously, if the project of colonial education was to modernize India, Ramanujan epitomized the hold of caste sentiments that, from the colonial perspective, impeded the advance of knowledge and held back India from the fruits of technological progress. And yet. . . Ramanujan was acknowledged as a genius, grudgingly or otherwise. Was his brilliance a testament to the success of colonial education, or rather its failure? For indeed Hardy’s efforts to secure Ramanujan’s passage to Cambridge can easily be construed as a stinging rebuke of colonial education’s utilitarian narrowness, geared as it was to a clerical mindset that satisfied the immediate goal of public employment but not much else. It should also be noted, however, that education in Britain had come under a similar critique for producing mechanized, utilitarian thinking, and the intuitive energies that might have produced a modern Newton or Priestley were being channeled into more professional, standardized directions.

And yet, even as criticisms of utilitarianism in education mounted, there were some detractors who cautioned against using Ramanujan as an excuse for bringing back a Rousseau-like return to nature as the basis of educational theory. The frame of reference here, of course, is Jean-Jacques Rousseau’s Emile, or On Education (1762), which immortalized autonomous conceptions of self, romantically associating education with the development of personality set apart from a foundational prior community.[6] The conviction that mathematics is cumulative and inevitable, as E.H. Neville (another key player in Ramanujan’s career) was prone to saying repeatedly, rationalizes the importance of institutional study and exposes the particular handicaps that beset Ramanujan. But the very circumstances of his mathematical prodigy also had an unsettling effect on accepted modes of scientific learning. Ramanujan seemed to rely very little on the existing structure of mathematics, and his work did not follow the path of the formal mathematical knowledge of his time. J. E. Littlewood, one among the small circle of mathematicians with whom Ramanujan worked intensely at Cambridge, remarked that Ramanujan “had no strict logical justification for his operations. . . If a significant piece of reasoning occurred somewhere, and the mixture of evidence and intuition gave him certainty, he looked no further.”[7]

This leads one to ask whether Ramanujan’s special appeal to his contemporaries was not simply for the quality of his mathematical contributions but more fundamentally for his being “untutored,” a diamond in the rough who reached sublime mathematical insights outside a systematized, institutionally certified method of analysis. Ramanujan’s mathematical gift is seen as almost mystical and occult, a view seemingly fortified by Ramanujan himself who credited his inspiration to the Hindu goddess Namagiri. But even on this point there is disagreement among those who knew Ramanujan: While some acquaintances insisted that his first exposure to mathematics came about through his mother’s preoccupation with astrology, others, like his family friend M. Anantharaman, noted that “after his return from England. . .  he had completely changed . . . [on mention of] gods and temples, [he said] that it was foolish talk, and they were only devils.”[8]

The sharply differing interpretations of Ramanujan’s religiosity—some claiming he was steeped in a deeply mystical ethos and others insisting that he inhabited an autonomous mathematical space that was separate from religion—prompt one to ask what is at stake in maximizing the effects of cultural and religious difference in the writing of his biography. The biographies follow a common pattern, accentuating the circumstances of his life and work as being at odds with the structure of modern mathematical knowledge. The effect is to put his thought processes into an antithetical relation to the orthodoxy of the mathematical establishment, which set the standards for acceptable knowledge and the means by which to arrive at it. Much is made of Ramanujan’s Brahminical background to explain the fascination he had for numbers as magical instruments for manipulating fate. His mother’s astrology may have helped to reinforce ritual boundaries for self-protection and calculate auspicious moments by mathematical means, but the world of dreams was even more powerful for him, as it was for his mother. He inhabited an occult world of dreams and prophecies that made him even more ill-suited to the logical requirements of mathematical thinking. While his writings do not make explicit references to his dreams, he apparently shared them with his friends, one of whom noted that “. . . Ramanujan had some intuition in interpreting dreams. I remember when my eldest brother M. M. M. Ganapathy told him that he dreamt something. Ramanujan told my brother that there would be a death in the street behind my house, and so it happened an old lady passed away in the house just behind mine and it was really a strange coincidence. There were other occasions also when his interpretations came correct.”[9]

The following story is also very much part of the standard biography, adding to the cumulative sense of Ramanujan’s occult personality. At first reluctant to let her son go to England, Ramanujan’s mother was moved to change her mind when, in a dream, she had a vision of him feted by Europeans; in the same dream the goddess Namagiri ordered her to cease resisting his departure. Not only did the mother impart to her son the conviction that his mathematical ability was a gift bestowed by the goddess Namagiri, who had blessed him by writing on his tongue, but Ramanujan also subsequently claimed that sometimes in his dreams the god Narasimha revealed his divine tongue in the form of scrolls covered by complex mathematical calculations, superimposed on drops of blood. Indeed, the visual imagery of divine gifts of imagination and supersensory perception, imprinted on the body as numbers, created a somatic identity for Ramanujan as a mathematician, no less powerful than the role of mental faculties. Numbers, for Ramanujan, were part of an invisible mythic order, yet ironically they had a bodily presence in divinely inspired dreams, as is strongly suggested in the dramatic image of divine forces imprinting numbers on his tongue or revealing their physical presence as a mathematical scroll.

Ashis Nandy notes that when systems such as divine numerology are declared delusional, it is tantamount to saying that there is no science behind numerology. But the notion that numbers have properties that can be analyzed for predictive value is not alien to mathematics. So, what appears as a rejected cosmology (i.e., the occult relation between numbers and events) enters into science as a study of the characteristics of numbers, and to that extent may be considered one of the bricks from which the edifice of science is constructed. He adds, “[T]he difference between magic and science is expressed not so much in their content as in their internal organizational principles, methodologies, the permeability of their boundaries, and the justificatory principles they use.”[10] Interestingly, Nandy appears to suggest that the distinction between magic and science does not necessarily mean that magic is science’s opposite, but rather constitutes the past on whose back science has constructed its knowledge systems, while transcending magic. The marker of difference, of course, is verifiability—the standard required for ascertaining scientific truth. Curiously, verifiability is exactly the test that Ramanujan applies in his letter to Hardy quoted earlier: if the same result occurs independently of the other, repeatability is all one needs to know to determine truth, not how the solution is reached. In his inimitable way Ramanujan closed further questioning. On the other hand, magic is what it is—a discarded stage of knowledge—because it cannot be explained or rationalized. The further removed it is from validation procedures, the greater does magic become forced into the silo of unacceptable, heretical knowledge.

Ramanujan’s associations with occult worlds affect even the way his story is told, if not by himself then by others. There are telling silences, especially in contemporaneous accounts. S. R. Ranganathan, a professor of mathematics at Presidency College in Madras, writes that he vetted his draft biography of Ramanujan to the Vice Chancellor, Dr. MacPhail, in March 1924. After going through the whole draft, MacPhail returned to Ranganathan’s first paragraph, which alluded to the impoverished circumstances of Ramanujan’s life as the cause of his meager intellectual and cultural nourishment. Ranganathan’s original draft included these lines: “At the turn of the twentieth century, hardly any extent of any tradition of higher mathematics [existed] in India. For it had gone into a state of cultural exhaustion and sleep before modern mathematics took shape in Europe.”[11] In the liminal border between colonial transformations of academic study and the emergent disciplines of modern knowledge in Europe, Ranganathan identified an occult, nebulous space between pre-science and science. It is within that space, he suggested, that Ramanujan combined the open inquiry of science, unrestrained by governing paradigms, with the ethos of dreamworlds, numerology, astrology, and other occult sciences. In a paragraph speculating on transmigration of souls, which was to provide great offense to chroniclers of Ramanujan’s scientific temperament, Ranganathan declared: “It is not possible to explain the phenomenon of Ramanujan except on the hypothesis of the ever-increasing Purvajanma-vasana—the Psycho-genetic force—gaining in momentum all through the march of a soul from embodiment to embodiment.”[12] Ranganathan drew on then current theories of metempsychosis, which, during this period, the London-based Society for Psychical Research was dedicated to demonstrating (or disproving, as the case may be), along with other occult phenomena. Indeed, in virtual lockstep with the SPR, Ranganathan proposed that not enough statistical data had been gathered about the frequency of appearance of phenomenal men of genius like Ramanujan to generate any empirical laws about genius and creativity.

Having ventured to explain Ramanujan’s genius as a demonstration of accumulated knowledge over successive lives (purvajanma-vasana), Ranganathan awaited the Vice Chancellor’s comments on his draft biography. MacPhail stone-facedly examined the passage, turned to Ranganathan, and remarked brusquely: “I find in this paragraph the fact of your being a Hindu and a student of mathematics and particularly statistical science. As a historian, I am concerned only with facts—well-established facts.  I am striking out this paragraph.”[13] MacPhail’s action is chillingly reminiscent of a scene in Aldous Huxley’s Brave New World, in which the controlling figure Mustapha Mond finishes reading a paper on “A New Theory of Biology” and responds thus: “He sat for some time, meditatively frowning, then picked up his pen and wrote across the title-page: ‘The author’s mathematical treatment of the conception of purpose is novel and highly ingenious, but heretical and, so far as the present social order is concerned, dangerous and potentially subversive. Not to be published.’[14] MacPhail’s editing out of Ranganathan’s occult speculations makes it clear that he considered them no less heretical and dangerous.

By forcefully excising interpretations of Ramanujan’s mathematical ability as a form of occult knowledge, and hence heretical by the standards of empirical thought, the Vice Chancellor’s action exposed the mathematical establishment’s discomfort in using words like genius or mystical intuition to discuss Ramanujan’s prodigious ability. A.G. Bourne writing to Francis Spring, a figure in the British administration who was instrumental in bringing Ramanujan to wider attention, firmly rejected the suggestion that “access to a library would ruin any genius; it savours of the middle ages and if his genius is so elusive or mysterious that good mathematicians possessed besides of much common sense cannot recognise and appreciate it even if it carries them beyond their scope, I should doubt its existence.”[15] Such uneasiness revealed the fragility of the boundaries around science that clearly distinguished it from the modes of thinking it presumably superseded, such as magic and superstition. Let us consider Hardy’s much quoted lines: “Ramanujan’s work . . . would be greater if it were less strange. . . . He would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and, no doubt, of greater importance.  On the other hand, he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain.”[16] Hardy’s lurking discontent with the “European professor” as a figure trapped by the disciplinary boundaries that determined authentic discoveries led him to overvalue Ramanujan’s outsider position—as Hindu, Indian, and colonial subject—as the heretical space from which new ideas could emerge.

In his psychosocial reading, Ashis Nandy surmises that Ramanujan’s occult leanings gave him access to the substance of contemporary mathematics but not to its culture. Perhaps if this culture had penetrated Ramanujan’s thinking more fully, it might have had the effect of occluding a more magical system of ideas. As it turned out, however, “his imperfect socialization to modern mathematics encouraged him to believe that he could enrich and extend the systems of magical mathematics through modern mathematics and make them even more powerful.”[17] Hardy sensed that Ramanujan’s greatness lay precisely in his uncertain positioning between superseded knowledge and institutionalized knowledge, with the freedom and license such a position allowed, even if that meant, as Hardy conceded, that he was “a poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe.”[18] Or, as E.H. Neville starkly observed, “Ramanujan was beginning every investigation at the point from which the European mathematicians had started 150 years before him, and not at the point which they had reached in 1913.”[19]

Indeed, the notion that Ramanujan, through his solitary labors, was merely recapitulating the discoveries of the past hundred and fifty years might not be as dismissive as it sounds, for it serves to re-present him as a rationalist figure affirming the course of modern mathematical knowledge. This reading of Ramanujan enabled British academics to explain his solutions to mathematical problems—provided without proofs—as a case of reinventing a wheel already in place in Western knowledge systems. His genius could be placed in proper perspective either by appreciating that he encapsulated centuries of advanced mathematical work in a few years of his own development (an echo of phylogenetic development, whereby the life of the individual mirrors the life of a species), or by disparaging the originality of his work with the claim that he was basically reinventing the wheel by covering the same ground already established by European mathematicians. The admiration for his talent is thus a concession to the fact that an individual could perform singlehandedly what in essence represented a cumulative effort over the centuries.  This assessment had echoes in an unlikely comparison: referring not to an individual but an entire nation, Karl Marx observed that India’s late emergence into modernity telescoped the years that led to the industrial revolution in Britain within a much shorter space of time.[20] But what could be said of the nation under colonial conditions might not be true for the state of learning. Europe’s accumulated knowledge over many centuries could be rationalized through its archiving in the institution, whereas an individual’s cumulative wisdom over many lives (as Ranganathan proposed) could not be explained in any reasonable terms. Thus, even though the ways in which knowledge is understood as “accumulated wisdom” might be startlingly applicable to both self and institution, the power of the institution determines what is accepted or rejected, turning untrained thinkers like Ramanujan into heretics if they do not appear to follow procedural norms regardless of the brilliance of the mathematical outcomes.

While Ramanujan’s circle of friends and biographers in India were painting a picture of him enveloped by dreams and prophecies and drawn towards occultism, the later Hardy edited his retelling of Ramanujan’s life to make him look like a fully rational, agnostic man, even going so far as to question the relevance of Ramanujan’s religious devotion. In a letter to the astrophysicist S. Chandrasekhar in February 1936 Hardy wrote: “My own view is that, at bottom and to a first approximation, Ramanujan was (intellectually) as sound an infidel as Bertrand Russell or Littlewood. . . Ramanujan was not in the least the ‘inspired idiot’ that some people seem to have thought him. On the contrary, he was. . .  a very shrewd and sensible person.”[21] While acknowledging Ramanujan’s occult proclivities, Hardy denied that his young Indian colleague had a manipulative interest in mathematics to produce magical effects. This was an important point for Hardy, since it allowed him to recognize the expansive possibilities of Ramanujan’s occult personality for doing a kind of mathematics that institutionalized study had cut off, without at all subscribing to primitivist, nonmodern, and heterodox notions of magic. Hardy recognized the hold of the occult imaginary in which early twentieth century thinkers and writers lived, grasping something of its importance when he wrote that Ramanujan “had a passion for what was unexpected, strange and odd” and that “all his results, new or old, right or wrong, had been arrived at by a process of mingled argument, intuition and induction, of which he was entirely unable to give any coherent account.”[22]

In dwelling on Ramanujan’s religiosity, however, Hardy revealed his own difficulties in reconciling the two contrary aspects of Ramanujan’s mind, one driven towards spirituality and occultism and the other to discovery of first laws in mathematics. Hardy’s investment in Ramanujan’s rationality was shared by other individuals, inhibiting the writing of Ramanujan’s biography from occult perspectives, which might partly explain actions like those of MacPhail in editing out Ranganathan’s theory of metempsychosis to explain Ramanujan’s mathematical insights. Not only did the Vice-Chancellor react in this way, so too did Indian students in Cambridge, who were discomfited by details of Ramanujan’s “trans-rational” preoccupations, such as with the goddess Namagiri and astrology.[23] The students feared that such accounts perpetuated the Orientalist notion of India as prone to superstition and religious, nonrational ideas, whereas Ramanujan’s mathematical achievement should be rightly invoked, in their view, as proof of the scientific temperament that defined India’s rational modernity. These generational differences appear in the responses of a younger generation of Indian students in Cambridge, in contrast to older professors like Seshu Ayyar and Ramachandra Rao, who accented Ramanujan’s nonrational side and were castigated for publishing these details. At the same time these same friends were not beyond self-orientalizing, repeating the Macaulayan view that India had fallen behind in the knowledge business, and that “the thought created in the West had not even been disseminated in the country.”[24]

If Orientalism as defined by Edward Said is the retelling of the East by the West, the fields of science and mathematics have been less clearly defined in the narrative than other fields like literature, anthropology, and history. Ramanujan’s life-story is a signal instance in which the dynamics of Orientalism were played out in glorious detail. Ramanujan’s well-wishers in India, however, were less concerned with how he derived his mathematical talents than with how he might realize them in a more conducive setting, deliberately de-romanticizing Ramanujan’s exceptionalism in order to draw attention exclusively to his mathematics, “the clue which would have to be sought in the autonomous, intellectual structure of his work, the drama of his life being at worst a red herring and at best an irrelevance.”[25] Ramanujan’s religious temperament was downplayed in accounts by the English mathematicians who collectively sought Ramanujan’s passage to England. Heeding his mother’s initial protests against his travels across the seas, which would cause him to lose caste, Ramanujan almost considered declining the invitation to Cambridge when first approached, but his tentativeness was not interpreted exclusively in religious terms. E. H. Neville, writing candidly about the tense relations between the English and the Indians, explained it thus by maintaining that some of Ramanujan’s friends “saw in this invitation a mean attempt to transfer to the English University the glory that belonged to Madras.”[26] So Neville was all the more taken aback when Ramanujan offered his notebook to him, “for the English were objects of suspicion not as individuals but as components of the governing machine.”[27] And of course there were pragmatic explanations for the famous lack of proofs in Ramanujan’s theorems, namely, the anxiety that if shared with English mathematicians his ideas would be appropriated and claimed as the Englishmen’s discoveries. So it certainly leads to considerable speculation that Ramanujan’s caginess about revealing his proofs was a pragmatic form of self-protection under conditions of unequal exchange in colonial India.

For all of Hardy’s rationalization of Ramanujan’s mathematical prowess, Hardy also exoticized him, describing him as one of the great romantic figures of modern mathematics and wistfully noting that his discovery of Ramanujan was the “one romantic incident in my life.”[28] Hardy may have seen in Ramanujan a personification of the speculative, intuitive, and aesthetic elements which, although receding into the past in the ultra-positivist culture of western science, were the very stuff of pure mathematics.[29] Hardy was acutely aware of the intuitive, even mystical, culture of mathematics with which Ramanujan was linked and which was gradually superseded by the culture of professionalism. Hardy, no doubt, may have well been the one individual most instrumental in furthering the perception that Ramanujan had scored a victory over modern mathematics by being totally outside the system, in other words, by occupying a heretical position with regard to institutional Western scientific discourses.

Hardy’s intense interest in perpetuating this myth is not altogether easy to understand, unless it were indeed to salvage the potency of cultural and religious difference in legitimating a way of thinking about science that had been displaced by formal study. Randall Styers in Making Magic observes that scholars in the late nineteenth and early twentieth centuries remained interested in magic in order to construct ideas of modern subjectivity, knowledge, and selfhood. Their disciplinary interest in magic was not for its own sake, but rather in order to understand and define modern relations to the material world and thus regulate modern forms of subjectivity. To that extent, as Styers notes, “magic has functioned as a powerful marker of cultural difference.”[30] The boundaries of modernity are constantly being negotiated in academic scholarship, just as much as in modern mathematics, and a form of thinking that can roughly be described as heterodox is one of the means by which this re-negotiation takes place, allowing for an articulation of identity and subjectivity in relation to social and material worlds.

While in no way can it be said that Hardy was interested in magic, or saw Ramanujan’s mathematical ability as occult in origin, he still salvaged Ramanujan’s occult propensities as enabling a vital space for the practice of mathematics outside the regularized institutional frameworks that became the governing paradigms for scientific knowledge. Indeed, the appeal of Styers’ argument about magic is that he makes a strong case for understanding modern fields of knowledge, spanning from anthropology to sociology to comparative religion, in terms of magic’s usefulness as a foil to religion and science on one hand and to modernity itself on the other. If scientific rationality demands the construction of the secular for its claims to knowledge to hold up, heterodox magic infiltrates the boundaries between science and religion and permits an entrée into the pre-history of science lost to modern formal study. Hardy’s romanticizing of Ramanujan was in tune with his implicit recognition that modern mathematics’ self-construction as autonomous and resting on a stable field of knowledge was just that—a construction. Modern mathematics’ disciplinary constraints exposed Ramanujan’s way of doing mathematics—without proofs or evidence of procedures—as a vital heretical practice that science could not effectively expunge without losing an important source of its creative energies.

Let me again quote Hardy’s words: “[Ramanujan’s] work would be greater if it were less strange. . . He would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and, no doubt, of greater importance.  On the other hand, he would have been less of a Ramanujan, and more a European professor, and the loss might have been greater than the gain.” Hardy registers modern mathematics’ loss as the fundamental loss of modernity itself, in exchange for what Charles Taylor describes as notions of subjective autonomy and freedom, “purchased only at the price of potent new forms of social control and organization.” [31] These new organizational structures entail that the modern subject employs rationalized modes of thought and properly disenchanted relations with the material world. Ramanujan’s evocation of the Hindu deities Namagiri and Narasimha imprinting numbers on his body and revealing a divine tongue covered with mathematical scrolls violated this understanding by re-enchanting human relations with the material world.

It may be the case that modernity’s norms are established by placing magic and other heresies as modernity’s ‘other,’ but the new fields of knowledge emerging in modernity did not follow such oppositional logic in its entirety. At the back of Hardy’s rationality is a nagging suspicion that the mathematics practiced by his profession was marked by a profound absence at its core, a view that entered his imagination only after his acquaintance with Ramanujan. The excessive focus of attention in most biographies on the details of Ramanujan’s life-style—his austere vegetarianism, his prayerful devotion to the goddess Namagiri, his ongoing fascination with astrology and numerology—served not only to paint him in the colors of cultural and religious difference but also keep alive an earlier, outmoded practice of mathematics that had no place in formal study at Cambridge. For superseded mathematical practices, especially those that were deemed heretical because of their occult associations, were a vital part of the generation of knowledge that ultimately supplanted its predecessors. Ramanujan preserved a mode of thinking lost to modernity—call it heterodox, if you will—that evoked, in Hardy, a romanticist longing at odds with his mathematical training. Ramanujan opened a window onto the expansive possibilities of a way of thinking that Hardy could not do without either, and it led to what he achingly called the “one romantic incident in my life.”

 * * * This essay is dedicated to the memory of my father, T. V. Viswanathan, a mathematician. * * *


[1] S.R. Ranganathan, Ramanujan: The Man and the Mathematician (Bombay: Asia Publishing House, 1967), p. 32.

[2] Robert Kanigel’s The Man Who Knew Infinity: A Life of the Genius Ramanujan (New York: Charles Scribner’s Sons, 1991) is perhaps the best-known of recent biographies and recapitulates details of Ramanujan’s early life that have become part of recent media presentations. For the most part, however, I have turned to biographical accounts by Ramanujan’s contemporaries to illuminate an editing process already at work in presenting the subject (both the man and his mathematical contributions) for public consumption.

[3] Srinivas Ramanujan, “Letter of S. Ramanujan to G. H. Hardy, 27 February, 1913,” in Ramanujan: Essays and Surveys, eds. Bruce C. Berndt and Robert A. Rankin (American Mathematical Society, 2001), pp. 53-54.

[4] The word discovery is Hardy’s, who proudly took credit for being among the first to recognize Ramanujan’s genius. See G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (Cambridge: Cambridge University Press, 1940), p. 1.

[5] See Gauri Viswanathan, Masks of Conquest: Literary Study and British Rule in India (rpt. 2014; New York: Columbia University Press, 1989), pp. 148-51.

[6] I have argued elsewhere, in the 2014 preface to Masks of Conquest, that so persistent has this understanding of modern Western education been that little questioning has gone into whether it has historically concerned itself with the development of personality in the first place and whether indeed it is not the case that the obverse pertains: namely, that the institution of modern Western education has always been in the business of a certain amount of standardization from the time it took over from the family the task of preparing youth for the world. By the same token, it is also worth asking whether the management of disparate social groups, with contending desires, aims, and interests, would have ever been possible without experiments in colonial education.

[7] Quoted in Ashis Nandy, Alternative Sciences: Creativity and Authenticity in Two Indian Scientists (Delhi: Oxford University Press, 1995), p. 92; J.E. Littlewood, Letter to Hardy Add. MS a 94 (1-6) Trinity Papers.

[8] M. Anantharaman, “Our Family Friend,” Ramanujan: Letters and Reminiscences, Memorial Number, vol. 1 (Madras: Muthialpet High School, Number Friends Society, n.d.), p. 101. The astrophysicist and Nobel Laureate S. Chandrasekhar reinforced this more skeptical perspective and contradicted the heightened emphasis on Ramanujan’s devotion to the goddess Namagiri, insisting that religious observances did not necessarily imply belief. In fact, Chandrasekhar suggested that Ramanujan observed certain Hindu practices largely for the purposes of not offending the sensibilities of parents, friends, and community. See S. Chandrasekhar, “On Ramanujan,” in Ramanujan: Essays and Surveys, eds. Bruce C. Berndt and Robert A. Rankin (American Mathematical Society, 2001), p. 25.

[9] M. Anantharaman, “Our Family Friend,” p. 96.

[10] Nandy, Alternative Sciences, p. 106.

[11] Ranganathan, Ramanujan, p. 17.

[12] Ranganathan, Ramanujan, p. 17.

[13] Ranganathan, Ramanujan, p. 17.

[14] Aldous Huxley, Brave New World (1932; New York: Harper, 2005), p. 162. Emphasis in original.

[15] A. G. Bourne, “Letter of A.G. Bourne to Sir Francis Spring, 14 November, 1912,” in Ramanujan: Letters and Reminiscences, eds. Bruce C. Berndt and Robert A. Rankin (American Mathematical Society), p. 13.

[16] Hardy, Ramanujan, p. 7.

[17] Nandy, Alternative Sciences, pp. 104-105.

[18] Hardy, Ramanujan, p. 10.

[19] E. H. Neville, “Srinivasa Ramanujan,” in Ramanujan: Essays and Surveys, eds. Bruce C. Berndt and Robert A. Rankin (American Mathematical Society, 2001), p. 109.

[20] Karl Marx, “On Imperialism in India,” in The Marx-Engels Reader, ed. Robert C. Tucker (New York: Norton, 1978) pp. 653-664.

[21] Chandrasekhar, “On Ramanujan,” p. 25.

[22] G. H. Hardy, Collected Papers of G. H. Hardy, Including Joint Papers with J. E. Littlewood and Others (Oxford: Clarendon Press, 1979), p. 714.

[23] Ranganathan, p. 15.

[24] Ranganathan, Ramanujan, p. 21.

[25] Nandy, Alternative Sciences, p. 90.

[26] Neville, “Srinivasa Ramanujan,” p. 109.

[27] Neville, “Srinivasa Ramanujan,” p. 110.

[28] Hardy, Ramanujan, p. 2.

[29] Nandy, Alternative Sciences, p. 119.

[30] Randall Styers, Making Magic: Religion, Magic, and Science in the Modern World (Oxford and New York: Oxford University Press, 2004), p. 14.

[31] Styers, Making Magic, p. 13.


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