The scale of internationalism
The international scale is, by definition and by common imagination, decidedly large. It links nations and spans continents, oceans, even the world. The scale of internationalism, by contrast, is rather more personal. The ideas and values and aspirations that make the international scale meaningful have historically been formed and negotiated across friendships and rivalries, through the quirks and turns of individual biographies and small (if geographically diffuse) communities.
Internationalism and the connected worlds that made it thinkable and urgent grew up over the course of the nineteenth century and came in many respects to define the twentieth century. For mathematicians and mathematics, as for many different sorts of people and institutions, the possibilities, challenges, and contradictions of reaching across borders and hemispheres characterized many of the century’s central organizational, political, intellectual, and infrastructural problems and projects. Across this period, the scale and substance of international itineraries and connections, as well as the scope and significance of internationalist values and imaginations, transformed time and again in a vertiginously changing world.
In mathematics, the twentieth century started with the dominance of a small circle of mutually proximate but only loosely interlinked European mathematical communities. Mathematicians tended to organize themselves locally, nationally, and along colonial networks. They sometimes took an interest in people and ideas from other countries, especially when they were not themselves based in dominant regions and institutions, but those interests were not necessarily pivotal to their work or their identities as mathematicians. By the century’s end, especially in the discipline’s elite, the international and intercontinental scales mattered tremendously. Careers and collaborations crossed continents, and mathematicians developed dependencies that tied everyday facets of their work to far-away people and places, many of whom they would rarely or never meet or see in person.
Many of the terms for the transformations in scales and ideals from either end of the twentieth century were negotiated in the pivotal decade in the century’s middle. In the aftermath of World War II and the nascent Cold War, mathematicians reckoned with the values and conflicts of the decades just passed and debated what to make of new resources and opportunities opened up by the war and by postwar reconstruction. When the world’s mathematical eminences began to reimagine and rebuild an international mathematical community, when they saw a newly independent India as part of this mathematical world, they turned to Damodar Dharmananda Kosambi (1907–1966).
International connections
At the time, Kosambi had not travelled abroad for a decade and a half. Yet he was nonetheless among the most internationally recognized and best internationally connected mathematicians in India. He boasted particularly strong ties, maintained primarily through postal exchanges, with influential mathematicians in the American Northeast. Having emerged from the war in a strong financial, personal, and geopolitical position, these mathematicians aspired to organize the first postwar International Congress of Mathematicians and to re-found an International Mathematical Union to go with it.
Kosambi’s connections to this American network had roots in the 1920s. During that formative decade, the young Kosambi learned mathematics in the close community of Cambridge, Massachusetts, home to Harvard University, where he eventually earned his undergraduate degree. Fortuitously situated among many of the current and future titans of American international mathematics, a result of his father’s collaborations at Harvard as a scholar of language and religion, Kosambi forged lasting bonds with peers and mentors and developed a confident sense of his place in the world of mathematics.
He returned to India in 1929 and spent a short but invigorating spell working in Aligarh with André Weil, a brilliant young French mathematician whose brash outlook and sardonic wit were well-matched to Kosambi’s own. Kosambi then built a career and established his scholarly reputation at Fergusson College in Pune. This positioned him to lead the School of Mathematics in the newly founded Tata Institute of Fundamental Research, in 1945. The TIFR put Kosambi near the intellectual and political core of an internationally-oriented Indian scientific elite during a crucial period of partition and independence.
During this period, Kosambi maintained and built from his Harvard connections, becoming a reliable and opinionated correspondent with numerous foreign mathematicians. An especially interested and vigorous counterpart in correspondence was Marshall Stone, whose early career at Harvard intersected with Kosambi’s formation there and who taught Kosambi in at least one course. An enthusiastic international traveller and networker, Stone maintained voluminous exchanges with mathematicians across the globe. In the latter years of the war, Stone worked in military signals intelligence in Asia, including extensive travels in India. This allowed Stone to renew his personal contacts with Kosambi, and formed a basis for future visits to India after the war.
As his compatriots planned for an International Congress of Mathematicians in 1950, Stone led the American effort to negotiate a new International Mathematical Union to replace the IMU of 1920 that had collapsed a decade prior. For this, Stone drew on his personal network of foreign correspondents, focusing especially on contacts outside of Europe as a counterweight to alternative efforts at international organizing led by European mathematicians. Kosambi was an especially valuable interlocutor for Stone in this regard: known in Europe, well-connected to the United States, optimally positioned in elite Indian science at the TIFR, and already an established personal contact for Stone himself.
In 1948, Kosambi’s strong international connections, especially to prominent Americans, formed part of his case for a grant from the recently formed United Nations Educational, Scientific and Cultural Organization (UNESCO) to learn about new electronic computers being developed abroad. Preparations for that trip, his first foreign travel since starting his mathematical career in India, involved reinvigorating American acquaintances and planning personal visits, with Stone’s University of Chicago and the Institute for Advanced Study (IAS) in Princeton of primary importance. Kosambi was accordingly on the minds of the 1950 International Congress organizers when they determined whom to invite for the Congress’s committee with the greatest foreign representation, the committee to select recipients for the Fields Medal. His planned proximity to Marston Morse, another member of the committee, at the IAS for part of his trip, combined with the relative ease of engaging in correspondence with the committee from the United States compared to Bombay, made it possible for him to be appointed without worrying that postal delays would keep him from contributing actively.
Kosambi was ultimately unable to attend the Congress itself. He remained active in both official and unofficial capacities in discussions around the new International Mathematical Union, ultimately inaugurated in 1952. Later years brought a few further chances to travel abroad, not just for mathematics, before succumbing to the limits of ill health and ill-temper—the latter reflecting his alienation from key figures in India who could facilitate or make obstacles for foreign travel. His spirited written international connections continued to his death, which itself prompted condolences posted to Pune from many countries.
Kosambi’s archives
The primary surviving archive of Kosambi’s international connections on paper is the collection he personally maintained, a portion of which was secured from his final home in Pune and deposited in the Nehru Memorial Museum and Library (NMML) in New Delhi. Like many scholars of his generation, he kept books and files of letters to refer to as he continued his exchanges with distant interlocutors. Bits and pieces remain from his early years, tucked alongside other papers and notes, including a number of student notebooks. Most of his available letters are from after 1956.
The next largest trove is Kosambi’s personal file preserved in the TIFR archives in Mumbai. The file consists of letters and notes from, to, and about Kosambi that arrived at and were filed at the TIFR in connection with Kosambi’s career there. Currently archived across five folders of varied thickness, Kosambi’s TIFR papers span his life in Bombay somewhat unevenly, with papers concentrated around moments of particular interest or controversy for Kosambi or the Institute.
To complement these collections specifically curated around Kosambi, one can add materials from and about the mathematician from a variety of sporadic sources. For this essay, I consulted Kosambi’s visitor file at the IAS, Kosambi’s letters to Stone in the latter’s personal archive at Brown University in Rhode Island, and a 1952 memorandum and report of Stone’s comments about Kosambi in Stone’s file compiled by the United States Federal Bureau of Investigation.
Together, in their convergences and contrasts, these archives shed light on the personal scale of Kosambi’s international career. Kosambi was by no means representative of a typical internationally-engaged mathematician of his time, to the extent such mathematicians fall into identifiable types. He was an outlier in his geography, background, network, temperament, and much else. At the same time, the mundane features of his correspondence reflect much that was common, not just to well-connected mathematicians in India but to most mathematicians who engaged in one way or another with the system of paper and travel that joined the mid-century mathematical world together.
Paper communities
By sheer volume, the archives of internationalism are dominated by dull and bureaucratic matters. To get multiple people in multiple countries on the same page, whether for a voyage or a grant or an organization, requires copying and sharing and recirculating numerous written pages. Even the personal letters could be a bit formulaic, touching on obligatory points of note and coordination. A commitment to internationalism, in practice, required a commitment to typing, sending, accumulating, and sorting file after file of dry points of agreement and reference. Form letters, statutes, and reports from the International Mathematical Union’s founding lend particular heft to Kosambi’s TIFR files. They attest to an internationalism built on having a common paper-based foundation with fellow mathematicians abroad, on being a part of a community that agreed on something actively and in writing.
This agreement was, crucially, sometimes fungible into other forms of connection. Form letters and formal reports were openings for financial and operational support for long-distance travel. Kosambi’s archives, especially at TIFR and IAS, are laden with the particulars of funding, accommodation, and other logistical matters for his half-year abroad in 1949. Housing in Princeton, a perennial concern for IAS visitors, occupies several letters in the IAS file and appears in personal and formal correspondence elsewhere, covering matters such as cost, availability of meals, and expectations for the social milieu. Materials about the International Mathematical Union included regular notice of funds from UNESCO and other sources to support participation in organizational meetings. Though Kosambi did not ultimately attend these meetings, he was closely involved in identifying beneficiaries for the earmarked support, who would thus be representatives for the nascent union’s articulation.
The implications were not just financial and organizational, but a matter of who speaks for whom on an international stage. A series of letters and consultations in the wake of Partition asked whether M. Raziuddin Siddiqi1 could continue to represent India in negotiations surrounding an International Mathematical Union after re-establishing himself on the Pakistan side of the new border. Kosambi considered Siddiqi an eminent representative of India’s mathematical community, regardless of Partition, and even saw diplomatic advantages in maintaining Siddiqi in that role (TIFR Kosambi-DD3: 26). While Siddiqi remained liked and respected among India’s mathematical elite, formalities and politics of citizenship ultimately weighed against Kosambi’s preference, and Siddiqi represented only Pakistan instead.
Other letters collect the expected comings and goings of planned and prospective international travellers so that invitations could be extended to make the most of journeys that were expensive and complex to arrange. Participating in an international community meant tracking where other mathematicians were and plotting the most effective ways to make itineraries cross, one way or another. Kosambi and his fellow mathematicians traded news of professional relocations, invitations, and voyages, advising each other so that possible encounters would not be lost due to ignorance or inattention. Sometimes word came too late, and the archives also hold evidence of missed connections and expressions of regret.
Crossing perceptions
The effort to identify, evaluate, appoint, and give news of people occupies a considerable number of letters, extending well beyond situations where money and travel are immediately at stake. Kosambi participated in an internationalism built up of people who only rarely saw each other face to face, relying instead on written introductions and assessments to extend and order their personal networks. These missives could be warm or formulaic, laudatory or calculating. A letter from Kosambi to Stone in the latter’s archive, identifying a delegate for the IMU meeting that Kosambi could not himself attend, declared that “I have no personal interest” in the substitute, “but only a national interest in the sense of getting a maximum of respectable mathematical attendance” to increase mathematical research in India accordingly.
Kosambi may not have thought much of Stone’s discernment when it came to Indian contacts. A 1946 letter in the TIFR files from Kosambi to Homi J. Bhabha updating on various foreign contacts and itineraries grumbled about “People like Stone, who can’t tell one Indian from another” (Kosambi-DD1: 8). Forming personal connections over long distances demanded this kind of acute awareness of those connections’ limitations, of the biases and blind spots and insufficiencies of even the most earnest attempts to bridge unfamiliar people and contexts.
Stone, for his part, worried how his relationship with Kosambi might be perceived. In December of 1952, Stone presented himself at the Washington DC headquarters of the United States Federal Bureau of Investigation to set the record straight on a number of matters that had come up in his recent successful clearance process for military consultancy. The meeting focused on the implications of the FBI’s interpretations of Stone’s professional relationships with several men with alleged links to espionage or Communist politics, with Stone insisting the FBI should not regard his purely mathematical connections as politically or otherwise problematic. As the meeting wound to a close, Stone volunteered that the FBI should be aware of his longstanding contact with Kosambi, whom he described as a Marxist and “a rebel.” Though “all Indians act very strangely,” Stone remarked, Kosambi’s strangeness derived from political convictions that he urged the FBI not to confuse with a threatening allegiance to a Communist Party. Stone urged the FBI to see his relationship with Kosambi as purely scientific and professional.
The FBI’s report of the meeting makes clear Stone was right to worry about how the FBI might interpret this association. Two confidential informants had separately named Kosambi in accounts of participation in activism considered politically suspicious. One noted Kosambi’s repeated membership among groups advocating for world peace in a way that tended to criticize the United States as a rising military power, and linked him to “carrying on agitation among the peasants and workers.” (Putting peasants and workers at the centre was key to one of Kosambi’s most famous interventions in the field of Indian history, a major part of his scholarly legacy.) The other informant invoked Kosambi’s alleged Communist activism to cast suspicion on Bhabha’s hosting of an international conference on atomic energy at TIFR in 1950. News clippings further linked Kosambi to anti-imperialist (that is, anti-American) activities in China.
Links between well-connected foreign mathematicians could be a resource and a risk in each direction. International scientific ties created international political entanglements. Stone built his international career around military and government travel that exposed his foreign contacts to scrutiny. Kosambi maintained international connections out of political, intellectual, and personal convictions that had different implications for different foreign interlocutors, including Stone. Whether one routinely expected to be in the centre of things, as Stone did, or had to participate as one could from positions of relative disadvantage, international communication involved identifying and managing perceptions and misperceptions and their effects on current and future relationships.
Validation and identity
It is clear in Kosambi’s paper trail that he took internationalism personally, and that international correspondence, travel, and recognition were essential elements of his identity. A biographical sketch in his NMML archive (box 6, folder 5) starts with his grammar school education in the United States and his Harvard degree. A brief report of his professional appointments and recognitions in India covers the period to 1947, including a parenthetical note that he “Does not get on at all with H.J. Bhabha,” underlined for emphasis. After that, he defined his entire career by his international travel and invitations, from his UNESCO fellowship to lectures in Moscow, China, and London. The sketch concludes with the real import of his Bhabha antipathy in terms of Kosambi’s international self-conception: “Many other foreign invitations have had to be declined because of Bhabha’s hostility.”
Both the NMML and TIFR archives strongly reflect the conflict between Kosambi and Bhabha, particularly over international travel from the late 1950s. As the two strong personalities clashed in that decade, Kosambi appears to have invested significantly in his personal relationships with foreign mathematicians as a source of professional and moral authority. Letters and telegrams show Kosambi’s efforts to bring sympathetic mathematicians to TIFR. From 1954, for instance, there are enthusiastic notes of thanks from Norbert Wiener (17 February) and of excitement from Laurent Schwartz (15 August) regarding their respective past and anticipated visits (NMML box 14 folder 5). Advertising his acquaintance and even friendship with such mathematical celebrities bolstered his domestic prestige, and also reinforced his sense of worth and relevance when his scientific and professional life in India did not proceed as he hoped or expected.
The final years of Kosambi’s career were strongly coloured by his claimed proof of the Riemann Hypothesis, which remains today among the most celebrated open problems of mathematics. Kosambi’s TIFR colleagues were sceptical of the proof and worried openly about the reputational ramifications of Kosambi’s insistence on promoting his result by all means available to him. A successful proof could put the TIFR and Kosambi in the worldwide centre of conversation. A flawed proof risked embarrassment, magnified by the standing of those to whom Kosambi sent his work. Bhabha and others at TIFR did not exclude the possibility that Kosambi had made a profound breakthrough, but they rather suspected that he had not.
In this light, Kosambi’s international connections took on new significance. His ties to Chinese mathematicians, first established as a student at Harvard, gave him a particularly important claim to international standing as his domestic standing appeared to crumble. Hua Loo-Keng, director of the Academia Sinica’s Institute of Mathematics, had invited Kosambi to lecture in China in 1957. The visit was still fresh in their respective memories when, in 1958, Kosambi began circulating drafts of his Riemann Hypothesis proof to foreign mathematicians. A return invitation in 1960, during which Kosambi proposed to speak about his Riemann Hypothesis results, let Kosambi claim a measure of international validation at a time when his correspondents almost uniformly doubted his asserted achievement.
By the time of his Riemann Hypothesis claims, Kosambi had a long record of collegial postal exchanges of manuscripts and offprints. Sharing new work was a means of intellectual connection, but it was just as importantly a means of social connection among mathematicians who were not necessarily working in the same research directions. Kosambi maintained such connections with elite mathematicians in many countries, who in turn were in a position to share his work with other notable experts. A few greeted Kosambi’s draft proof in 1958 with congratulations. Václav Hlavatý protested that he was not an expert but hoped the experts would agree it was “one of the greatest mathematical achievements of this century” (NMML box 7 folder 2). Some politely declined to opine. Others, like Norbert Wiener, insisted on seeing the argument in the best possible light as a hopeful theoretical contribution while identifying reasons to doubt the Riemann Hypothesis itself had been definitively resolved.
Two series of exchanges continued long after most mathematicians had become exhausted or exasperated with Kosambi’s persistent revisions and conviction in his fundamental correctness. Chester Feldman, with whom Kosambi maintained a lively correspondence after they met in Chicago during Kosambi’s UNESCO fellowship, was not himself an especially distinguished researcher. Feldman’s letters to Kosambi take part in his frustration and urge him to carry on seeking recognition for his proof. Both Feldman and Kosambi, for different reasons, came by the early 1960s to resent aspects of the leadership and organization of American and international mathematics. They bonded further over the response to Kosambi’s proof, which reinforced their perception of a mathematical elite that operated as an intellectual clique resistant to heterodoxy.
The other series of exchanges, involving letters, postcards, drafts, and offprints shared and discussed all the way until Kosambi’s death in 1966, was with the famously itinerant Hungarian mathematician Paul Erdős. The latter mathematician was never convinced of Kosambi’s proof. But as Kosambi’s correspondence followed Erdős around the world, Erdős continued to read and comment on each attempted clarification and rectification. Erdős himself had won acclaim early in his career for a startling new approach to the Prime Number Theorem, related to the Riemann Hypothesis, so was a perceptive and interested reader and one whose endorsement would make a major difference if it ever came. The durability of their exchange over Kosambi’s proof reflects how both mathematicians respectively approached their international communication, as a source of stimulation, community, validation, and much else.
Conclusion
Internationalism, from its first entry into the lexicon of political, economic, and social commerce, has been a shifting and difficult locus of values and ideals. It has often been a backwards-looking way of defining and judging past relationships. But it has more significantly been a way of discussing, contesting, imagining, and building different kinds of futures. In places like India and in fields like mathematics with historically ambiguous, problematic, or oppositional relationships to the context of European nation-states where internationalism was coined, internationalism was simultaneously a source of challenges and contradictions alongside aspirations and alternatives. Internationalism is deeply personal in a way that reflects the deeply personal foundations of projects for greater human cooperation, solidarity, and exchange.
Kosambi’s life and career were defined by his internationalism. His archives help one see Kosambi’s internationalism as a complex, multifarious, and deeply personal constellation of convictions and circumstances. It framed his efforts to maintain and expand upon relationships from his formative years in the United States. It established what mattered in his friendships and scientific endeavours at the start of his mathematical career. It motivated his active participation in postwar mathematical institutions and political movements. It refracted his local and national situations and his relationship to those of his interlocutors. It gave him a sense of identity and a source of validation during a turbulent later career. It outlined his aspirations, their unravelling, and their very partial salvaging (or at least salving) after he convinced himself of a major theoretical breakthrough.
Kosambi’s internationalism tied these different aspects of his life and career together and gave them significance. Its kaleidoscopic character made striking patterns from the elaborate patchwork of long-distance connections reflected in the paper files he left behind. Rather than attempt to define internationalism as a set of principles or postures, asking what internationalism was for, for Kosambi, shows themes and undercurrents in a complex character responding to a complex time. The personal, institutional, and ideological purposes of Kosambi’s internationalism hinge on the situated and perspectival quality of putting oneself in a mathematical world. Rather than see internationalism as a coherent, idealistic, large-scale project of unification, Kosambi’s archives offer an account of internationalism that is often ambivalent, sometimes cynical, frequently mundane, and always personal. Internationalism could be fragmented and contradictory, and these aspects often contributed towards purposes of uniting and reconciling.
The limitations and difficulties of Kosambi’s personal travel during his career make the significance of his archive all the more striking. Often unable to cross borders in person, he found other ways to cross borders and to define what borders and their crossing could mean. Mathematicians today, in an era of pandemic and climate change, of high-speed internet video conferencing and electronic publication, are still renegotiating the challenges that mattered for Kosambi and his internationalism.
This essay coincides with the first “virtual International Congress of Mathematicians,” held primarily online rather than in a common city and venue. The rapid pivot to online meetings responded not (primarily) to a novel coronavirus pandemic that continues to associate special risks with long-distance travel, but to the ongoing and devastating reality of war and its associated geopolitics. Obstacles to travel and technologies of long-distance communication, together with their human and geopolitical contexts, in Kosambi’s time and our own, accentuate and confront the personal relationships, values, inequalities, and contradictions on which grand projects are built.\blacksquare
Archives
- Papers of Damodar D. Kosambi (503), Nehru Memorial Museum and Library, New Delhi, India.
- Damodar D. Kosambi Personal File D-2004-003[87-91], Tata Institute of Fundamental Research, Mumbai, India.
- Kosambi, D.D., Director’s Office: Visitor and Assistant files, box 6, Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, NJ, USA.
- Papers of Marshall Stone (A95-32), John Hay Library, Brown University, Providence, RI, USA.
- United States Federal Bureau of Investigation Headquarters File 100-HQ-193907, Marshall Harvey Stone.
Bibliography and Further Reading
- Michael J. Barany, 2016, Distributions in Postwar Mathematics. Ph.D. dissertation, Princeton University.
- Michael J. Barany, 2018, “The Fields Medal should return to its roots.” Nature 553: 271-273.
- Michael J. Barany, 2020, “Organizational Practice in the Heterolingual Archive [Prática organizacional no arquivo heterolingual]. Em Construção: arquivos de epistemologia histórica e estudos de ciêcia 7: 19-27.
- Michael J. Barany, 2020, “Impersonation and personification in mid-twentieth century mathematics.” History of Science 58(4): 417-436.
- Manu Goswami, 2012, “Imaginary Futures and Colonial Internationalisms,” American Historical Review 117(5): 1461-1485.
- Olli Lehto, 1998, Mathematics Without Borders: A History of the International Mathematical Union, Springer.
- Karen H. Parshall and Adrian C. Rice, eds., 2002, Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945. American Mathematical Society.
- Ramakrishna Ramaswamy, ed., 2016, D.D. Kosambi: Selected Works in Mathematics and Statistics. Springer.
- Glenda Sluga and Patricia Clavin, eds., 2016, Internationalisms: A Twentieth-Century History. Cambridge University Press.
- Geert J. Somsen, 2008, “A History of Universalism: Conceptions of the Internationality of Science from the Enlightenment to the Cold War,” Minerva 46: 361-379.
Footnotes
- I have spelled the surname as it appears in the archive documents under discussion. The spelling “Siddiqui” appears to be more standard today.↩