How to Read the Mathematics Index Cards

By J.P. Ascher, Michael J. Barany, and Bo van Broekhoven, from the SIGMA Project Team

Our research team has been studying the history of international and global mathematics, building on Barany’s longer-running investigations of this topic. The Rockefeller philanthropies and their fellowship programmes played a considerable role in the transformation of mathematics in the twentieth century into a discipline where routine long-distance travel and communication were commonplace expectations of elite professional activity. Rockefeller money as well as Rockefeller ways of evaluating people and projects left a lasting legacy for mathematicians, which Barany has examined (for example) in the context South America’s intercontinental connections or the changing personae of elite mathematics. This research has also involved extensive consideration of Rockefeller bureaucratic practices, including close readings of fellowship files and index cards for specific mathematicians.

If Rockefeller loomed large for mathematics in the first half of the twentieth century, the same could not be said in reverse. While the field was a sustained interest of officers of various grant and fellowship initiatives in the Rockefeller orbit, it was never an especially large part of any Rockefeller portfolio. Mathematics does not seem ever to have occasioned special consideration or exceptional handling, while at the same time was among the fields where the mobility of researchers could be presumed (often incorrectly, as Barany has shown) comparatively unproblematic. It is thus a good index subject for getting a sense of normal Rockefeller operating procedure, while in aggregate still keeping to a scale that can be taken in and appreciated by hand.

This blog post looks at the ‘Mathematics’ subcorpus within the impressive and important larger Rockefeller Index Cards project. Our team has examined the few hundred records tagged as ‘Mathematics’ from the 14,650 total records of fellowships between 1921 and 1971. We report some initial observations and contextualisations at several different scales, from the subcorpus as a whole to clusters and individual cards to typographical details within a single card. These shed new light on how Rockefeller philanthropies intervened in mathematics, and what their interventions in that field can tell us about the wider operation of Rockefeller fellowship funding and intelligencing.

A Bird’s Eye View of Mathematicians’ Mobility

The fellowship cards captured by the extraordinary digitisation project are stored in the Rockefeller Foundation archives in long boxes, with fellows filed by name within groupings by the fellow’s home country. (We shall see below how the attribution of countries to fellows could be more problematic than first meets the eye.) On the physical cards, the country is typically typed in a capital letters in a heading at the top, so that one could quickly locate a country of interest while flipping through a file of cards from above. In the digital database, these country headings appear as the “benefiting country”. and then by the name of the fellow.

This filing system embeds a core principle of Rockefeller fellowships: that they are temporary.
A fellow lives permanently, as some cards describe it, in one place, but goes temporarily to another place to advance their scientific career. This temporary move, whether domestic or international, stands primarily to benefit the country where the fellow is permanently based, where the return on the Rockefeller investment will accrue year upon year as long as the fellow remains active in science.

Destination countries were, correspondingly, established centers where fellows could be expected to acquire the experience, skills, and connections to make for a profitable investment. Fellows had some influence on where they were sent, but were also heavily influenced by the views of their field developed by those responsible for awarding the fellowships. A consequence is that a map of fellows’ destinations reflects the Rockefeller-mediated consensus of where the international centres of scholarship were.

Consider the two maps below, one for 1921 to 1930 and another from 1930 to 1945.

Figure 1: Mathematical fellow mobility from 1921 to 1930:

The first map uses size to show how many fellows travelled to that location. Thus we can see that Paris, Göttingen, and Rome, followed by Chicago, Princeton, Cambridge (US), Munich, and Amsterdam, received the most fellows. The colour in the map represents how many fellows travelled from that place, with darker indicating more fellows. Thus both Göttingen and Paris were prominent as both origins and destinations. Princeton and Rome were origin points for similar numbers of fellows, closely followed by Cambridge (US), Cambridge (UK), and Hamburg.

We know from the secondary literature that there were significant changes to the Rockefeller mathematics profile from the 1930s, and these come out by comparing our first chart to the second.

Figure 2: Mathematical fellow mobility from 1930 to 1945:

The sizes and colours follow the same approach as above, so we can immediately see that Princeton has come to dominate the number of fellows received. Similarly, Ann Arbor and Chicago have both grown, as has New York. Paris and Göttingen, however, have nearly disappeared.

The colours tell another story too. The lines on both graphs represent a fellow travelling from one place to another. On the first graph, the dark Paris and Göttingen seem to host a number of exchanges with the core. Princeton, Rome, Göttingen, and Paris seem to exchange fellows back and forth. On this new graph, no major places to visit are directly connected. Every other major centre is connected by a smaller place–small here meaning that it doesn’t host many fellows.

This seems to suggest a shift around 1930 from exchanging fellows between centres in Europe and the US, to a system where fellows coming from all over the world are brought to centres in the US or Rome. From a bird’s eye view, we see Rockefeller fellowships shifting to a hub-and-spoke model of elite centralization, departing from a pattern of inter-elite integration from the 1920s.

Looking Closer: Mobility in the Cards

The details on the recorder cards tell a more complicated story, one that nuances and enriches the big picture we have just seen. Consider a typical card, like the below for Alexander Weinstein.

The cover card for Alexander Weinstein’s records: © Rockefeller Archive Center. Reproduced with permission.

Weinstein was born in Saratov, Russia but his family emigrated to Germany early in his life. After graduating from Göttingen, Weinstein moved to Zürich, Switzerland, which is where he was when he received his Rockefeller Fellowship. Much of this trajectory can be found on his index card, but most of it was added after the card was initially produced.

The mathematics cards seem to have been produced when the fellow received the award, with more details added later. Here we can see that the card initially did not record Weinstein’s age or place of birth, but his permanent address. The first typing regime, which can be distinguished by the shade of ink as well as the shape of the capital letter ‘A’ describes his name and proposer. Later on, specific dates and countries were added. Look, in particular, at the cross bar of the capital ‘A’ in Russia, Switzerland, and Alexander. The first typing event, in the lighter ink, has a lower cross bar, but the darker and later event has a slightly higher bar indicating a different typewriter was used. Notice too that the fellowship year is typed in the lighter ink, but both countries in darker ink and out of line. This card would appear to have been initially organised by fellowship year, but later by country. When it was organised by country, it was initially as Switzerland or Russia, then for some period as both (perhaps even only a moment during revision), and later as just Switzerland.

Yet, at the foot, we also see the card being distinguished from the American geneticist and drosophila researcher of the same name. A later card in Weinstein’s file shows the moment of confusion, where it is not clear if the mathematician Weinstein studied biology at Johns Hopkins or not.

A later card for Alexander Weinstein’s records: © Rockefeller Archive Center. Reproduced with permission.

By the 1950s Weinstein had immigrated to the United States, though the card still preserves his benefiting country as Switzerland. Whatever administrative activity had come up, someone had confused him with another American, leading to the wrong fact on this card that is noted on the cover to prevent further confusion.

What this demonstrates is that the Rockefeller Foundation itself was deeply concerned with countries of origin, even where a country of origin does not make a lot of sense for the individual. The additions of the filing country on the headline appear around the 1930s, which is why we chose to divide by that year when generating the above maps. The typographical details of Weinstein’s card suggest that, more than a reflection of the changing geography of mathematical research, the shift between our two charts is indicative of a change of the foundation’s understanding of its own task. Beneficiary countries became, at that juncture, a new organising salient for Rockefeller programmes. Staff accordingly re-filed cards, matching bureaucratic practice to programmatic shifts in emphasis and attention.

Thus the closing map, the home—permanent—benefiting location of maths fellows from 1930-1945 shows whom the foundation was bringing to the US, Rome, or Cambridge. The size here indicates the number of fellows sent and the colour red indicates very few received, whereas blue indicates comparatively more fellows received.

Figure 5: Fellows leaving from 1930 to 1945:

Here we can see large numbers of fellows going from Paris to Rome or Berlin, Göttingen to Rome, or between Princeton and Cambridge (UK). Most of the fellows going to Ann Arbor, New York, or Chicago were in the United States already, although there are a significant number going from Frankfurt am Main to Chicago. Princeton, Rome, and Cambridge (US) seem to receive the most fellows. This does not reflect the post-1930 structure of knowledge, but the way that the Rockefeller Foundation was imagining the social community of mathematics should function after 1930. For them, there seem to be three international centres, Princeton, Paris, and Cambridge (US), whereas every other centre seems to be closer to regional.

The Rockefeller directories of fellows as collateral evidence

The Foundation published two directories of fellows and a supplement. As part of our investigation, we looked at the the 1972 directory of fellows from 1917 to 1970 at the Royal College of Physicians of Edinburgh, the 1951 directory of fellows from 1917 to 1950, and the supplement of fellows from 1951 to 1955. That the only local copies of these directories that we could locate was at the RCPE is testament to the broader systemic relevance of the fellowship programmes in the fields of health and medicine, a fact corroborated by the statistical profile of fellowships in the larger corpus. The introductions to these directories state the intention to create a model like we can see in the above charts. From the supplement to 1955, Dean Rusk writes in the introduction about how the fellows are sought worldwide to be placed temporarily at a new location.

Typically, the Rockefeller Foundation Fellow lives in a foreign country, although since 1914 more than 1,250 have come from the United States. He has completed his formal training and the usual advanced degrees. He is employed in a university, research institute, or in a post of government. … If the prospect is highly promising and the institution is anxious for him to have this opportunity and will have a post for him on his return, the next question is whether available funds can meet his needs in competition with others similarly qualified. (iii–iv)

This practice of awarding fellows who have a secure position, typically not in the United States, for travelling to another location to study with the best is repeated in each directory. There is no clear place where the introductions suggest that all mathematicians should go to a handful of places, but the concept of merit seems to be sufficient. The Foundation’s officers had close ties with the mathematical communities at the University of Chicago, Harvard, and the Institute for Advanced Study at Princeton. Some they funded directly, others occasionally, but the Foundation generally sought to spend money efficiently by focusing on few known and established centres. Whether or not particular centres of mathematics themselves were inevitable, the award pattern would deveolp some centres of mathematics over time. Additionally, past fellows often supported identifying and reviewing new fellows: the officers had limited mathematical training themselves, so relied on people in the same social and scholarly communities as their beneficiaries.

The situation then is that the officers and mathematicians would think that these particular places were the centres of the best mathematics, and their general consensus about where the best centres of mathematics were would drive additional support and funding to those centres. The charts above also seem to reflect this increasing centralisation.

The directories themselves also arrange fellows by country as an appendix at the end. For the 1951 and its supplement, they arrange the fellows by country of current residence, while marking deceased fellows with a small cross. This demonstrates the world-wide scope of grant making, but also seems to serve as a sort of map of where to find the best and the brightest.

These directories were presumably the result of rearranging the cards being discussed here. The introductions describe sending out a questionnaire to update their records and using those records to write entries. Spot checking some of the mathematical entries, it seems clear that they were written from the contents of the cards, which matches with the written evidence on the cards of them being used for several activities. It seems plausible that the rearrangement that occurred in the 1930s was to order the cards based on country of current residence. This would serve the internal functions for identifying particular people in each country to review and recommend. The directory, then, represents a printed version of an internal document.

The 1971 directory, however, has been arranged another way. Rather than by current country, it arranges fellows based on country of origin, but warns that there are some omissions and errors. In particular, fellows who couldn’t have responded to the questionnaire for the 1951 directory because of the disruption after the war have been omitted from both the 1951 and the 1971. The directory explains,

Every effort has been made to reach by mail each of the awardees who responded to the Foundation’s questionnaire in 1950, as well as those who have held fellowships or scholarships between that time and December 31, 1968, in order to obtain up-to-date information concerning their careers. Unsettled conditions and the disruption or communication during and following the two world wars seriously interfered with attempts in 1950 to locale many award recipients; as a result, several hundred former Foundation fellows were not listed in that directory. In view of the lapse of an additional twenty years, the decision was made not to attempt now to remedy this situation. we regret that it may disappoint some former fellows who might wish to have their names included. (x)

The fellows, then, have been rearranged under the country that “is usually that from which the fellow or scholar was appointed or in which he has been pursuing his professional career.” (x) The new arrangement makes sense practically: more and more of the fellows are no longer living, and the foundation did not get updated information for all the fellows, but every fellow came from somewhere and worked somewhere. The appendix can then list one of these countries easily because it is already on the card. The main body of the directory is alphabetical, so it presumably draws on the set of cards arranged alphabetically, but not necessarily physically rearranged. The directory may have been generated with the aid of computers.

Omit for IBM: © Rockefeller Archive Center. Reproduced with permission.

A few of the cards have a note to “omit for IBM” like the above, but most of the cards have a five digit number in the same colour ink and similar hand as below. These numbers have a check mark in another coloured ink, which likely represents a checking process. It seems plausible to me that IBM assisted with a preliminary digitisation of these cards for making the 1971 directory. Whatever the order the cards were in, a 1970s era database or collection of punch cards could produce the appendix and–possibly–the alphabetical list for the directory. The IBM System/3 appeared in 1969 and required hand-coded punch cards, so it seems plausible that the numbering and checking are the result of manually entering these various cards into a database.

Possibly included for IBM: © Rockefeller Archive Center. Reproduced with permission.

These directories, however they were produced, were reorganised and indexed in different ways. The information architecture and design of their reorganisation seems to have been done to reflect the strategies and beliefs of the Foundation as much as reflecting the underlying cards. Thus as historical data, these cards need to be used carefully with external checks: the patterns they illuminate may be actual, aspirational, or even artificial.

The cards as evidence for the Rockefeller Foundation’s evaluation of and engagement with its fellows

Next to recording the international movement of fellows and showing the internal processing of Rockefeller Foundation fellowships, the cards also function as historical evidence for how a distributed Rockefeller bureaucracy evaluated and engaged with its fellows. In addition to the fellows’ benefiting country, the institutions they visited, and their career trajectory, some of the cards contain further biographical information. Though the information varies in nature, including remarks on fellows’ language abilities, their political activity, their character, and even their physical stature, these notes seem to relate to the successes and difficulties of the fellows in their pursuit of mathematical studies and research.

The Rockefeller Foundation seems to have been sensitive to imposing personalities and their potential to support mathematical work and influence. The cards on Luis Fernando Nanni’s 1942-1944 fellowship, for instance, link together his language abilities, mathematical abilities, character and his impact on international mathematics. In a comment added to the card on 12 January 1943, S.S. Wilks first informs HMM (Harry Miller) that Nanni has caught up on the necessary deficiencies in mathematical knowledge and English ability. In addition to this diligence, Nanni “has a pleasant personality which should be a distinct asset to him in extending his influence when he returns to Argentina.” ^[Rockefeller Archive Center, Rockefeller Foundation records, fellowship recorder cards, SG 10.2, Luis Fernando Nanni fellowship recorder card, card #2 front and back] The concern here seems not to be for Nanni’s personality in itself, but for his personality as a tool for and indicator of his future impact on Argentinian mathematics.

Similarly, Morris Sika Alala’s personality seems to have been considered in light of its ability to ensure Alala’s integration into academic institutions. Three evaluative notes, dating from after the end of Alala’s fellowship in early October 1966, all describe Alala as having an agreeable personality. In two of these notes, the statement is followed up by descriptions of Alala fitting in well in the institution, both in terms of his relationships with colleagues and staff as well as his ability to do good work at the university (figure 8). ^[Rockefeller Archive Center, Rockefeller Foundation records, fellowship recorder cards, SG 10.2, Morris Sika Alala fellowship recorder card, card #1 back] The choice of the administrators of the Rockefeller Foundation to include both these elements on Alala’s card suggests that the cards served to record all information that might be relevant to a fellows’ future trajectory, not solely their mathematical merit or achievements.

Figure 8: Permanent recorder card for Morris Sika Alala’s 1965-66 fellowship (card #1, back). © Rockefeller Archive Center. Reproduced with permission.

Like personality traits, political leanings and activity seem to have been recorded on the cards in relation to the consequences they might hold for a fellow’s mathematical future. The cards on Jose Luis Massera’s 1947-1948 fellowship document a complex tension between Massera’s remarkable mathematical talent and his increasingly evident identification as a Communist. ^[Rockefeller Archive Center, Rockefeller Foundation records, fellowship recorder cards, SG 10.2, Jose Luis Massera fellowship recorder card, 2 cards] Notes from 12 and 29 March 1948 detail speculation regarding Massera’s Communism and its possible discrediting of an extension of his fellowship. Whereas Professor Friedrichs had initially supported the extension, he had changed his mind in relation to Massera’s Communism. A. Franklin had not expected an extension, presumably for the same reason (figure 9). ^[Rockefeller Archive Center, Rockefeller Foundation records, fellowship recorder cards, SG 10.2, Jose Luis Massera fellowship recorder card, card #2 front] While Massera’s mathematical qualities were clearly valued, his political affiliation thus seems to have made continued support from the Rockefeller Foundation a less straightforward and somewhat delicate affair. The cards attest to a complex dynamic, whereby conflicting politics certainly need not prevent a mathematical future.

Figure 9: Permanent recorder card for Jose Luis Massera’s 1947-48 fellowship (card #2, front). © Rockefeller Archive Center. Reproduced with permission.

The card on Aristoteles C. Economou’s 1925-1926 fellowship further attests to this: An extended note from 27 June 1945, the only comment on Economou’s card, treats of Economou’s experiences in a concentration camp in Greece. The comment states that Economou was taken from Greece to Germany in 1943 as a forced labourer, but is still alive and may be freed soon. The note ends by endorsing that, despite Economou’s “previous association with a political party now very much in ill repute”, he remains “valuable material if he can be saved for the future”. ^[Rockefeller Archive Center, Rockefeller Foundation records, fellowship recorder cards, SG 10.2, Aristoteles C. Economou fellowship recorder card, back of card] The card thus notes continued interest in Economou and his mathematical potential despite his problematic political position, likely a Communist one. While differing in the results of their evaluation, the cards on Massera and Economou both seem to reflect the Rockefeller Foundation’s engagement with mathematicians’ political activity as a factor in their possible future in mathematics.

As our team continue to tack between scales of analysis with the Mathematics fellowship card subcorpus, we expect to develop further patterns in the cards’ organisation and contents that show the intersections of Rockefeller intelligencing practice and the disciplinary worlds in which the fellowships and fellows intervened. We are, for example, in a process of analysing distinctions and ambiguities in the cards regarding the kind and level of mathematics that the fellow pursued, and how this related to their career trajectories and the information sought and recorded for their index cards. The modest scale of mathematics within the full Rockefeller portfolio enables us to identify the significance of details as wide as the geopolitics of disciplinary elites and as small as the variations of a typed letter, and to connect them into a richer story of a fast-moving mathematical discipline.