Tautosakos darbai 68, 2024, p. 15–27
ISSN 1392-2831 | eISSN 2783-6827
DOI: https://doi.org/10.51554/TD.24.68.02

Epistolary Becomings: Archival Traces and Diffractive Readings

Maria Tamboukou
University of East London, United Kingdom
https://ror.org/057jrqr44
m.tamboukou@uel.ac.uk
https://orcid.org/0000-0002-6380-4415

ABSTRACT. In this paper, I offer the concept of diffraction as both a methodological approach and an epistemological lens. This dual move has guided my archival research, encompassing various types of archival documents, and has shaped my reading, understanding, and analysis of letters by European women mathematicians, who lived and worked in the eighteenth and nineteenth centuries. The discussion draws on a Leverhulme-funded research project of writing a feminist genealogy of automathographies, tracing the process of becoming a woman mathematician, philosopher, and scientist. I argue that analogue, digitised, and photographed letters should be regarded as distinct types of archival documents, each positioning the researcher in unique, but entangled ways relative to their sources and data. Furthermore, recognizing the interweaving of personal and scientific elements in the correspondence of women mathematicians is crucial for understanding the formation of the female self in the realms of gender, science, and mathematics.

KEYWORDS: archives, diffraction, letters, the personal and the scientific, women mathematicians.

Epistolinis tapsmas: archyviniai bruožai ir difrakcinis skaitymas

SANTRAUKA. Šiame straipsnyje mano siūloma difrakcijos sąvoka veikia ir kaip metodinė prieiga, ir kaip epistemologinė prizmė. Vadovaudamasi šiuo dvejopu požiūriu atlikau archyvinį tyrimą, apėmusį įvairiausio pobūdžio archyvinius dokumentus: skaičiau, gilinausi ir analizavau laiškus, rašytus europiečių matematikių, gyvenusių XVIII–XIX amžiuje. Tyrimas remiasi Leverhulme fondo finansuotu projektu, kurio tikslas yra sukurti feministinę automatografijų genealogiją – atsekti, kaip moteris tampa matematike, filosofe, mokslininke. Mano nuomone, analoginiai, suskaitmeninti ir fotografuoti laiškai turėtų būti laikomi skirtingais archyviniais dokumentais, kurių kiekvienas, priklausomai nuo jame užfiksuotų šaltinių ir duomenų, kreipia tyrėją vis kitokiu sudėtingu keliu. Negana to, atpažinti matematikių susirašinėjime susipynusius asmeninio ir mokslinio gyvenimo momentus yra būtina, jei norime suvokti moters asmenybės tapsmą lyties, mokslo ir matematikos sankirtoje.

RAKTAŽODŽIAI: archyvai, difrakcija, laiškai, asmenybė ir mokslas, matematikės.

Received: 05/09/2024. Accepted: 07/10/2024

Copyright © Maria Tamboukou, 2024. Published by the Institute of Lithuanian Literature and Folklore Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

LETTERS AND FEMINIST GENEALOGIES

In this paper I draw on a research project of writing a feminist genealogy of automathographies, a concept denoting the autobiographical desire of becoming amathematician, which was coined by Paul Halmos (1985). By gendering P.Halmos’ desire, I argue that it is essential to throw light onto the social, cultural and political practices that some women mathematicians deployed in surpassing the restrictions and limitations of their gendered position and in following an academic career in the field of mathematical sciences.¹

In thus working genealogically, I look at the personal, literary and philosophical writings of six women mathematicians: the French Émilie Du Châtelet (1706–1749) and Sophie Germain (1776–1831), the Italian Maria Gaetana Agnesi (1718–1799), the Scottish Mary Fairfax Somerville (1780–1872), the English Ada Lovelace (1815–1852) and the Russian Sofia Kovalevskaya (1850–1891). Apart from their mathematical and scientific work, É. Du Châtelet, S. Germain and A.Lovelace wrote philosophical essays, M. F. Somerville and S. Kovalevskaya wrote autobiographies, while S. Kovalevskaya also wrote poetry, novels and theatrical plays. What unites these six women, however, is that they all wrote letters, so letters have become very important in this research.

Letters in general and epistolarity in particular have been at the heart of my research for several years and I have written extensively about the intricacies of reading letters in excavating hidden genealogies in women’s lives (see Tamboukou 2003, 2010, 2015). What I have observed, however, is that the rich body of literature around letters has not considered the importance of scientific correspondences in general, and mathematical correspondences in particular, in the excavation of the female self, that is, in understanding the process of becoming a woman mathematician and scientist. I have been struck by this omission, and this paper focuses precisely on epistemological and methodological issues in analysing women mathematicians’ letters in the process of writing a feminist genealogy of automathographies.

In reading the letters of women mathematicians – whether addressed to their tutors, supervisors, fellow mathematicians, or even friends and lovers – I have employed the lens of what I have configured as “epistolary sensibility” (Tamboukou 2020). This approach involves engaging with letters not merely as “documents of life” (Plummer 2001), but also paying close attention to their epistolary traits. These include their relational and dialogic nature, their ephemerality, the power dynamics within the correspondence, the significance of salutations and greetings, the varied time frames of writing, posting, reading, and responding (or not) to aletter, the material aspects of the epistolary act, and the narrative extravagances inherent in letter-writing. An important part of my “epistolary sensibility” has always been the fact that all letters are always, already archival documents and in situating my subject position, I am both a researcher in the archive, as well as “an external reader” of them, to use Janet Altman’s (1982) famous term. In this context, an important aspect of my research is the experience of working in different archives and with different epistolary documents, both analogue, digital, digitised, and photographed (see Tamboukou 2023a). I have also worked with published renditions of letters, some edited and selected, others full publications, most of them transcribed, but also some published as photographs of the originals – what Liz Stanley has called the “ur-letters” in her famous theorisation of “the epistolarium”:

The idea of the epistolarium can be thought about in (at least) three related ways, with rather different epistemological complexities and consequentialities: as an epistolary record that remains for post hoc scrutiny; as “a collection” of the entirety of the surviving correspon­dences that a particular letter writer was involved in; and as the “ur-letters” produced in transcribing, editing and publishing actual letters (or rather versions of them) (Stanley 2004: 218).

A growing body of literature has emerged on digital and digitised archives, exploring how they have transformed the epistemological nature of archival research as a whole, and specifically how we approach, understand, and analyse epistolary documents.² Moreover, most archival researchers know by now that even when we work in classic archival spaces like museums and libraries, and have access to analogue documents, the scans and photos that we are usually allowed to take – often without restrictions and expenses – have gradually changed the ways we experience archival work, as well as the ways we analyse digitised epistolary documents. As L. Stanley and colleagues have simply put it in creating an online archive for Olive Schreiner’s letters, “transcriptions are not ‘the letters’ themselves– but then, neither are jpeg images of letters ‘the letters’ either, but another two-dimensional representation”.³ Contextual loss is amongst the most important epistemological issues in the understanding and analysis of archival documents in general and letters in particular.

What is the difference then between reading a handwritten letter in the archive, and later its image version in the researcher’s files, a digitised version of ahandwritten letter in an online library or archive, a published version of handwritten letters, or atranscribed and published letter in both historical and contemporary publications? This is a question that I have considered through the lens of diffraction, a notion that derives from optical physics. As an optical phenomenon in classical physics, diffraction follows the bending of waves as they move through passages or encounter small obstacles: think of how a rainbow of different colours is being formed when white light enters a prism. What happens when two or more waves arrive at the same point is also interesting, since unlike particles, waves can overlap at the same point in space creating superposition effects. Consider the all too familiar moment when we throw pebbles in a lake: the waves that appear as an effect of this disturbance interfere with each other in different ways, depending on their properties and corresponding forces: they can create a more intense wave together, producing constructive interferences or they can cancel each other out in the mode of destructive interferences. Thesuperposition of most waves, however, produces a combination of constructive and destructive interferences, which vary from place to place and time to time. For feminist philosopher Donna Haraway (1997), diffraction becomes a metaphor for the effort to see difference and its effects at the bottom of the mirror or on the surface of a pond: “Diffraction patterns record the history of interaction, interference, reinforcement, difference. Diffraction is about heterogeneous history, not about originals” (1997: 16).

Following a vibrant body of feminist literature that has deployed diffractive methodologies in research,⁴ I have taken diffraction as an approach for reading ideas and approaches through one another, attending to the nuances of theoretical, epistemological and methodological differences – in the case of this paper, differences in the modalities and forms of epistolary documents. Put simply, diffractive ways of reading and analysing epistolary documents are not only about how I understand the content and discourse of a letter as a static entity or meaning. It is also about how I tune into the various rhythms of meaning and understanding. In the light of wave phenomena, the meanings that are enacted through the reading and analysis of different types of epistolary documents keep creating a variety of superposition effects, producing constructive and destructive interferences. Finally, diffraction not only alters how I perceive differences in epistolary documents by tracing their “archival trails” (Nygaard 2024), but also influences how I position myself in relation to the letters I study, as I seek to understand the process of becoming a woman mathematician in the eighteenth and nineteenth centuries.

In the mode of diffraction then, touching actual letters in physical archives has triggered intense feelings of connection with corporeal and material traces, in short, the tactile properties of the epistolary act – the paper, the envelope, the ink, the handwriting. Touching is a pathway to feeling and understanding, although tactile ways of knowing have been downplayed and devaluated, since “visual detachment has replaced tactile engagement, entrenching the divide between body and mind”, as textile artist Solveigh Goett has remarked (2010: 170). The tactile and visual properties of the epistolary documents are thus entangled in the researcher’s perception and understanding, since while the letter in the archive is always visible, it also has a specific smell and even a specific sound, as its pages and leaves are turned, while the researcher flicks through them, arranges and rearranges them, immersing themselves in a particularly tactile process of making sense. But “touch is slow, sight is fast”, Goett has further observed (ibid.), and indeed the slowness of the tactile process runs in parallel with the slow rhythms of reading and copying in the archive that Arlette Farge has influentially theorised:

In the digital age this act of copying can seem quite foolish. [...] And it would indeed be foolish, stubborn, maybe even pridefully obsessive... if this exact recopying of words did not feel somehow necessary, an exclusive and privileged way of entering into the world of the document, as both accomplice and outsider [...]. This flow of words can sweep you off into unexpected directions, taking you to a place poised somewhere between the familiar and the exotic (2013: 16).

In my previous work, I have explored the trance-like states of meaning-making and understanding that arise from the slow process of handling, reading, and transcribing letters in the archive (see Tamboukou 2016). However, I have also acknowledged that due to constraints of budget and time, the “real letter” will inevitably be scanned or photographed, leaving the researcher to return primarily to its visual image. This is where the visual and the tactile create superposition effects in the researcher’s diffractive reading, since it is in the middle of this slow process of touching, reading, copying, and in effect rewriting letters that the researcher’s understanding emerges, and new ideas and insights arise. In this context the letters themselves are being transformed, not just as analogue or digitised documents, but rather as components of complex entanglements between the analogue and the digital within the space/time/matter of archival research.

But while memories of engaging with real documents in the archive are diffused and diffracted with reading and writing practices at the researcher’s desk, what happens if the researcher only has access to online or published letters, often edited and inevitably selected? Since “the digital revolution” is well under way, we need to accept that in the future more and more researchers will only have access to digitised or published documents, whether online or in print. Even when given the opportunity to visit an archive or library, the original manuscripts may be unavailable due to preservation and protection concerns. This was the case with S. Kovalevskaya’s letters at the Mittag-Leffler Institute in Sweden, where Iwas granted access only to copies rather than the original documents, with the exception of three photographic albums. I have to admit that when engaging with manuscripts, notebooks, papers and “real” letters of women mathematicians, either in the Ambrosiana Biblioteca in Milan, the Moreniana Biblioteca in Florence, the British Library in London or the Bodleian Libraries in Oxford, I could not believe the fact that I was still allowed to unbox, touch and flicker through such important documents without restrictions. I was almost feeling guilty that I was not asked to wear gloves, and I was frightfully apprehensive of the way I handled these documents. Above all, I was feeling really lucky that I was still able to do it. For how long more though, I kept wondering.

There is no question that the researcher’s feeling of touching the imaginary real cannot be substituted by the visual or the digital. But since digitisation is increasingly becoming “the new real”, we just need to accept it and get on with it. Thus, when considering the epistemological implications of working with digitised documents – ideally better curated, organised, and presented – the first point to acknowledge is that “wholeness” or the notion of “touching the real” is ultimately unattainable. This holds true even when dealing with analogue or unpublished epistolary documents. As Carolyn Steedman has influentially observed, “you find nothing in the Archive, but stories caught halfway through: the middle of things: discontinuities.” (2001: 45) In this context, the letter preserved and discovered in the archive should always be considered alongside the one that was lost or destroyed. Just as we interpret voices, we should also begin to interpret silences and absences, or find ways to incorporate them into our analysis and understanding.

In the case of women mathematicians’ letters, it is not only the differences between analogue and digitised letters that we should consider, but also that many of their letters have only been found in draft forms, that many letters have been lost, damaged or destroyed, and that even in several extant letters we have very few traces of personal feelings and thoughts. And yet, multi-modal, fragmented and discontinuous as they are and will always be, analogue, digitised, edited, translated and published letters have left traces of “epistolary waves”, which, as they ebb and flow, create a pattern that has a meaning in understanding the process of becoming a woman mathematician in post-Enlightenment Europe. Here, the researcher’s imagination is important and in my most recent book, I have used this motif of “epistolary waves” in analysing the letters of four revolutionary women in the nineteenth and twentieth centuries (see Tamboukou 2023a). What is also important when working with fragmented letters and documents in the archive is that the researcher should not prolong and further obscure their fragmented state, but should rather attempt to mark and trace their “archival trails” (Nygaard 2024) in the process of reassembling the archive, as I have argued elsewhere in my work (Tamboukou 2017). In the next section of the paper, I will draw on an example from S. Germain’s scientific correspondence to illustrate some of the points I have previously discussed.⁵

THE PERSONAL AND THE SCIENTIFIC IN SOPHIE GERMAIN’S CORRESPONDENCE

S. Germain was a French mathematician, physicist, and philosopher who made significant contributions to number theory, elasticity theory, and the study of acoustics. Born in Paris to a wealthy family, S. Germain pursued her passion for mathematics against societal norms that discouraged women from studying the sciences. She educated herself using books from her father’s library and initially corresponded with prominent mathematicians like Carl Friedrich Gauss under the male pseudonym “Mr. LeBlanc”. When she eventually revealed her true identity, C. F. Gauss expressed great admiration for her abilities. S. Germain is best known for her work on Fermat’s Last Theorem, where she developed what is now known as “Germain’s Theorem”. Her research in elasticity led to her winning the prestigious Paris Academy of Sciences prize in 1816, making her the first woman to receive such recognition.⁶

S. Germain never married or had children, and after her untimely death at 55 from breast cancer, her letters were scattered, lost and partially found in different collections all over Europe and in addition, some of them were found only as drafts, since not all of her recipients kept her letters. In her correspondence with the famous mathematician Adrien-Marie Legendre, for example, we only have her draft letters and not the ones that were actually sent. And yet, draft letters can sometimes reveal more about the disposition and frame of mind of the sender, as the following draft letter that I found in Moreniana Biblioteca in Florence, which Ivisited in May 2023, vividly demonstrates: “I have read with the greatest attention the memoir that you have made me the honour of sending me”,⁷ S. Germain wrote on 2 July 1819, in a letter that, according to the archives’ catalogue, is still marked as addressed to Libri.⁸

Since this is a draft of the letter that was actually sent, we can see that she had initially written “the greatest satisfaction”, but this word was deleted and was replaced by the more appropriate “attention”. I was very much interested in this deletion, which does not appear in the published transcription of the letter by Andrea Del Centina, although he comments that “Germain paid much attention to the choice of appropriate words and phrases in the letter” (2005: 63). And yet a general reference to “the choice of appropriate words”, as well as the omission of the deletion of “satisfaction” from the transcription diminishes the analysis of S. Germain’s epistolary discourse, given the importance of feelings in her overall philosophy of science, as Ihave discussed elsewhere in my work (see Tamboukou 2023b).

The date of the letter is also important, since it was sent five years before S.Germain and Libri actually met in person in Paris in May 1825. Libri’s biographers have previously asserted that his relationship with S. Germain started in 1819, based on this draft letter (see Maccioni-Rujo, Mostert 1995: 342, n. 27). But Libri was only sixteen years old in 1819, and although he was about to graduate from the University of Pisa, his first important paper, Memoria sopra la teoria dei numeri, which was praised by eminent mathematicians of his time like Charles Babbage, Augustin-Louis Cauchy, and C. F. Gauss, was only published in 1820. So important was this paper that in 1823, Libri was appointed to the chair of Mathematical Physics in Pisa, a position he would soon leave to pursue a career in Europe.⁹

Their different position in the field of mathematical sciences notwithstanding, S. Germain would never feel uncomfortable and in search of “appropriate words” while addressing a sixteen-year-old mathematician, neither would she know of him at this stage. As A. Del Centina has further commented in his careful reading of this letter, S. Germain refers extensively to Louis Poinsot’s memoir, Sur l’application de l’algèbre à la théorie des nombres, which had been read at the Institute on 27 April 1818. S. Germain had also mentioned this memoir in her correspondence with C.F. Gauss, in a letter dated 12 May 1819. According to A. Del Centina, these two letters are helpful in reconstructing S. Germain’s mathematical work on Fermat’s Last Theorem (2005: 64).

What transpires from the Moreniana draft letter then is that in writing to an established mathematician like L. Poinsot – who had just written a memoir so close to her long-standing interest in number theory – S. Germain must have felt that intense feelings, like “satisfaction”, had no place in her epistolary discourse. There are actually two drafts of this letter in the Moreniana Library. The second draft has more deletions of more substantial mathematical parts, which shows that S.Germain was really struggling to be perfect, not only with her prose – “attention” instead of “satisfaction” – but also with the mathematical parts of her epistolary exchange with L. Poinsot. What is definitely interesting to consider here is how an error in the archives’ catalogues can lead to misconceptions in the history of mathematics, how accurate transcriptions are important in filling the gaps of contextual loss, but also how important it is to consider letters as “units within aunity” (Altman 1982), as A. Del Centina’s careful study of S. Germain’s two letters to L. Poinsot and C. F. Gauss demonstrates, not only in identifying the recipient, but also in terms of the evaluation of her contribution to mathematics.

S. Germain’s relationship with Libri was significant not only because they exchanged ideas on mathematical problems, but also because they developed afriendship mostly through correspondence. Eventually, Libri became her first biographer and took on the role of archiving her letters and papers. It is therefore in their correspondence that we can trace her feelings in relation to how she was treated in the Parisian mathematical circles. This is what she wrote to him on 15 September 1826:

I am not surprised at your eagerness to renew conversations that cannot be found elsewhere than in Paris, all the doors are open to you. As I am not allowed to go to any sessions, I find myself almost as foreign to the movement of sciences as if I lived in another country. And yet, I prefer to be here even more than elsewhere because sometimes it happens to me to find by chance an opportunity to instruct myself.¹⁰

This intimate letter reveals indeed how women mathematicians felt knowing that it was only through letters that they could have a sense of belonging to the academic community, although they continuously felt the effects of exclusion. And yet it was in the same letter that she exchanged ideas about mathematical problems and formulas, thus bringing together what I have identified as the couplet of “the personal and the scientific”.

In further considering S. Germain’s meta-archive, her “ur-letters”, I was also particularly interested in the importance not only of different transcriptions and translations but also of different citations. This is especially significant because S.Germain’s mathematical and philosophical works, including her letters, have not been translated into English, except for her correspondence with C. F. Gauss (see Musielak 2020) and a few selected letters or fragments included in her two major scientific biographies. It is here that full and accurate citations can direct researchers of S. Germain’s work in tracing “archival trails” (Nygaard 2024) of her extant correspondence but can also enable the analysis of her epistolary discourse and the transferability of her ideas. Throughout the writings emerging from my project, I have thus given full references not only to the archival sources of women mathematicians’ letters, but also of their transcriptions, publications, as well as existing translations, including my own. Here I have followed Sara Ahmed’s important remark that “citation is feminist memory”, it is “how we acknowledge our debt to those who have come before; those who have helped us find our way when the way was obscured because we deviated from the paths we were told to follow” (2017: 15–16).

DIFFRACTIONS AND ENTANGLEMENTS

In this paper, I have looked at the role of letters in tracing the process of becoming a woman mathematician in the eighteenth and nineteenth centuries in Europe. Indoing so, I have deployed the notion of diffractions, as a way of reading and analysing epistolary documents in different formats, as well as in a variety of archives, both analogue and digital. Following L. Stanley’s important argument that letters exhibit “emergent properties” (2004: 203) and thus resist “researcher-determined concerns” (ibid.), I have drawn on examples from S. Germain’s epistolary archive. My focus has been on the interplay between analogue, digitised, and published letters in terms of their form, as well as the intricate entanglement of personal and scientific elements in their content.

What I have argued is that analogue, digitised, and photographed documents need to be treated as diverse types of documents that position the researcher differently vis-à-vis their sources and data and thus raise a range of methodological and epistemological challenges that need to be embraced and acknowledged in the analysis, as well as the writings that emerge from the research. In terms of content, mathematical correspondence has often been hailed as the way par excellence of filling the gaps of women’s exclusion from institutionalised and formal science education in the eighteenth and nineteenth centuries.¹¹ In this context, S.Germain’s correspondence has been mainly discussed and analysed in terms of the mathematical problems that it has tackled and addressed, as evidence of her overall contribution to the history of mathematical sciences. But while “the personal and the political” is a recurrent motif in feminist theories and research,¹² the couplet of “the personal and the scientific” has not been considered in the literature of gender and science, with the exception of the theme of domesticity in science.¹³

What are the effects of considering the personal and the scientific in women mathematicians’ correspondence then? As I have suggested in this paper, S.Germain’s epistolary exchanges are the only traces we have in tracking the process of how ayoung girl excluded from all formal educational and academic institutions managed not only to study mathematics, but also to make some important contributions in pure and applied mathematics, as well as in the philosophy of science. Apart from some short biographical notes, however, there is very little we know about S. Germain’s life and even less about her personal feelings and relations. And yet her letters offer some glimpses in the way she positioned herself in the margins of the Parisian mathematical community. Whether addressed to the famous C. F. Gauss, the members of the French Institute, or her friend Libri, S. Germain’s letters have become important documents in the history of mathematical sciences, at the same time of encompassing her love and passion for mathematics, as well as enlightening her feelings and sufferings. The process of becoming an acknowledged woman mathematician was long and complex and although S. Germain chose not to leave behind any autobiographical traces, such as journals, diaries, or memoirs, her mathematical correspondence can be taken as a collection of “documents of life” through the rare entanglement of “the personal and the scientific”. More widely the project has revealed the complexity of the six women mathematicians’ archives and meta-archives, along with the polyvalent discourses and mythologies that have developed around them (see Tamboukou forthcoming).

ACKNOWLEDGEMENTS

I would like to thank The Leverhulme Trust for supporting the research underpinning this article with a Major Research Fellowship [MRF-2021-004]. Many thanks also to the organisers and participants of the International Methodological Seminar on “Heritage of Ordinary Letters: Research Goals and Methodologies”, held at the Institute of Lithuanian Literature and Folklore, 25-26 January 2024, for the lively discussions we had, when this paper was first presented there.

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Edited by Jeremy Hill