Activities
BRICS Mathematics: Histories and agendas of mathematics in the context of ‘large emerging economies’
Provincializing Modern Mathematics Transactions 16 April 2025

Provincializing Modern Mathematics Transactions 16 April 2025

April 16, 2025

Meeting programme: https://sigma.mathsworlds.org/activities/brics-icms/provincializing/

TUESDAY 15 APRIL

9:15-9:30 - Welcome

The name and conceit for this event comes from Dipesh Chakrabarty’s book Provincializing Europe, which expands on the 1992 article ‘Postcoloniality and the Artifice of History’ in Representations. These works point out the focalization of scholarship, especially historical scholarship, on Europe as the universalist centre of modernity. Similarly, the works out point that current research requires non-European historical scholarship to consider Europe, but not vice versa.

9:30-11:00 - Methods for the Margins

Panel: Stefanie Gänger, Scott Mandelbrote, Sonia Wigh; Moderating: J.P. Ascher

Mandelbrote: Can we explore early modern history and mathematics in provincial terms? The calculating society, and with it early-modern objectivity along with its accompanying systems of knowledge, had to come into being in particular ways including in the societies that came to be modern English society. Consider the texts of Gilbert Clerke, a late 17th-century reader and critic of Newton: Clerke was provincial in a way, but also up to date, connected. Historians have struggled to understand early modern and premodern literacy, and we should also be thinking about what numeracy means in these societies. Early modernists will know the classic article by Keith Thomas. Consider the correspondence between Clerke and Collins: Collins was not an extensive user of mathematics but facilitated the exchange of mathematical ideas, used calculating practices, was interested in improving teaching of mathematics. Not all figures involved in the creation of a mathematical culture in early-modern period currently have a place in the history of mathematics. Can we change the nature of the problems that we think mathematics was trying to solve, not just as natural philosophy but answering problems from everyday lives.

Queries raised:

  • What does numeracy mean in time, place, and within communities?
  • What are the provinces provincial to?
  • How are mathematics taught within and outside of provinces?
  • What problems are mathematics trying to solve?

Gänger: Consider the global history of science, medicine, botany, archaeology, which itself is an analytic and one we’ve chosen to adopt for this conversation. Gänger’s book outlines how Cuzco is centre of a network of archaeologists. Consider lay medical culture, self-medication in the Enlightenment when that was particularly common (healing selves and families was a common expectation)—historians have given new attention to non-doctor medical practitioners around 1800. Gänger has been looking at a different scale of how professional scientists tried to distance themselves from lay knowledge, and this relates to questions of elites and class. There is a strong relationship between class and access to people, resources, materials, and knowledge. We can think of a theory and method of global history: fields of science have a built-in telos of global integration; but historians of science reject grand teleological histories. Integration is pervasive in global histories through interest in connectors, entanglements, and so on. The categories of analysis build in these integrative assumptions.

Queries:

  • What is the role of the amateur?
  • Where does lay knowledge begin?
  • Who are the “other knowers” within your community?
  • What is the topology of the social ground within your community?
  • How do you work on global knowledge without teleology, universalism, or a central global system?
  • How does abstraction relate to

Wigh: Addresses this group as a historian of gender and medicine. She asks: “Are gender and sexuality useful categories of historical analysis beyond the modern?” (from Afsaneh Najmabadi, ‘Beyond the Americas: Are Gender and Sexuality Useful Categories of Analysis?’, 2006, p.11.). The decoupling of gender and sex has driven a lot of work in the field of gender and medine, particularly moving away from European perspectives. The western perspective creates a relationship between sex and gender, and their relationship to rights (for instance the work of Monica Green), but this may not be meaningful outside of that context. Research has looked at texts from the subcontinent that are explicitly defining and categorising sex and gender, using different categories than the standard ones in European scholarship. These texts were used to correct and standardise behaviours. To try to move beyond the provincilizing standardisation of the European gaze, Wigh is currently looking at relationships between physicians and female medical practitioners (not: ‘midwives’ but a wider/different category), texts about fertility that indicate existence of class of women who were first contacts for examining and treating disease. These texts indicate a cast of characters who raise questions about locations, contexts, activities, narratives. This history aims to write meaningful histories using problematic categories.

Queries:

  • How does gender move globally?
  • How do we understand gender, sex, and other social categories outside of dominant narratives?
  • How do we move from one dominant social system to another without adopting the second system? Or do we seek a superior dominant system?
  • What do we do when we use the terminology of the dominant system to describe another? Is this just a translation problem?
  • How do we read what a text does not tell you? Who is “someone told me”?
  • How do we react to “so-and-so has already done this work for Europe or such-and-such”?
  • How do we make provincial histories more global?

How do we make histories that are not add-ons to dominant Western narratives?

  • SG we are often starting with European categories in global histories, starting with a kind of lingua franca to bring things together. These disfigure the histories we write. From the 1860s or so our historical actors shared many of these categories, but before then they did not.
  • SW always in danger of essentializing certain things. In SW’s archives, the recipes in texts become simpler and more precise over time. Is this a kind of South Asian Enlightenment? That is completely wrong, a category error, even though this evidence could support that kind of argument.
  • SM are we repeating stories with the same narrative but different details?

Loyiso Nongxa: concerned with divide between Global North and Global South; there can be on-paper non-exclusion that is undermined by different ways people end up excluded: gender discrimination, migration controls, etc.

  • ref: Gänger’s recent article on ‘bourgeois virtues’
  • SW shared experience of researching 19th century Iran; connect with authors of relevant articles. The way to be mindful of not excluding groups that have traditionally been exluded is to broaden your search.
  • SM what is the mathematics needed to build something like a custom house or estate house, how do you approach this question without access to scholarship?
  • SG of course the vast majority were excluded from science in the 19th century, this is a story of inequality. There is now a good secondary literature on epistemology of global history. Danger of connected-ness monopolising our attention. So many more people did not move than did move. There is a danger of looking too much and disproportionately at those who move. Global historians presume increasing integration, but this is a problem.
  • Barany look for evidence of incomprehension and non-movement of ideas, contra implicit universalism
  • SM local practices of numeracy can well be incompatible with one another (how do we understand this in context of ’the world is the same’ – different comprehensibility); the notion that everything is the same everywhere, that the same principles constitute truth, even within language/religious/trading communities does not hold up. Complicatedness of interactions of propagating things that may be understood as universal.
  • SW humoural medicine, e.g., in the different environmental and knowledge contexts of South Asia would not work in the same way in contrast to the portability of textual recipes; ingredients localise universal ways of writing histories of sex. Thinking in terms of ideas and praxis can be helpful.
  • JPA universality can be an important category in the local contexts we’re looking at.

JPA: how can the history of things being understood to be universal be part of provincialized histories?

  • SW e.g. Avicenna. Some ideas on how to solve a problem can be universal, but the way in which these ideas travel and how problems are solved can be localised and context-dependent.
  • SM going back to origins (Hippocrates etc) involves adopting built-in ideas from Greek medicine that locality is essential to health; contrast to histories of Greek mathematics based on claims to universality; one can complicate the reception of that story by looking at the domains of mathematical experience (abstractions, practical domain, practical philosophy). ‘What domain does mathematics, as it is experienced by people, belong to?’ The domain has implications for the set of skills, the agenda, the questions that come with it.
  • MB we can even take this approach to challenge assumptions of universalism attributed to canonical ancient mathematics, recognising univeralism as constructed in particular early modern contexts; historicising and thereby problematising universalism in Western mathematics. Comparison to e.g. Chinese or more recent Western contexts.

JPA: Is universality a method, technique of empire? Is it only a dream?

  • SG standardisation is a technique of empire. Historians of science have a habitus of declaring things provincial and local. Contrast to global historians.

Ursula Martin: What is the relationship between religion and universalising?

  • JPA research on colonial evangelism, mathematics education, and constructing universalism. John Elliot, translation of Bible in Mass., promoted by Robert Boyle. Something potentially akin to translatio imperii - a new empire picking up where the previous left off. What is the role of religion in preparing people for the concept of universalism?
  • SM universalism projects a capability of understanding and assimilation, on colonial frontier or otherwise. When incorporating people into what are held to be universal standards, there is an assumption that the standards are easily understood and absorbed, because universal. Is there ever a conversation about what can be a universal, or is the universal an assumption which then becomes regulative? These conversations occurring in tense places (e.g. colonial frontier) or less tense places such as schools.
  • JPA strategic (vs sincere?) universalism
  • SW looking at texts that start by explaining a concept before describing what is happening. Translating concepts through time and space often alters them; this becomes complicated when the concepts are supposed to be universal ones. Sites of translation (as vs of violence) and understanding, encountering contrasts where there is an expectation of universality.
  • JPA this turns back to intimate relationships, sites of love and community
  • SW sites of sex are almost always still also sites of violence, differential rights, coercion and inequality
  • SG traditionally historians of science and mathematics (pre-1970s positivist tradition) have argued things have moved because it is true ie based on mathematics, ecumenical epistemology. In the 19th century numbers did indeed move more easily, were believed by those in power to move more easily and this became effective, it made the stuff move more easily in fact.

11:15-12:15 - Outsiders, diasporas, migrants, voyagers, connectors

Panel: Michael Barany, Petra Stankovic, Yi Fong Loh, Snezana Lawrence

Petra Stankovic: is working on a project on two Russian mathematicians who emigrated to Yugoslavia in 1920s after October Revolution and left for Belgrade. They were Anton Bilimovich and Nikola Saltikov. Both Bilimovich and Saltikov were known to French and German mathematical circles where they were educated before coming to Yugoslavia. In Belgrade there was a very small existing community of maths and science, so these migrants made quite a big difference. The research draws on several archives including the Serbian Academy of Arts and Sciences with a special interest in the Field of mechanics, e.g. Anton Dimitrija Bilimovich. Both were rapidly assimiliated and integrated, naturalised and made members of the Mathematical Institute of the Serbian Academy of Sciences. They participated in ICMs in 1928, 1932, 1954. There is significant evidence of their social acceptance and integration in the archive that cites political, economic, cultural mutual benefits. Serbia is presented as a refuge for mathematicians, because it allowed continuation of mathematical work. The mathematicians were beneficial for Serbia in providing sufficient mathematicians for an internationally-competitive school. Cultural context include Pan-Slavism, transition from Austro-Hungarian rule to Slavic integration. The Russian involvement in Balkan Wars of 1912-13 resulted in reciprocity in receiving Russian refugees in Baltic countries. This created a polyglot community whose ethnic bonds lead to integration.

MB: this kind of story gets picked up as a trope in the 1930s e.g. in the Bourbaki narrative.

Snezana Lawrence: The Slavic diaspora is very important for development of mathematics as a profession. It is the context of popular psyche that valorized mathematics. The result of this valorization is that Yugoslavian mathematicians were high status, rather than a marginal activity. Mihailo Petrovic was considered an idol. The German sphere of influence extended through Austro-Hungarian empire to Halle, Vienna, etc. which were centres of scholarship for students and researchers from across the region. French engineers and mathematicians made connections to people from Greece and Serbia. These connections were made possible by financial support for studying in France at the Ecole Polytechnique or Ecole Normale. Students from not-yet-independent countries studied in France and came back and established mathematical schools. Mihailo Petrovic (1868-1943) is an example of this migration; a bohemian figure who played music (and travelled for this). He went on expeditions to North and South Pole, attended presidential ball in France, and had a passion for fishing: he was the new image of mathematician. Refugees found a fertile culture for establishing themselves as mathematicians. A Bilimovich (1879-1970) translated Euclid during WW2. The lateness of this translation shows the extent of work still to be done. The diaspora underlines the importance of communication and intercultural contact. Another example that shows how the development of mathematics is interlinked with politics and culture is Gaspard Monge (1764-1818), a friend of Napoleon and called father of descriptive geometry. Monge’s ideas were not well-received in Western Europe, largely because they came through a person who was in the political spotlight. He had a bad reception in England due to wars between England and France at the time. It is important to keep in mind the contexts of communication of mathematics.

Yi Fong Loh: Consider the postcolonial moment at Nanyang University during 1955-1980. The Singapore region influenced by Dutch postcolonial Indonesia geopolitics among other political contexts. For example, contrast the Bulletin of Nanyang University Maths Society 1959 (cover includes Malay script, Chinese – nationalism/regionalism, English – British Malaya colony) and 1980 Southeast Asian Bulletin of Mathematics (different geopolitical configuration). The continuity of community of practitioners was part of the disjunct in the presentation of those practitioners separateness. The source of this is the University Commission report, which includes a table of birthplaces of students. This all occurs in the context of campus protests and political instability. English language is the norm for work. There are many connections and ideas about relationship between SEAMS and national societies and organisations. Th shift to post-colonial context connects to campus protests, while the wider idea of Nanyang as South-East Asia also lives on. Consider the development of mathematics in connection to geopolitics and mathematics as a material practice.

MB: comparison of context of political upheaval and student protests, transnational influence of motifs/tactics of student protest (thinking of comparisons e.g. to Buenos Aires in the late 1950s) YFL link between protests and mathematics itself: centres of expertise; graph theory, transistors, pure mathematics -> different modes of transnationality MB: homology/recognisability of institutions, cultural forms, etc as a condition of localisation and international connection

Themes: national and international relationships, mathematical migrations, the social standing of mathematics, attitudes toward mathematicians in society and the image of mathematicians, use of archives for history, small scientific and mathematical communities, mutual benefits political and economic and cultural, cultural environment of reception, foundations for societies and universities along with their cultural reception, translation, organisation of mathematics as an activity.

Chris Hollings: Suggests the theme of mathematical core courting up-and-coming mathematicians from peripheries. E.g. of German commentary on French-Balkan connection as something to emulate.

  • SL: francophone hegemony; 1930s math journal in Belgrade. e.g. Maurice Frechet correspondence with Yugoslav mathematicians.
  • MB idea of linguistic connectivity between German and slavic is extremely strong until WWI. Geopolitical developments create an opening for other languages, i.e. Francophone, Anglophone mathematics to take up some of that role. There seems to be something distinctive going on when looking at regional differences in greater Europe that might have interesting parallels and contrasts in colonial and post-colonial contexts.

YFL connection between protests and the ‘pureness’ of mathematics theoretically. How is the most technical form linked to transnational movement. How does the pure form of mathematics lead to many forms of speciality in science?

MB importance of the ability to perceive similarity in institutional structures. Connects to an earlier conversation on 20th century structuralisms. Conjunction between thinking institutionally about mathematics and thinking conceptually about mathematics. An important element in possibilities for transportation is modeling organisational practice on other formats, for instance Nanyang university conforming to British universities. Enables a lot of the connectivity that is of interest to the project.

JPA: mathematical nationality, regional identity; can Stankovic speak to this?

  • PS: comparing Belgrade to e.g. French/German centuries-long mathematical traditions, there is an attraction to working in an environment where one can ‘plant one’s own seeds’. When Petrovic returned to Belgrade from Paris there were only 6 PhDs in mathematics there. Culturally proximate environment for refugees.

UM: University of Illinois Urbana Champagne hiring European mathematicians in 1940s-50s with a large international library of mathematics. People who present as outsiders, e.g. Stephen Wolfram.

ref: Graeme Cohen, Counting Australia In discusses academic mathematical research in Australia, based primarily on Australian Mathematical Society materials.

13:30-15:00 - South Africa, Pan-Africa

Loyiso Nongxa, Jerstin Jordaan, Diran Soumonni, Eder Kikianty

Loyiso Nongxa: has been collaborating with EK on history of mathematics in South(ern) Africa. In this collaboration they have been encountering methodological and disciplinary barriers to developing and publishing the work. Among these barriers is the connection to citizenship and nationality deriving–in part–from the long-term negative impact of apartheid, including on mathematical careers. He shared apartheid-era quote rejecting Black PhD mathematician from a role with authority over white students. He also read from a 1977 letter about segregated conference facilities. AMS Notices paper on South African mathematics, had to take out and translate some themes. His research asks various questions: what has shaped the landscape, PhD training trends, research specialisms, and involvement of marginalised groups? The periodisation of the work breaks into four sections that have different characteristics: pre-1910, 1910-1961, 1961-1990, and post-1994. South African archives are difficult to use to study this. The contain no written histories of mathematical ideas and research themes in South Africa. By and large mathematics were excluded from surveys of South African science and the major reference sources. South African Mathematical Society has a history on website, but it is brief. Mathematical departments have histories including Stellenbosch University maths dept and the CSIR for the first 40 years.

The four divisions are characterised as follows. Pre-1916: the development of university colleges; 1916-1959, by the appearance of the first autonomous universities; 1959-1976, by racially segregated universities; 1976-1994, by ‘independent’ homeland universities; post-1994, by Higher Education Act creating a unitary and differentiated university system across the whole country. There is a strong influence from the Oxbridge schools, Scottish missionaries, university funding (quantity of research), racially segregated funding, academic boycott from 1961(?), the 1983/84 Foundation for Research Development rating system for individual funding, and immigration of academics from Eastern Europe PhDs from 1950s. In 1958 the first Black South African PhD was awarded, Wits (student working in Ghana). The year 1971 saw the first female PhD recipient in South Africa. The first Black South African woman with a PhD received hers in 1992.

ref: A History of scientific endeavour in South Africa fails to cover mathematics

Eder Kikianty: has been considering the migration from Eastern Europe to South Africa. There is a longer timeline for South Africa she wants to consider too: starting with the VOC Colony to the Cape Colony to the Batavian Republic Colony to the Cape Colony to the 1910 Union of South Africa to the 1948 National Party around apartheid to the 1961 Republic to the 1990s and the end of apartheid. Union years included research centred in universities. Universities formally start in this Union period, with the exception of the Cape of Good Hope. She’s still examining them and they’re not a teaching university. The Council for Scientific and Industrial Research (CSIR) began in 1945 and implemented of apartheid. She’s produced a survey of PhDs from South African institutions. The most prominent in the survey are 5 universities: University of the Witwatersrand and University of Cape Town, followed by University of Natal, University of Pretoria, and University of South Africa (Unisa). Many people have studied overseas training for South Africans, especially Cambridge which trained many South African mathematicians, generally through specific advisers such as J.E. Littlewood. She produced a survey of publications that includes under 50 with South African author in a database search between 1933-1996(?). The articles are mainly in UK journals, from the same 5 PhD-granting South African institutions. Most published mathematics has an emphasis on analysis, special functions, differential and integral equations. Future research include doing more on women in SA mathematics, understanding the rating and research funding system, and understanding the training system.

ref: EK and TL Kitagawa, A History of Mathematics in South Africa, Math. Intell. 2021

ref: EK and LN, National Rating System in South Africa, Notices of the AMS

Kerstin Jordaan: Started by showing the Mathematical Genealogy Project example of PhD lineage at Wits, whose trail ends at Colin J Wright. The South African Mathematical Society was founded 1957, but compare Southern African Mathematical Society (SAMSa). These societies, LMS/SAMS/SAMSa, collaborated in complicated ways with each other and the AMS. There is an existing MoU with AMS for the joint LMS/AMS/SAMS meeting at U Pretoria and subsequent meeting at Port Elizabeth (now Nelson Mandela University). But LMS only supported financially and didn’t send a speaker. African Mathematical Union had ties to the International Mathematical Union and ran the pan-African Mathematical Olympiad. AMU has an annual meeting and a journal, currently edited by a South African mathematician. The relatively new African Institute for Mathematical Sciences (AIMS) covers 5 countries, Cameroon, Tanzania, Rwanda, Ghana, South Africa. It provides masters-level intensive coursework for a year, and research-intensive institute since 2004. Other national entities include National G Academy for Mathematical/Statistical Sciences, which funds early career mathematicians, and was initially grant-funded with bottom-up development. Centre of Excellence in Mathematical and Statistical Sciences is funded by National Research Foundation. The community is working toward a National Institute for Mathematical Sciences. This institute will be based on a collaboration between National Academy and Centre of Excellence that is now formalised as the Institute for Mathematical Sciences and Applications, which is already somewhat funded and working on international collaborations.

Question: What is the funding landscape like?

  • LN: Department of Higher Education, funds universities including research based on publications; majority of uni research funding. Philanthropies, mainly local. Masaka (?) Mastercard? Fdn; Carnegie. Private sector funding, focused on areas like teacher education, not much for research. Exception: mathematical finance. Research grants from National Research Foundation, and Department of Science and Technology. Some international funders, e.g. British Council, through bilateral agreements with South African government.
  • KJ: NRF has overseas partnerships, e.g. with Royal Society, Newton Advanced Fellowships; not necessarily effective or working by design through national system. Fullbright scholarships etc. Department of Higher Education has Erasmus+ funding.

Mike Ogiugo: What about Nigeria? Is anything being done with pan-African funding, African Union collaboration with IMU? What archives/sources and where for SA history of maths? Plans to extend work outside of South Africa?

  • KJ SAMS archives, minutes are at University of South Africa library
  • LN older universities (pre-1960), few have information about e.g. department heads and their biographies; maths departments generally do not have their own archives; university library has things like the graduation programme; 1959-1990 the ethnically segregated university records are in very poor shape; LN alma mater (2016 centenary) personal records weren’t available when looked. Methodological barriers to publishing in journals, for this reason collaboration with historians of mathematics.
  • MB UNESCO records if read carefully? Bibliographical tools?
  • EK records can often be scattered, have to be attentive to point of view and how to string together. Looked for information about Joseph Mokoena. Records vulnerable to fire. Posthumous government award included a short bio sketch. Biography of Oliver Turnbull (?), a classmate, had some information.
  • EK UNESCO lectureship, where might those archives be? Doctoral information from MGP and S2A3 (Southern African Association for the Advancement of Science – good biographical information on their members)

LN: histories of academic institutions - what are the themes in existing institutional histories? question of contributions from the South to mathematical research; experience of LN on IMU executive, note of skew of speakers, awards, response is that it’s a question of relative standing of work; question: how does research take root and be represented? Graph theory as area of research in South Africa; cf. Wilson, Robin, John J. Watkins, and David J. Parks, Graph Theory in America: The First Hundred Years, 2022.

YFL: 1950s Bandung, Afro-Asian connections, wondering about histories outside of university archives (e.g. newspaper archives) and connections such as Indonesia - SA.

  • EK South Africa on Dutch colonial itinerary between Netherlands and Indonesia; EK went to university at Bandung. Emphasises that information is scattered, hence the importance of communication between people who have local knowledge.
  • MB SA-India connection, but doesn’t seem as strong as might expect in the research EK and LN shared?

JPA: narratives of pre-history, what backstories are part of the discourse in South Africa?

  • LN 1980s/90s interest in ethnomathematics (Paulus Gerdes) - studied packing drawings, esp Zambia and Malawi. PhD at U of SA on ethnomathematics in group games in Mozambique and SA.
  • MB interesting that Zaslavsky 1973 is still being ref’d in Cambridge in 2000s but doesn’t seem to register in SA.

EK in the zoom chat: https://www.gov.za/about-government/joseph-albert-mashite-mokoena

Excerpt from the above: After a short stint at Aston College of Technology (now Aston University) in Birmingham, United Kingdom in 1963, Mokoena returned to his beloved home continent where he was employed as UNESCO Mathematics lecturer at the then University of Rhodesia in Salisbury (now the University of Zimbabwe in Harare). The impending Unilateral Declaration of Independence saw Mokoena upping himself to neighbouring Zambia where he took up a position in 1965 at the fledgling School of Natural Sciences at the University of Zambia again as UNESCO lecturer, where he contributed to the development of the Mathematics curriculum of that new university.

https://www.s2a3.org.za/bio/Main.php — this is the website of S2A3 that we used also to get biographical information on the members of the society (one can filter by discipline).

MO thinking about how to conceptualise longer history of maths in Africa.

  • KJ some history of maths education; disconnect of traditions/heritage and institutions/funders/PhDs/research?

Valeria de Paiva: research field concentrations, comparison to Brazil focus on dynamical systems cf Littlewood / number theory / research emphases.

Critical Mass as a theme?

Marginalisation as a theme!

INI/ICMS and more in-person collaboration.

Themes: location of archives, transfer of skills, international cooperation between societies and universities, racial exclusion, development of programs based on Oxbridge models, authority to join universities and programs, migration and training, periodisation, exclusion of mathematics from broader scientific histories, nation-building alongside mathematics, location of the teaching of mathematics even when awarded in South Africa, contributions to South African mathematics by other countries, genealogy of mathematicians,

15:30-17:00 - Brazil and South America

Valeria De Paiva, Rodrigo Ochigame, Luciana Vieira, Mariana Cavalari, Michael Barany

Valeria De Paiva: Brazil and South American history of mathematicas has lots of commonalities with the South African history. She’s particularly interested to hear a version of LN’s question about what kinds of data and sources we need to give a proper understanding and even influence on the Brazilian mathematical community. She’s thinking about the uses of history for current mathematicians, especially thinking about inequalities in recent mathematics.

Rodrigo Ochigame: has experience researching history of mathematics in Brazil, especially history of paraconsistent logic. He describes the book of poetry by Lars Erickson (suspected pseudonym), Paraconsistency (Newton da Costa) which relates to this research. (Ayda Arruda) There are connections between what would become the BRICS countries within mathematics: Brazilian mathematicians especially interested in work of Nikolai Vasileev as precursor to paraconsistent logic. The book was translated from Russian to Portuguese, which he found out by talking to Vasileev’s family. There is a Maoist interest in dialectical materialism in Brazilian mathematics. Paraconsistent logic is simultaneously formal and dialectical, which appeals to Maoist thinking. There are also connections to formalising ancient Indian philosophy in ‘Jain logic’. He has some interest in Evans-Pritchard account of Azande in central Africa, who tried to formalise things from ethnographic descriptions.

  • VDP: logic not considered ‘IMPA mathematics’ / proper mathematics in Brazil.
  • RO: this was a disciplinary struggle, logicians had mathematical training, participated in institutional networks of modern mathematics before the consolidation of the maths/logic disciplinary split.
  • Gisele Secco (zoom chat): I would like to know more about the interactions between the Paraconsistent community and the Mathematics one. Is there any historical work done on that topic? If someone is interested in knowing more about Aida Arruda’s life and work, here is my contribution (she was the first to write historical texts about Paraconsistent Logics, by the way) https://www.tandfonline.com/doi/full/10.1080/09608788.2021.2006139
  • RO: (book recommendation, Itala) Gomez and D’Ottaviano, Para além das Colunas de Hércules, uma Historia de Paraconsistência, 2017 ?
  • Mariana Cavalari: shared ref: https://www.rbhm.org.br/index.php/RBHM/article/view/185/172 Vista do UMA HISTÓRIA DA LÓGICA NO BRASIL: A ERA DOS PIONEIROS
  • LN: e.g. of foundation of research groups in algebraic logic, quasilogic, starting with a migrant to South Africa; quite identified as matheamticians – foundations of mathematics

Luciana Vieira: studied first in a Department of Mathematics in Brazil. She thinks about universities from perspective of colonisation and decolonisation. The Colony of Portugal was settled by Brazilian elites, Coimbra especially. In the 19th century, the first institutions of higher education appeared, which had medicine, law, and engineering faculties. The first universities were created in the early 20th century: they included initiatives in Amazons, Paranha. The first ‘modern’ university was established in 1930s: U de Sao Paulo and U de Rio de Janeiro. Sao Paulo had the first mathematics department. Within that university, there was a connection to international relations in the maths department. The department was created by Sao Paulo state elites. The newspaper owner funded university to counter federal power of Getúlio Vargas (?). The faculty of sciences and letters hired European professors, especially French, but in mathematics hired Italian professors. This was because of the Italian migration to Sao Paulo in 19c and 20c, the local elites wanted to be represented in the new universities. Human sciences were typically French thinkers (Levi Strauss, Braudel); maths and physics were Italian (Fantappie, Wataghin). In the 1930s, the fascist politics required the hiring of Italian professors. The Fantappie archives in Italy and diplomatic archives can be used to understand LF political role. Not all the professors were fascist, but LF was, and did political propaganda through mathematics; cf. Italian hismtmaths (e.g. work of R Tazzioli). LF wore the fascist party symbol, participated in fascist party events and talked about fascist party in his teaching. He stocked a library including fascist texts. Wataghin (not fascist) stayed in Brazil a long time too. Fasist professors returned to Italy sooner, e.g. Fantappie returned in 1939 to work in institute with Severi in a position formerly held by a Jewish mathematician. Engineers were dominant in previous institutionalisation of mathematics education.

  • VDP how do we get from there to Zariski and Grothendieck? Quine?
  • Ref: https://journals.openedition.org/mefrim/4430 ‘An Italian mission at the University of São Paulo’, Luciana Vieira Souza da Silva et Rogério Monteiro de Siqueira
  • LN cf. Mozambique mathematicians studying in South Africa. Is there Portuguese intercolonial connection?
  • LV Bourbaki reflects French focus of USP founders. Italy and France seem dominant after waning of Portuguese presence.

Mariana Cavalari: is thinking about the history of women in mathematics in Brazil and about the Brazilian mathematical community. Since 1934 from the foundation of USP to 1990, the documentation from the university archives demonstrates that women were underrepresented in departments and institutes. Only 4 women reached equivalent of full professor. There were many Italian, French, and North American influences. E.g. a German migrant who supervised 90+ PhDs, who was also the founder of SBM, first chief editor of SBM journal, and creator of Brazilian Mathematics Colloquium. Only a few textbooks were in Portuguese, many were rather in Italian.

  • LN (zoom chat) Karin Howell, who is Academic Director at the African Institute for Mathematical Sciences in Cape Town is very interested in issues on Women in Mathematics in South Africa and would be very keen to connect, I am sure.
  • VDP importance of the colloquium and the olympiad. Do we have student / PhD number statements. IMPA blog posts have some data. USP - coffee money; UdeRio (‘U de Brazil’ at the time); relocation of capital. SBM connection to IMPA from political-military funding establishment. 1970s ‘Brazilian miracle’ military funding of science, promoting incoming migration of scientists, nuclear and space and antarctic programmes.
  • YFL ‘philosopher kings’ and the notion of development/science ‘miracles’; the pure-applied mobility of mathematics is significant, the philosopher king is someone who appropriates power from the West.
  • JPA in the chat: I like Yi Fong’s connection with the philosopher king: this is the sort of transmission akin to the translatio imperii that I was wondering about; the great thinker brings the knowledge to their new community, which creates a new narrative of biopower and community (maybe nation?)
  • LN ‘IBSA’ (India Brazil South Africa) academic forum; didn’t move forward. Cf. BRICS. Interacted with P Picione as counterpart president of SBM, introduced to J Mesquita; KJ connected SAMSa to SBM. KJ quite involved with maths olympiad in South Africa; cf role of Olympiad in Brazil.
  • VDP translation: teach mathematics in Portuguese in Brazil; open-source/open-access of back catalogue (AMS, SBM) is a future issue.
  • MC in the chat and voice: In Brazil, we have a Brazilian Society for History of Mathematics (SBHMat), publications are all free; hard to sustain societies financially, role of publications as a support for this
  • EK open source textbooks, access to texts; alternatives to Olympiads for identifying talent.
  • RO since 1990s or so, open access has become a norm in Brazil and Latin America that appears to be a success story; how was that achieved? Contrast to USA/European academia. On the translation discussion: Cold War iron curtain abstracting/translating infrastructure was a key source of information, produced Vasileev connection.
  • Helena Durnova: Olympiads and connection to mathematical cultures of different countries (more tomorrow)
  • LV: Italian, French, German professors at USP in 1930s, you studied in the language of the professor. Significant internal publication market sustains Portuguese publishing.
  • MB: international demand for Grothendieck’s lecture notes, relation between internal and external markets for Brazilian mathematics; context of economic history of import substitution.
  • HD linguistic localisation of math olympiads.
  • Anna Pratoussevitch filled in information about olympiad marking
  • GS: But it is a very important point. The same goes with the Philosophy Olympiads (in Brazil there are two models too: one focused on training students for the International one, other decolonial). It’s also important for our purposes: we need translations from the papers written in Portuguese, say.
  • UM This is quite a witty report from 2010 by Geoff Smith, the leader of the UK Olympiad team that year0. https://www.imo-register.org.uk/2010-report.pdf

RO want to pick up the USP/IMPA comparison, gender, other themes from here.

Participants from the day: Sayori Ghosal (online) Clemency Montelle (online) Helena Durnova (online) Stefanie Gänger (online) Loyiso Nongxa (online) Mariana Cavalari (online) Eder Kikianty (online) Ursula Martin (online) Kerstin Jordaan (online) Alkisti Kallinikou (online) Bo van Broekhoven (online) Michael Barany J.P. Ascher Sonia Wigh Scott Mandelbrote Isobel Falconer Jinyun Yuan (online) Anna Pratoussevitch Yi Fong Loh (online) Snezana Lawrence (online) Christopher Hollings Petra Stankovic Luciana Vieira (online) Rodrigo Ochigame (online) Valeria de Paiva (online) Slava Gerovitch (online) Gisele Secco (online) Shengyin Jia (online) Jinyun Yuan (online) Emma Baxter Katya Babintseva Liesbeth De Mol

Collected references:

WEDNESDAY 16 APRIL

9:00-10:30 - China, East and Southeast Asia

Jan Vrhovski, Jiyun Yuan, Han, ?Li, ?Ghosh

Vrhovski: has been focused on history of mathematical logic particularly between 1920 and 1960s. He has been combining Republican Period and the People’s Republic of China (PRC) periods. These periods regard the opening with intellectual history of modern China and mathematics. There are two big problems of this history:

Problem 1: comes from the traditions of area studies. The need to address things through essentialism obscures the topics that can be studied because the topics too close to Western areas in math and science. That is, the sense that mathematics is a thing and is the same thing in one place or another, that the area may change, but the math is the same. This way of thinking prevents us from seeing how the mathematics might actually be different. Furthermore what a mathematics outside of the Western projection onto China might be has been overlooked. The local Chinese essentialism also has its own character. Approaching China with a global essentialism makes it hard to see Chinese intellectual history and mathematics clearly on its own terms.

Problem 2: comes from postcolonial theory in considering the absence of agency in the colonised subject. When postcolonial theory thinks of the post-colony, it denies a local logic or a local essentialism. Modern history occurs in a framework of alienation, where modernity demands an alienation from the local in favour of itself. The alienating modern history of the West posits that the Chinese passively accepted Western ideas rather than having an active role in intellectual appropriation. This results in a untrue and unhelpfully eurocentric percieved lack of historical agency. This is not merely a problem for Western historians, but many Chinese historians may also think that logical thinking and other concepts have come from the West.

Niccolo: Example of the activity of intellectual appropriation?

  • JV: it is a big question, but can be seen in terminology; how to represent mathematics in native language? Chinese characters from the late Qing period are singular and known by the scholars and the discussion of these terms require an etymological approach as part of the their use at the time; translation needs to pay attention to patterns of terms more than individual words; linguistic modernisation was driven by figures educated abroad who brought back different expectations of the language the language itself becomes part of the cosmology;

MB: How do we think of China in a postcolonial lens?

  • JV: the downfall of the Qing dynasty began the process of relating to Western empires; Chinese culture was sinocentric: they were the middle of the world; the intelligentsia of China in this period thought that the West’s concept of science was something to appropriate into their intellectual sphere.

Themes: ’emulation’ (perception of emulation as devaluing subjects for historical research) alienation in Chinese self-formulation of modernisation; denial of hermeneutic agency: trope of passive acceptance of ideas. (Question: how do we have to adapt our understanding of the colonial/postcolonial as frameworks for China; cf. Latin America); glimpses of independence. Qing Empire downfall as result of Western Imperial incursion. ‘Middle Kingdom’/‘Central Empire’ self-conception; Sinocentric narrative of no need/interest in colonising; location of study creating intellectual exchange;

Reinvention of history of traditional Chinese mathematics as part of the creation of Chinese mathematical history/identity.

MB: The whole event relates to the subaltern history of non-Western-European places and modes of thinking; quasi-colonial states change how epistemology (ways of knowing) function; Latin American and Chinese received histories seem to have staged models of growth and a premise around the necessity of Western injection of disciplines, but this is obviously untrue;

NG where do international/Western collaborations start?

  • JV usually from connections started/maintained by Chinese scholars who go abroad. Confidence in national character and national identity. By 1930s huge number of Chinese students studying in Göttingen; interactions with Neugebauer (bibliography/ ancient historiography), Jian Yun (?) + Liyan (?) composed bibliographies to prove continuity of long history of Chinese mathematics.

LN colonialism as disruption; continuity of social/cultural activities

  • JPA everyday mutual incomprehension
  • MB what is at stake in different kinds of engagement and appropriation of mathematical research?

MB what is the basic historical geography of mathematical research in China?

  • JV distinction based on the educational background of figures at different institutions. 1911-1930s quite diverse. Beijing and Xinhua universities had quite large communities of mathematicians. Soviet connections since 1948, engagement with Soviet reports. Chinese Academy of Sciences became a safe place to continue mathematical research, not necessarily to publish freely.

(periodisation?) No major centres except around particular individuals.

context of dialectical materialism affects research on mathematical logic, foundations/axiomatisation: these are claimed to improve the efficiency of dialectical reasoning (c. 1956-57)

Soviet influence of research toward differential equations, algorithms, computational mathematics, abstract algebra; these were politically supported. Chinese delegates to Soviet conferences also attended the unlicensed seminars in Moscow (e.g. Gelfand Seminar), Steklov Institute

Geometry: already a research theme in the 1920s, but FJ (?) who published this work was targeted in the Communist period. Topology had a fruitful life in China: T Zehan (?) 1937-45 wartime

JPA training as a mechanism for global connections; generational dimension of training and interconnection

LN bilateral agreements between governments, partnerships between academic institutions, training connections, international exposure to early career academics

MB how could/should we provincialise the IMU narrative about (in IMU view) Chinese refusal to join, Taiwan recognition?

Philanthropy: comparisons between Rockefeller (historical) and Simons (contemporary)? British Boxer Indemnity funds. Guggenheim? less of a factor.

Jiyun Yuan: explains that he was raised and later an undergraduate in China, earned his PhD and had a career in Brazil. He notes the european origins of mathematical research directions and describes the French influence on South America. IMPA was a grad programme in Brazil, students come to Brazil and IMPA for PhD training; the Olympiad project in 2005 spent money in context of corruption and school mathematics. Later 2017 and 2018 were official Mathematics Years that were funded by the same source. The Chinese government has a baseline posture of support for mathematics, unlike most governments. From 1998 onward, there was an improved funding environment for academic mathematics in China, but there remains a political context of research.

The BRICS Mathematics Conference was first in Beijing. The last planned event in South Africa was skipped due to the pandemic. This year BRICS will be December in Beijing. There will be interveningq events in Brazil, India, Russia. BRICS has really expanded. He is interested in starting BRICS Mathematical Union to promote integration across BRICS group. In the future he hopes to see work on the cooperation programme ICM2018 paper on applied maths in Brazil. The first PhD in Brazil was in 1848.

10:45-12:15 - India, South Asia

Montelle, Kumar, Ram Ramaswamy, Aravinda, Sayori Ghoshal, ?Banerjee, ?Patel, ?Ghosh

MB provided some provocations linking to previous discussions: relationship between construction of heritage and modern disciplinary institutions; national/regional/international networked institutions like ISI, TIFR, IIT

Sayori Ghoshal: described the history of modern statistical sciences, particularly a late 19c census, and the modern disciplinary history of statistics from 1910s/20s. Major figures and themes include: PC Mahalanobis, institution-building, producing nationalist discourse of instiution-building and science in service of the everyday life of the masses. The discursvie orientation of the project of modern statistical sciences is toward national welfare. That is the purpose of statistical surveys and analysis are to improve the social condition. E.g. a random sample survey, taken up internationally 1940s/50s means to improve the people. Earlier years works with or against Karl Pearson’s work in biometry.

Emulation and appropriation questions from previous session: PCM work as original contributions, uses KP racial similarity coefficient, PCM sees quantifying extent of similarity as important in national context, PCM distance measure now used in many areas.

Some aspects of provincialising history:

  • literal meaning: geographic regions, identifying mathematics in metropoles as well as colonies and provinces
  • provincialisation of actors, centring colonised subjects, their national (sometimes colonial) identity is signicant and leveraged in their work in particular directions
  • identity of actors as organised subjects, reframing who could be an expert in these sciences; statistical work depended on deriving/collecting data, social/economic data collection depends on understanding of context
  • provincialisation as methodological/historiographical : PCM sought validation/collaboration from Western centres, aspires to universals and universally applicable science
  • provincialising should not be a one-time project; biases even when looking at India in what places and institutions we emphasise; upper-caste/elite/Hindu, major cities, missing e.g. radical Dalit voices.

ISI history: home institute in Bengal/Culcutta, further institutions come up later; mainstream template and replication model, is it effectively provincialising simply by being in different locations.

Ram Ramaswamy: has a particular interest in DD Kosambi (1907-1966) who worked in maths, but also stats and probability. Kosambi was working in India 1930 onwards, educated in Cambridge Masschusetts. So his education was entirely in America, in contrast to Mahalanobis, Bhabha, etc. who were exposed to the Cambridge style. There is a distinction between the American vs English style of mathematics which we can see in his work. DDK was influenced by Birkhoff, Graustein, and Stone. He was one of first to bring this influence to India. DDK never identified too strongly as Indian and had a disciplinary arrogance about his ability to contribute, along with a sense of entitlement to correspond with elites in research fields. He had a relationship with Andre Weil, who functioned as a sponsor to DDK. DDK cites Bourbaki while Weil calls the journal ‘provincial’. DDK at TIFR breaks with the Cambridge tradition, Bhabha (initially) liked this and invited DDK to start school of maths at TIFR. DDK recruits K Chandrasekharan and Raganathan who become nemeses. DDK writes letters to Bhabha about building up a school of mathematics to cover aspects like fields of research, attempting to get Harish Chandra, Minakshisundaram, etc. to return to India. He is antagonistic to PC Mahalanobis. It is difficult to see what sparked it, but seems to come as reaction to PCM institution-building role and his national, political, and international influence, also that he had Nehru’s ear. Maybe DDK was not jealous but he writes disparaging letters about PCM, particularly to Wiener. Kosambi also had a distance function, which is still used to measure genes on chromosomes. Applied statistics were particularly important to DDK, especially birthrate and death-rate. For him, social context was very important and he ‘combined method’ in his work. His supposed Riemann hypothesis proof damaged his reputation. Prior to this attempt at a proof he was on 1950/54 Fields Medal committee and seen as representative of Indian mathematics. The success of K Chandrasekharan threatened DDK’s preeminence at TIFR. He also wrote an important paper in Russian on Hindu-Aryan nasal index, which debunks colonial preoccupation with caste and nose width.

Kosambi’s connection with SS Chern was that he was the first foreign visitor to TIFR in 1946. DDK didn’t see himself in provincial terms. Didn’t (initially) think partition should apply to mathematicians.

JPA: de-universalizing technical history when it is part of global history (re: Mahalanobis Distance).

SG the distance function has seemingly been deracinated by current/recent users, e.g. in global finance applications. Pearson thought there was a lack of capacity for abstract thinking. Colonial infrastructure created the data that PCM used; racial/caste difference was the primary motivation for PCM. Impact of technical verification, validation against presumed racial characteristics of caste difference in India based on upper-caste Hindu biases.

JPA wins the prize for bringing in Derrida’s false money vignette: wants the article “Whitening Mathematics”; as money only has value in circulation, mathematics developes abstract (technical?) value in global appropriation (see RR below on DDK analysis of coins)

Tinne H-K what did PCM understand by stats benefiting the people and how did he convey this? Were there changes to statistical questions from the goal of social/economic benefit? PCM method as a development of KP’s method: did that spark new research directions in statistics?

  • SG PCM proximity to state apparatus drew sceptics. PCM quite entwined with KP observatory/work/journal initially. KP did not see PCM work as new/significant. PCM uses the Pearson/Fisher hostility, courts Fisher’s encouragement and support for recognition.
  • MB version of this question for DDK and his heterodox Marxism?
  • RR DDK at World Peace Conference (F Joliot Curie), asserts India’s position as anti-nuclear, pro-Soviet; considered Indian Marxism to be backward (denigrates as ‘OM’ = ‘Official Marxism’). After 1956 DDK distances himself from the World Peace Conference, less idealised view of Soviet Communism, left ‘peace’ activism. Fisher was also very pro-Kosambi.

SG how to understand metropole-colony relationships, friendships – equal-seeming but in a very unequal context.

  • RR DDK never collaborated. Riemann proof in Indian Journal of Agricultural Statistics. DDK saw the opposition to his work on Riemann as motivated by racial prejudice. Chester Feldman correspondence about this is extensive.

MB DDK’s historiographical legacy and connection to his mathematics?

  • RR started with statistical analysis of coin hordes, connecting rate of usage to variance in distribution of coin weights. This connects him to historians interested in analysing coin data, broader interest in quantification in history; interested (indep of PCM) in statistical understanding of caste history.
  • do we know what PCM thought of DDK? DDK’s hostility seems to come late 1940s, first interaction is 1938. Competition over UNESCO computing between TIFR-Bombay and ISI-Calcutta. Views of Western (mis)perception of Indian mathematicians seemed to drive DDK sense of competition with PCM. Haldane fell out with Mahalanobis.

13:30-15:00 - Russia, USSR, and (historical and former) Soviet Bloc

Hollings, Tatarchenko, Gerovitch, Babintseva, Durnova

Chris Hollings: describes Euler as the start of Russian maths in the Russian historiography. He functioned as imported expertise. The question was asked, were mathematical practitioners coeval or earlier? There’s some Soviet literature from the 1970s with an ethnomathematics frame that looks prior to the St Petersburg Academy and Euler. The research examines the eighteenth-century Moscow University, nineteenth-century explosion of universities, e.g. Khazan, Kharkov. The Moscow Mathematical Society develops in the mid-19c (approx coeval with London Math Soc) as a counterpart to St Petersburg. It is more inward-looking initially (compared to St Petersburg Academy) and established an audience for Russian language mathematics. By the early twentieth-century, the Moscow Math Soc seemed aloof from international scene. The internationally-connected Russian mathematicians were coming from Khazan, St Petersburg, e.g. A Vasileev. By the 1920s, the idea of trying to make a more internationally visible society encouraged the more widespread use of Western languages in Russian journals, principally Math. Sbornik. Of course, there is some precedent from Kharkov. After 1948 Soviet mathematics journals would be in Russian by official decision. There is an appetite elsewhere for people to read this material. There is a worthhile subsequent story about translation.

Slava Gerovitch: Explores the famous case of Lobachevsky’s geometry. NL was president of Khazan University, a provincial university within Russia, and this affected how his work was viewed in Moscow. His administrative position at Khazan allowed him to publish his work. He followed a tradition rooted in Russian Orthodoxy and had a rigid and conservative political-philosophical outlook associated with Moscow in late 19c. This outlook was also associated with the Moscow Mathematical-philosophical School. In the 1920s there was a reorientation toward contact with French mathematicians, especially in exchanges to or with Paris, along with publishing in French. (see Graham and Kantor ref: Naming Infinity, a somewhat controversial argument). During the later period, the social mechanisms of working in Soviet maths community charged, particularly with regard to the context of education and research, along with discrimination against social and ethnic groups such as Jews, Germans, political dissidents and their children, graduates of specialist mathematical high schools. This discrimination included restrictions on educational admissions and awarding, careers, and recognition. Mathematicians developed mechanisms to circumvent these barriers that included special training toward college admissions, underground university, open research seminars, informal advising, creative publishing strategies (‘Russian style’ of short papers without proofs), informal international communications in private and semi-private spaces: dachas, apartments: parallel infrastructure of mathematics (ref: SG article “Parallel Worlds”). These practices were illegal and left very little paper trail, so are very difficult to track in the archives. The existing archives are quite distorted even if one gets access. The current best method is to conduct oral history (he’s done 19 and counting). But these oral histories are inflected by community folklore, distortion through repetition, etc. However, it is the best hope to reconstruct history of discriminatory practices by studying counter-practices and informal institutions made in response.

Ksenia Tatarchenko: asks what happens to graduates of the special mathematical schools? They were incorporated into specialist jobs especially in Siberia. Who belongs to the mathematical community? This is always a somewhat open question. She is looking at individuals who have to make their way into the community. Marginalisation and marginality have become major themes.

Looking into consolidation of academic community under auspices of Siberian branch of academy of sciences (1957), which hosts the Soviet-American 1963 PDE symposium. Provincialisation and internationalisation are intertwined. (ref: KT article on Novosibirsk as scientific showcase) The geography of decentralization causes new centres to emerge, and a movement to East in Akademgorok. This new center is a Mathematical-Physical school of early 1960s, which includes “Wild West” imagery, and narrative. The movement to Omsk is seen as the spirit of new mathematics.

New administrative unions in later Soviet period; mathematical identity and applied work in internationalisation context.

  • MB establishment/counter-establishment interaction as a theme?
  • KT different understandings of what service to the state means. ‘parallel’ mechanisms can look/work differently in more peripheral geographies.

Katya Babintseva: is thinking about Dmitri Pospelov, how he relates to computing and AI. DV holds prestigious positions such as the editorship of Technical Cybernetics journal. He has a possible relationship to Germigan Pospelov.

Q to SG: how do you talk about the role of nepotism in your scholarship?

Q to KT: does the turn toward idealism help explain rise of special mathematics schools in USSR? ref: CH article on Soviet idealism: maths as universal language in Soviet discourse.

  • SG Soviet academic elite was very tight-knit in friend connections and kin relations; this did not necessarily favour those with the connections, e.g. Sergei Novikov, son of a prominent mathematician, easy entry into academic community, nephew of Kheldysh, president of Soviet Academy of Science, however Novikov’s mother supported Soviet dissidents, intrafamilial tension, Novikov banned from attending ICM to receive Fields Medal due to political dissidence. Family connections created opportunities but also additional constraints. Friend networks facilitated parallel informal infrastructures, blurred work-friend relationships.
  • SG Special maths schools cultivated a spirit of mathematics as a higher calling, but this was not necessarily the reason students went to these schools. They were ways of segregating/protecting children of Soviet intelligentsia. Political suspicion of statement ‘our homeland is mathematics’ - expression of mathematical idealism as creating a politically neutral niche.
  • KT Akademgorodok examples: e.g. Marchuk, computational maths for nuclear project, creates material opportunity for him, returned to meteorology and climate science; e.g. ?Lomonov? more idealist motivation, maths as modernity.
  • KT families and class reproduction, esp. intelligentsia. The violence is not connected to the state but to the communities themselves. Real and artificial families, social engineering of mathematical schools; competition with Moscow and St Petersburg.

Emma Baxter: maths and literature in early 20c, religion and Moscow school of mathematics (Graham/Kantor argument) and Pavel Florensky explicitly combining maths, religion, philosophy. Q: how do differences within imperial Russia manifest?

  • MB are there endogenous modernities in Russian/Soviet maths?

  • KT argument developed with L de Mol, extend the notion of intelligentsia science (ref Gordin et al Osiris volume) into late Soviet period. Anya’s work on Odessa school. 1960s Akademgorodok example, based in domestic spaces.

  • SG two trends in geographic mobility of maths community: generally very low mobility, low migration out of city of birth, stable intergenerational schools of narrow research interests, concentration of effort/talent in those areas but also self-isolation. Soviet move from St Petersburg to Moscow of academy of sciences, suction of talent from provincial sites to the capital, not much exchange. E.g. Pospelov visit to US and difficulty of American interlocutors to grasp idiom of Pospelov school.

  • VdP comparison of the schools’ isolation to e.g. Newton da Costa and Brazilian example

  • MB how should we provincialise the historiography of disciplinary specialisation and its relation to institutional geography?

  • EB polymathy/multidisciplinarity as counter to specialisation as a theme. Q: what about mathematical pedagogies and political disruptions (esp 1917)?

  • KT cf Chemla’s historiography of peripheral communities, intertwining of pedagogy and historiography, including questions about the language of mathematics.

  • SG post-revolutionary major reform of university education, proletariat-oriented admissions, brigade system of collective learning modeled on factory training. This prompted professors to develop and focus on informal spaces of teaching/training. Mid-1930s mathematicians created a distance between professors and students, banned informal socializing over tea, institutionalised more traditional interaction. Conflicts of community norms and politial agendas.

  • EB 1920s-30s school maths textbooks, embedded e.g. in collective farms; publications of these early textbooks appear to be more localised (e.g. rural vs urban), shifted in 1930s to more traditional methods and less localisation

  • KB early 20c pedagogy and formalism; 1960s structuralism rose in Soviet Union and Soviet Bloc (e.g. in Tartu, Estonia).

  • KT should avoid Russian exceptionalism

  • EB late 20c drive in some communities to erase differences with Western counterparts; (ref: Eglė Rindzevičiūtė The Power of Systems)

  • VdP Soviet books, internationally known as inexpensive, intellectual/cultural influence

  • SG extensive academic publishing infrastructure, programme of translation into Russian, accessible book forms; limited availability of original foreign language publications, including journal – just a few top libraries had subscriptions. Reviewing, abstracting, copying allowed somewhat wider circulation; informal infrastructure of preprints; nostalgia of having just 1 night of access to an article.

  • VdP was there a Russian proto-arXiv? (Cf. Hypatia in London.)

  • SG Soviet Institute of Scientific Information did article abstracting: Ref. Zhurnal. Computers introduced haphazardly in Soviet academia. Computers/printers seen officially as undermining force of information dissemination. Specialised maths schools had lots of handmade / handcopied materials, pedagogical materials reproduced on same tech and by same people as dissident literature.

  • KT paper shortage in the 1920s; regional differences in access and distribution of literature; importance of parallel infrastructures of dissemination. Ershov archives show importance of his personal library of Western mathematical literature.

Closing thoughts?

  • KB Soviet materials translated from English to Russian tend to be very high quality; Russian to English translations - 1970s machine translations basically unreadable.
  • SG mathematics gives contrary view of Soviet academic community contrasting to hierarchical centrally controlled view. Soviet Union was a patchwork with highly varied conditions of control, pressure, persecution, autonomy; grapevine supported reconfigurations toward autonomous communities, also crackdowns on these; fluid structure.

15:30-17:00 - Closing Discussion

What have you learned or what themes stood out so far?

What questions or challenges do you have for the continuation of this project?

JPA role of communication and printing technologies and their different applications in different places: as technical history and also medium of this historical work. New question: image of universalism, the persona of philosopher king, the notion of whitening?

VdP recalled LN’s question about where we get the evidence and sources we need for these histories. There are many peripheries in the world. How do we organise and connect and compare?

  • How can we carry on these conversations effectively?

LN two more things to raise: different societies, groupings, histories, e.g. of variety of cultural and national groups whose histories are incorporated in the history of mathematics in South Africa, cf. in South Asia the Hindu/Muslim and caste divides as affecting the historiography, cf. appearance (misleading?) of homogeneity in Chinese mathematical history. Can these histories address marginalisation? Underrepresentation? Can these histories change views of young people about their place wrt mathematics?

RO centre-periphery theme recurred: intranational, relative to Global North, disciplinary peripheries (institutions, fields of study), institutional structures (formal/informal), social.

KT methodological challenge: what methods can be shared for work on these different regions? parallel infrastructures, border institutions, practices. Experimental ways of decentring the narrative? E.g. of narrating through intimate partners of mathematicians.

UM digital region; cooptation of high profile mathematicians by tech/AI companies; can these conversations help us understand or oppose this? RO weighs in; KB is this about mathematical practice? UM discourse, political economy. OpenAI claims about the future of pure mathematics research here, supported by quotes from high-profile mathematicians https://epochh.ai/frontiermath/expert-perspectives VdeP points out there are many kinds of mathematics: UM clarifies she meant traditional “pure mathematics”

KB what is a periphery and why do we call it a periphery? E.g. AI as a periphery to ‘pure’ mathematical research but not in funding terms. E.g. Pospelov facing incomprehension in the USA.

MB incomprehension as a running theme and one that runs back (methodologically) from the peripheries to the centres

YFL digital as a region rather than as a periphery; contexts of strong states appropriating mathematics for state development, ‘miracles’ of mathematical/national development.

LV idea of circulation, recalled LN’s question about interaction between Portuguese imperial/postcolonial network; there were in fact some connetions in economics and social sciences between Brazil and Mozambique, e.g. Some common topics for comparisons: gender, decolonisation, institutions,… Have to organise narratives according to our questions.

SlG MIT maths dept context; questions about AI split mathematicians into very passionate camps. Reminiscent of past trends coming from recognised centres of mathematics to geographically peripheral locations, some are indebted(?) to the trends and others see them as external/hostile. Question of where innovation comes from, considered often to come from mathematical borderlands / disciplinary peripheries.

EK idea of what is classified as mathematics; collab with T Kitagawa: many people labeled as astronomers in South Africa were arguably/primarily mathematicians; mathematics in mining contexts: including training, textbooks, etc.

LN question of the role of the diaspora, e.g. Indian diaspora in South Africa as a basis for collaborations and networks; diaspora communities as having access to advanced training, PhDs.

  • MB also diaspora inflecting historiography and sources/evidence
  • YFL unpacking the appearance of Han Chinese homogeneity (linguistic, ethnic), diaspora historiography as a means for this

KT next time: not by regions, focus on themes, pedagogical/communication/disciplinary-borders. We are pushing against centralising narratives, thinking about analytic tools for understanding the production and maintenance of hegemonies.

  • MB practical question of timezones EK recommends Zulip
  • HD methodological lines could give good comparisons/contrasts. Q: is there a disadvantage to being the centre? Does this change over time?

LdM cf. DHST 24-hour rolling festival, tough as an organiser but worked very well for participants. There is a strong political undertone to the discussion, thinking of a talk by Mark Priestly about source by Azoulay, Potential History Unlearning Imperialism; potential history as an answer to official history.

SlG BRICS as a framework, question about how easy it is for mathematical communities to understand each other from different cultural backgrounds. As a gross generalisation, Soviet and Chinese scientists were able to collaborate in a shared context of socialist constraints.

LN BRICS Maths conferences going back to 2016

UM Cf. ABC Conjecture and Mochizuki

  • MB why haven’t mathematicians been more bothered about this? does it look differently from BRICS contexts? comparison between Kosambi RH and Mochizuki ABC.

MO who is working on history of mathematics in Nigeria? what countries are not represented here?

JPA who does the history? how do we find them?

  • MB worth exploring how this is a questions global historians share with historical mathematicians?
  • MO shared history among some African nations; e.g. Ibadan Uni founding in 1948; first PhD to a Nigerian mathematician appears to be from Cambridge, looked up 1950 thesis.

YFL environmental history conference, experience of participating in the structures we are trying to describe; question of labour and labour mismatches/inequalities as an analytic approach; pedagogy of proof perhaps gives more opportunity but makes omissions (e.g. history of maths of Nigeria?) conspicuous.

RO transnational circulation and complexities beyond centre-periphery relationships as an interesting theme

JPA ’navigation’ as more than a pun … mathematics and empire, metaphor for communication and interaction

KB for edited volume, need to develop an equally rich analytic framework (or several) for all the empirical material

Collected references:

BRICS Mathematics: online discussion series