Provincializing Shared Notes

Provincializing Modern Mathematics

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

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TUESDAY 15 APRIL

9:15-9:30 - Welcome

ref: Dipesh Chakrabarty, Provincializing Europe (book, expanding on the 1992 article ‘Postcoloniality and the Artifice of History’ in Representations)

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

Ascher, Gänger, Mandelbrote, Wigh

Mandelbrote: early modern history / mathematics in provincial terms: calculating society, early/modern objectivity, etc had to come into being in particular ways including in the societies that came to be modern English society. Shared some texts of Gilbert Clerke, 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: https://doi.org/10.2307/3679153 ) Clerke-Collins correspondence: 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. Change nature of the problems that we think mathematics was trying to solve, not just as natural philosophy but answering problems from everyday lives.

Queries:

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: global history of science, medicine, botany, archaeology. From SG’s book: Cuzco as centre of a network of archaeologists. 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. SG has been looking at a different scale of how professional scientists tried to distance themselves from lay knowledge. Relationship between class and access. 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: historian of gender, medicine. “Are gender and sexuality useful categories of historical analysis beyond the modern?” (in Afsaneh Najmabadi, ‘Beyond the Americas: Are Gender and Sexuality Useful Categories of Analysis?’, 2006, p.11.). Decoupling of gender and sex has driven a lot of work in this field. Western perspectives on the relationship between sex/gender/rights (for instance the work of Monica Green). Research has looked at texts from the subcontinent that are explicitly defining and categorizing sex and gender, using different categories than the standard ones in European scholarship. These texts were used to correct and standardize behaviours. 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. 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’ https://www.cambridge.org/core/journals/historical-journal/article/nonwestern-scholars-bourgeois-virtues-and-the-international-scientific-community-in-the-age-of-empire-18701920/7D3E0DD0613E5DB44EEDBE92E0E77EE8
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 connectedness monopolizing 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 provincialised 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 universiality a method, technique of empire? Is it only?

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: question about religion and universalisation

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 occuring 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

Barany, Stankovic, Loh, Lawrence

Petra Stankovic: project on two Russian mathematicians who emigrated to Yugoslavia in 1920s after October Revolution -> Belgrade. 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/science, so these migrants made quite a big difference. Archives: Serbian Academy of Arts and Sciences. Field of mechanics. e.g. Anton Dimitrija Bilimovich; rapid assimiliation/integration, naturalised and member of the Mathematical Institute of the Serbian Academy of Sciences. participated in ICMs in 1928, 1932, 1954. Evidence of social acceptance and integration. Political, economic, cultural mutual benefits. Serbia as a refuge for mathematicians, allowed continuation of mathematical work, beneficial for Serbia in providing sufficient mathematicians for an internationally-competitive school. Cultural context of Pan-Slavism, transition from Austrohungarian rule to Slavic integration. Russian involvement in Balkan Wars of 1912-13 -> reciprocity in receiving Russian refugees in Baltic countries. Polyglot community; ethnic bonds -> integration.

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

Snezana Lawrence: Slavic diaspora very important for development of mathematics as a profession, context of popular psyche that valorised mathematics. Yugoslavian mathematics were high status, rather than a marginal activity. Mihailo Petrovic as an idol. German sphere of influence extended through Austrohungarian empire -> Halle, Vienna, etc were centres of scholarship for students/researchers from across the region. French engineers/mathematicians made connections to people from Greece, Serbia: financial support for studying in France, Ecole Polytechnique / Ecole Normale; students from not-yet-independent countries studied in France and came back and established mathematical schools. Mihailo Petrovic (1868-1943) e.g. of this migration, bohemian figure, played music (travelled for this), expeditions to North and South Pole, attended presidential ball in France, passion for fishing: new image of mathematician. Refugees found a fertile culture for establishing themselves as mathematicians. A Bilimovich (1879-1970) translated Euclid during WW2, shows the extent of work still to be done. 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), 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. 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: postcolonial moment, Nanyang University 1955-1980. Singapore region influenced by Dutch postcolonial Indonesia geopolitics among other political contexts. E.g. contrast 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). Continuity of community of practitioners. Source: University Commission report, table of birthplaces of students. Context of campus protests, political instability. English language norm. Ideas about relationship between SEAMS and national societies/organisations. Shift to post-colonial context, connection to campus protests; while the wider idea of Nanyang as South-East Asia also lives on. 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: 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 (book on academic mathematical research in Australia, based primarily on Australian Mathematical Society materials)

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

Nongxa, Jordaan, Soumonni, Kikianty

Loyiso Nongxa: collaborating with Eder on history of mathematics in South(ern) Africa; encountering methodological/disciplinary barriers to developing/publishing this work. Connection to citizenship and nationality; longterm negative impact of apartheid, including on mathematical careers. Shared apartheid-era quote rejecting Black PhD mathematician from a role with authority over white students; 1977 letter about segregated conference facilities. AMS Notices paper on South African mathematics, had to take out / translate some themes. Questions: what has shaped the landscape; PhD training trends; research specialisms; involvement of marginalised groups. Periodisation: pre-1910; 1910-1961; 1961-1990; post-1994. SA archives: no written histories of mathematical ideas and research themes in South Africa; mathematics excluded from surveys of South African science. South African Mathematical Society has a history on website; dept histories including Stellenbosch University maths dept; CSIR - the first 40 years. Pre-1916: university colleges; 1916-1959 first autonomous universities; 1959-1976 racially segregated universities; 1976-1994 ‘independent’ homeland universities; 1994 Higher Education Act unitary/differentiated uni system. Influence of: Oxbridge, Scottish missionaries, university funding (quantity of research), racially segregated funding, academic boycott from 1961(?); 1983/84 Foundation for Research Development rating system for individual funding; immigration of academics from Eastern Europe PhDs from 1950s; 1958 first Black South African PhD, Wits (student working in Ghana); 1971 first female PhD recipient in SA; first Black SA woman PhD 1992.

ref: “History of South African Scientific Endevour” fails to cover mathematics

Eder Kikianty: migration from Eastern Europe, this connection -> EK’s link to SA. Longer timeline for SA: VOC Colony -> Cape Colony -> Batavian Republic Colony -> Cape Colony ->1910 Union of South Africa -> 1948 National Party, apartheid -> 1961 Republic -> 1990s end of apartheid. Union years: research centred in universities, unis formally start in this period; (exception: Cape of Good Hope -> examining, not teaching university); Council for Scientific and Industrial Research (CSIR) 1945; implementation of apartheid. Shared survey of PhDs from SA institutions. Prominence of 5 universities in SA: University of the Witwatersrand and University of Cape Town, followed by University of Natal, University of Pretoria, and University of South Africa (Unisa). Many studied oversees, esp. Cambridge; specific advisors e.g. JE Littlewood. Survey of publications: under 50 with South African author in a database search, 1933-1996(?); mainly UK journals, same 5 PhD-granting SA institutions. Emphasis on analysis, special functions, differential and integral equations. Future research: more on women in SA mathematics, rating and research funding system, 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: Mathematical Genealogy Project example of PhD lineage at Wits, trail ends at Colin J Wright South African Mathematical Society, founded 1957; cf. Southern African Mathematical Society (SAMSa); LMS/SAMS/SAMSa collaboration (existing MoU with AMS), joint LMS/AMS/SAMS meeting at U Pretoria; subsequent at Port Elizabeth (now Nelson Mandela University) but LMS only supported financially didn’t send speaker. African Mathematical Union, ties to International Mathematical Union, run the pan-African Mathematical Olympiad. AMU has an annual meeting and a journal, currently edited by a South African mathematician. Relatively new: African Institute for Mathematical Sciences (AIMS), in 5 countries (Cameroon, Tanzania, Rwanda, Ghana, South Africa); Masters-level intensive coursework for a year, research-intensive institute, since 2004. Other national entities: National G Academy for Mathematical/Statistical Sciences; funds early career mathematicians; initially grant-funded. Bottom-up development. Centre of Excellence in Mathematical and Statistical Sciences, funded by National Research Fdn. Working toward a National Institute for Mathematical Sciences. Collaboration between National Academy and Centre of Excellence that is now formalised as the Institute for Mathematical Sciences and Applications, already somewhat funded, 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: cf. Nigeria; 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.

YFL (question)

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

De Paiva, Ochigame, Vieira, Cavalari, Barany

Valeria De Paiva: lots of commonalities with the South African history. 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. Thinking about the uses of history for current mathematicians, especially thinking about inequalities in recent mathematics.

Rodrigo Ochigame: experience of researching history of mathematics in Brazil, especially history of paraconsistent logic. Book of poetry by Lars Erickson (suspected pseudonym), Paraconsistency (Newton da Costa). (Ayda Arruda) Connections between what would become the BRICS countries: Brazilian mathematicians especially interested in work of Nikolai Vasileev as precursor to paraconsistent logic. Translated from Russian to Portuguese, contacted Vasileev’s family. Maoist interest in dialectical materialism; paraconsistent logic as simultaneously formal and dialectical. Connections to formalising ancient Indian philosophy (‘Jain logic’). Interest in Evans-Pritchard account of Azande in central Africa and 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 dept of mathematics in Brazil; universities from perspective of colonisation and decolonisation. Colony of Portugal, Brazilian elites -> Coimbra (especially); 19th century first institutions of higher education, medical / law / engineering faculties. First universities created in early 20th century: initiatives in Amazonas, Paranha; first ‘modern’ university in 1930s: U de Sao Paulo and U de Rio de Janeiro. Sao Paulo had the first mathematics department. Connection to international relations in the maths department; dept created by Sao Paulo state elites, newspaper owner funded university to counter federal power of Getúlio Vargas (?); faculty of sciences and letters, hired European professors, especially French, but in mathematics hired Italian professors. Italian migration to Sao Paulo in 19c and 20c, local elites wanted to be represented in the new universities. Human sciences -> France (Levi Strauss, Braudel); maths, physics -> Italy (Fantappie, Wataghin). 1930s fascist politics and hiring of Italian professors; Fantappie archives in Italy, diplomatic archives 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 fascist party symbol, participated in fascist party events and talked about fascist party in his teaching; stocked library including fascist texts. Wataghin (not fascist) stayed in Brazil a long time; 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 dominant in previous institutionalisations 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: history of women in mathematics in Brazil and on the Brazilian mathematical community. Since 1934 / foundation of USP to 1990 documented from university archives women were underrepresented in departments/institutes. Only 4 women reached equivalent of full professor. Italian, French, and North American influences. E.g. German migrant who supervised 90+ PhDs, founder of SBM, first chief editor of SBM journal, creator of Brazilian Mathematics Colloquium. Textbooks 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: 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:

Barany, Michael. “The Mathematical Pranksters behind Nicolas Bourbaki.” JSTOR Daily, 24 March 2021. https://daily.jstor.org/the-mathematical-pranksters-behind-nicolas-bourbaki/.
Brown, A. C., ed. A History of Scientific Endeavour in South Africa: A Collection of Essays published on the occasion of the centenary of the Royal Society of South Africa. Cape Town: Royal Society of South Africa, 1977.
Chakrabarty, Dipesh. “Postcoloniality and the Artifice of History: Who Speaks for “Indian” Pasts?”. Representations no. 37 (1992): 1-26. http://www.jstor.org/stable/2928652?origin=JSTOR-pdf.
Chakrabarty, Dipesh. Provincializing Europe: Postcolonial Thought and Historical Difference. Princeton: Princeton University Press, 2000.
Cohen, Graeme Laurence. Counting Australia in: The People, Organisations, and Institutions of Australian Mathematics. Broadway: Halstead Press in association with the Australian Mathematical Society, 2007.
da Costa, Newton C.A. “On the Theory of Inconsistent Formal Systems”. Notre Dame Journal of Formal Logic 15, no. 4 (1974): 497-510. https://doi.org/10.1305/ndjfl/1093891487.
da Silva, Luciana Vieira Souza, and Rogério Monteiro de Siqueira. “An Italian mission at the University of São Paulo”. Mélanges de l’École française de Rome - Italie et Méditerranée modernes et contemporaines 130-2 (2018): 407-419. https://doi.org/10.4000/mefrim.4430.
Department of Mathematics at North Dakota State University in association with the American Mathematical Society. “Mathematics Genealogy Project”. https://mathgenealogy.org/index.php.
Gänger, Stefanie. “Non-Western Scholars, Bourgeois Virtues, and the International Scientific Community in the Age of Empire, 1870-1920.” The Historical Journal 67, no. 4 (2024): 769-84. https://doi.org/10.1017/S0018246X24000189.
Gänger, Stefanie. “The Mascapaycha: Collections of Incan Antiquities in Cuzco”. In Relics of the Past: The Collecting and Study of Pre-Columbian Antiquities in Peru and Chile, 1847-1911. Oxford: Oxford University Press, 2014. https://doi-org.eux.idm.oclc.org/10.1093/acprof:osobl/9780199687695.003.0002.
Gerdes, Paulus. “Reflections on Ethnomathematics”. For the Learning of Mathematics 14, no. 2 (1994): 19-22. http://www.jstor.org/stable/40248110.
Gomes, Evandro Luís, and Itala M. Loffredo D’Ottaviano. Para além das Colunas de Hércules, uma História de Paraconsistência: de Heráclito a Newton da Costa. São Paulo: SciELO - Editora da Unicamp, 2017.
Kikianty, Eder, and Loyiso Nongxa. “The National Research Rating System in South Africa: The Past Impacts the Future”. Notices of the American Mathematical Society 69, no. 2 (2022):239-247. https://doi.org/10.1090/noti2419.
Kitagawa, Tomoko L., and Eder Kikianty. “A History of Mathematics in South Africa: Modern Milestones”. Mathematical Communities 43, no. 4 (2021): 33-47. https://doi.org/10.1007/s00283-021-10068-8.
Moraes, Carlos Roberto. “Uma História da Lógica no Brasil: A Era Dos Pioneiros”. Revista Brasileira de História da Matemática 8, no. 15 (2008): 57-73. https://www.rbhm.org.br/index.php/RBHM/article/view/185/172.
Najmabadi, Afsaneh. “Beyond the Americas: Are Gender and Sexuality Useful Categories of Analysis?”. Journal of Women’s History 18, no. 1 (2006): 11-21. https://doi.org/10.1353/jowh.2006.0022.
Schappacher, Norbert. Framing Global Mathematics: The International Mathematical Union between Theorems and Politics. Cham: Springer, 2022.
Secco, Gisele Dalva, and Miguel Alvarez Lisboa. “History of Logic in Latin America: The Case of Ayda Ignez Arruda”. British Journal for the History of Philosophy 30, no. 2 (2022): 384-408. https://doi.org/10.1080/09608788.2021.2006139.
Smith, Geoff. “International Mathematical Olympiad 2010 UK leader’s report: Almaty and Astana, Kazakhstan”. UK IMO Register. Online HTML version last updated 5 January 2016. https://www.imo-register.org.uk/2010-report.html.
South African Government. “Joseph Albert Mashite Mokoena: Order of Ikhamanga in Gold”. https://www.gov.za/about-government/joseph-albert-mashite-mokoena.
S2A3 Biographical Database of Southern African Science. https://www.s2a3.org.za/bio/Main.php.
Thomas, Keith. “Numeracy in Early Modern England. The Prothero Lecture.” Transactions of the Royal Historical Society 37 (1987):103-32. https://doi.org/10.2307/3679153.
Wilson, Robin, John J. Watkins, and David J. Parks. Graph Theory in America: The First Hundred Years. Princeton: Princeton University Press, 2022.
Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Culture. Boston: Prindle, Weber, and Schmidt, 1973.

WEDNESDAY 16 APRIL

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

Vrhovski, Yuan, Han, ?Li, ?Ghosh

Vrhovski: focused on history of mathematical logic, 1920-1960s, combining Republican Period and the PRC; opening with intellectual history of modern China and mathematics; two big problems:

Problem 1: area studies, postcolonial essentialism obscures the topics that can be studied because the topics too close to Western areas in math and science have been overlooked; local Chinese essentialism and global essentialism make it hard to see Chinese intellectual history and mathematics clearly.

Problem 2: (postcolonial theory) absence of agency in the colonised subject; modern history occurs in a framework of alienation; it is percieved in the West that the Chinese passively accepted Western ideas rather than having an active role in intellectual appropriation; percieved lack of historical agency: among Chinese historians they 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: raised/UG in China, PhD and career in Brazil. European origins of mathematical research directions; French influence on South America; IMPA - grad programme, students come to Brazil/IMPA for PhD training; olympiad project 2005 spend money in context of corruption, school mathematics 2017/18 official Mathematics Years; Chinese government baseline posture of support for mathematics, unlike most governments. 1998 - onward, improved funding environment for academic mathematics in China ; political context of research. BRICS Mathematics Conference, first in Beijing; last planned event in South Africa skipped due to pandemic; this year will be December in Beijing. Intervening events in Brazil, India, Russia. BRICS has expanded. Starting BRICS Mathematical Union to promote integration across BRICS group. Future: cooperation programme ICM2018 paper on applied maths in Brazil; first PhD in Brazil 1848.

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

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

MB 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: history of modern statistical sciences, late 19c census, modern disciplinary history of statistics from 1910s/20s: PC Mahalanobis, institution-building, producing nationalist discourse of instiution-building and science in service of the everyday life of the masses. Discursvie orientation toward national welfare, purpose of statistical surveys/analysis to social condition. E.g. random sample survey, taken up internationally 1940s/50s. Earlier years works with/against Karl Pearson’s work, 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: interest in DD Kosambi (1907-1966): maths, but also stats and probability. Working in India 1930 onwards, educated in Cambridge Mass, entirety of education in America in contrast to Mahalanobis/ Bhabha / etc. exposure to Cambridge. American vs English style. DDK influenced by Birkhoff, Graustein, Stone, one of first to bring this influence to India. DDK never identified too strongly as Indian, had a disciplinary arrogance about his ability to contribute and entitlement to correspond with elites in research fields. Relationship with Andre Weil (functioned as a sponsor to DDK); DDK’s Bourbaki citation, Weil calls the journal ‘provincial’. DDK at TIFR, break with 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 letters to Bhabha about building up a school of mathematics cover aspects like fields of research, attempting to get Harish Chandra, Minakshisundaram, etc. to return to India. Antagonism to PC Mahalanobis, difficult to see what sparked it but seems to come as reaction to PCM institution-building role and his national/political/international influence, that he had Nehru’s ear; maybe not jealous but writes disparaging letters about PCM particularly to Wiener. Kosambi also had a distance function (genes on chromosome); applied stats was important to DDK, especially birthrate/deathrate, social context very important: ‘combined method’ in his work. Riemann Hypothesis proof damaged reputation. Prior to this he was on 1950/54 Fields Medal committee, seen as representative of Indian mathematics. Success of K Chandrasekharan threatened DDK’s preeminence at TIFR. Important paper in Russian on Hindu-Aryan nasal index, debunks colonial preoccupation with caste and nose width.

Kosambi’s connection with SS Chern, 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: Euler as start of Russian maths in the Russian historiography, functioned as imported expertise. Q: 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. 18c Moscow University. 19c explosion of universities, e.g. Khazan, Kharkov. Moscow Mathematical Society mid-19c (approx coeval with London Math Soc), counterpart to St Petersburg, more inward-looking initially (compared to St Petersburg Academy), establishing audience for Russian language mathematics. By early 20c, Moscow Math Soc seems aloof from international scene; the internationally-connected Russian mathematicians are coming from Khazan, St Petersburg, e.g. A Vasileev. 1920s idea of trying to make a more internationally visible society, more widespread use of Western languages in Russian journals, principally Math. Sbornik. Some precedent from Kharkov. 1948 Soviet mathematics journals in Russian by official decision. There is an appetite elsewhere for people to read this material. Subsequent story about translation.

Slava Gerovitch: Famous case of Lobachevsky’s geometry, NL was president of Khazan University – provincial university within Russia, and this affected how his work was viewed in Moscow; his admin position at Khazan allowed him to publish his work. Tradition rooted in Russian Orthodoxy and rigid/conservative political-philosophical outlook assoc with Moscow in late 19c: Moscow Mathematical-philosophical School. 1920s reorientation toward contact with French mathematicians, esp in exchanges to/with Paris, publishing in French (see Graham and Kantor ref: Naming Infinity, a somewhat controversial argument). Later period: social mechanisms of working in Soviet maths community in the period in context of education/research discrimination against social/ethnic groups (Jews, Germans, political dissidents and their children, graduates of specialist mathematical high schools). Discrimination included restrictions on educational admissions and awarding, careers, recognition. Mathematicians developed mechanisms to circumvent barriers: 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 very difficult to track in archives; existing archives are quite distorted even if one gets access. Current method: oral history (19 and counting), inflected by community folklore, distortion through repetition, etc. Can reconstruct history of discriminatory practices by studying counter-practices and informal institutions made in response.

Ksenia Tatarchenko: what happens to graduates of the special mathematical schools? incorporated into specialist jobs esp in Siberia. Who belongs to the mathematical community? Always a somewhat open question. Looking at individuals who have to make their way into the community. Marginalisation / marginality a major theme. Looking into consolidation of academic community under auspices of Siberian branch of academy of sciences (1957), host Soviet-American 1963 PDE symposium. Provincialisation and internationalisation intertwined. (ref: KT article on Novosibirsk as scientific showcase) Geography of decentralization: new centres emerge, movement to East in Akademgorok. Mathematical-Physical school of early 1960s. “Wild West” imagery, narrative. Movement to Omsk. 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: thinking about Dmitri Pospelov - computing and AI. DV holds prestigious positions, editorship of Technical Cybernetics journal, possible reln 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:

Azoulay, Ariella Aïsha. Potential History: Unlearning Imperialism. New York: Verso, 2019.
Gerovitch, Slava. “Parallel Worlds: Formal Structures and Information Mechanisms of Postwar Soviet Mathematics”. Historia Scientiarum 22, no. 3 (2013): 181-200.
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Provincializing Modern Mathematics Transactions 16 April 2025