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Virtues and Vice in Mathematics

Periodic Reporting for period 1 - VaViM (Virtues and Vice in Mathematics)

Reporting period: 2020-09-01 to 2022-08-31

The Marie Skłodowska-Curie action “VaViM: Virtues and Vice in Mathematics” looks at (some of) the ethical dimensions of the production of mathematical knowledge. The project addresses what kind of mathematical knowledge is produced and who gets to produce it. These are societally relevant questions because mathematical knowledge permeates our human lives: it shapes our social media feeds in the form of algorithms, it features in the development of militaristic technologies, and mathematical ability functions as an indicator of intellectual excellence. Furthermore, despite narratives about the objectivity of mathematical reasoning, what counts as new, relevant, significant, and worthy content is partially determined in the social processes of mathematical research activity, such as funding decisions, peer review, or collaborative efforts, which are prone to biases and exclusionary mechanisms. The ethics of mathematics thus has to do not only with how and where mathematical knowledge is applied to the world, but also with how it is produced and who is involved in these processes.

Mathematical communities are starting to pay more attention to the ethical dimensions of their research activities. They debate issues of social justice in mathematical research practices and point out that mathematics students are ill-prepared for the ethical challenges they will face when working as bankers, writers of computer codes etc. These are socially relevant questions that merit philosophical engagement, but philosophers have thus far largely ignored the ethical dimensions of mathematical knowledge-making. A primary objective of VaViM is to address this lacuna. The project provides detailed case study based arguments that reveal and discuss these ethical dimensions of the production of mathematical knowledge, and proposes concrete interventions to navigate these challenges. The project studies forms of exclusion from mathematical knowledge-making activities. Some forms of exclusion are justified, such as filtering processes that seek to ensure quality of mathematical research. Other forms of exclusion are unjustified, such as the evaluation of mathematical work based on epistemically irrelevant social identifiers (e.g. race, gender, geographic location). VaViM studies both forms of exclusion from mathematical knowledge-making.
Work was conducted via 4 work packages (WPs). WP1 dealt with the philosophical frameworks used to engage with the ethics of mathematics. Weekly reading groups with the host research group and numerous personal discussions with team members aided my literature review of diverse philosophical fields such as argumentation theory, social epistemology, feminist theory, and virtue epistemology. WP2 covered the philosophical analysis of the ethics of mathematical knowledge-making. It yielded four academic papers (two published, two in press), 13 presentations at academic events, and one manuscript to be submitted shortly. WP3 covered VaViM’s outreach activities, including the organisation of a conference on disagreement in mathematics and the guest-editing of a topical collection on the topic, an article presenting VaViM, the maintenance of a webpage (https://vavimproject.wixsite.com/home) a twitter account (@vavimproject), and a European Researcher’s Night presentation. Special focus lay on establishing connections with mathematical communities. This led to a joint publication with mathematician Eugenie Hunsicker, presentations at three academic events organised by mathematical communities, and a position as co-author for the report for one of these events (in preparation). WP4 covered training activities for me as an Individual Marie Skłodowska-Curie Fellow. These included the supervision of a BA thesis, teaching a BA level course in theoretical philosophy, student guidance, and a position on a committee to appoint a new assistant professor.
This Marie Skłodowska-Curie Action (MSCA) has pushed the frontiers of research on the ethics of mathematics forward in numerous ways. The conference on disagreement in mathematics has shed light on this important but previously largely ignored phenomenon, and the topical collection I guest-edited provides a collection of relevant insights on the matter. My publications have established new points of contact between mathematical and philosophical discourse by: revealing that the ethics of mathematics is relevant to the epistemology of mathematics; philosophical assessments of proposed structural interventions to foster ethically praiseworthy behaviour amongst mathematicians; speaking to the ethics of justified exclusions in mathematics.

This MSCA allowed me to develop agility with many research methodologies and to familiarise myself with various streams of research in philosophy, mathematics education, sociology of mathematics, and discourses about diversity, equity, and inclusion (DEI) policies for mathematics. The action enabled me to connect with mathematical communities and policy makers, e.g. my joint work with Eugenie Hunsicker, which will shape my future work. The MSCA also established me as a leading scholar in philosophical debates of the ethics of mathematics, as witnessed by invitations to contribute to conferences and a book project.

Further impacts anticipated from this MSCA are increased and improved: awareness of the ethics of mathematics amongst philosophers and the public at large; conceptual clarity in the DEI policy debate in mathematics; understanding of the exclusionary mechanisms of mathematical knowledge-making; and bridges between mathematical and philosophical communities. A final overarching impact is fostering a more humanised conception of mathematics.
Left to right: N. Ashton, C.D. Novaes, E. Delville, S. Attila, M. Talbi, E. Varini, me, & K. Furman
Studying the ethics of mathematical knowledge production