Mathematical Practice, Crowdsourcing, and Social Machines

Posted on by Simon Fokt

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend.

The Study of Mathematical Practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice – for example the community question-answering system mathoverflow contains around 40,000 mathematical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of “soft” aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal.

Crowdsourced mathematical activity is an example of a “social machine”, a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.

Transforming the inner circle: Dorothy Smith’s challenge to sociological theory

Posted on by Simon Fokt

Abstract: “Women have been largely excluded from the work of producing the forms of thought and the images and symbols in which thought is expressed and ordered,” suggests sociologist Dorothy E. Smith. “We can imagine women’s exclusion organized by the formation of a circle among men who attend to and treat as significant only what men say.” In this male discourse, “what men were doing was relevant to men, was written by men about men for men . . . this is how a tradition is formed” (Smith 1987, p. 18). Smith’s perspective aptly describes the outer circle that delineates sociology from other equally male-centered disciplines, but it also characterizes the important inner circle of sociological theory lying at the center of the field.

Feminist Epistemology and Philosophy of Science

Posted on by Simon Fokt

Abstract: Feminist epistemology and philosophy of science studies the ways in which gender does and ought to influence our conceptions of knowledge, the knowing subject, and practices of inquiry and justification. It identifies ways in which dominant conceptions and practices of knowledge attribution, acquisition, and justification systematically disadvantage women and other subordinated groups, and strives to reform these conceptions and practices so that they serve the interests of these groups. Various practitioners of feminist epistemology and philosophy of science argue that dominant knowledge practices disadvantage women by (1) excluding them from inquiry, (2) denying them epistemic authority, (3) denigrating their ‘feminine’ cognitive styles and modes of knowledge, (4) producing theories of women that represent them as inferior, deviant, or significant only in the ways they serve male interests, (5) producing theories of social phenomena that render women’s activities and interests, or gendered power relations, invisible, and (6) producing knowledge (science and technology) that is not useful for people in subordinate positions, or that reinforces gender and other social hierarchies. Feminist epistemologists trace these failures to flawed conceptions of knowledge, knowers, objectivity, and scientific methodology. They offer diverse accounts of how to overcome these failures. They also aim to (1) explain why the entry of women and feminist scholars into different academic disciplines, especially in biology and the social sciences, has generated new questions, theories, and methods, (2) show how gender and feminist values and perspectives have played a causal role in these transformations, (3) promote theories that aid egalitarian and liberation movements, and (4) defend these developments as cognitive, not just social, advances.