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# Mathematical Collaboration Workshop II

## April 7 - April 8

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This is a joint Arché-Oxford event, following up on the successful workshop Group Knowledge and Mathematical Collaboration held in Oxford in April 2017.

Mathematics is a deeply social discipline. The stereotype of the “lone genius” is one which does not fit the breadth and depth of mathematical work, which also features everything from one-on-one collaborations to massive collective efforts. Indeed, it is common for proofs of significant theorems to rely on work by many mathematicians working together and in parallel.

In this second edition, we will look at the social virtues that lead to good mathematics in such collaborative settings. We aim to draw on research in mathematical practice, social epistemology, sociology, ethnography and philosophy of science to answer questions about which features of our practices lead to successful and unsuccessful collaborations.

Confirmed speakers:

Stephen Crowley (Boise State University)

Benedikt Loewe (University of Hamburg/University of Amsterdam)

Ursula Martin (University of Oxford)

Katie McCallum (University of Brighton)

Alison Pease (University of Dundee)

Colin Rittberg (VUB Brussels)

Kamilla Rekvenyi (St Andrews)

Christoph Kelp (Glasgow)

Joe Corneli (Edinburgh)

Plus a panel discussion including Peter Cameron, Adam Dunn, Isobel Falconer, Louis Theran.

To register, please email Fenner at ft34@st-andrews.ac.uk Lunches will be provided. Please include any special or dietary requirements. A workshop dinner will be held, but not covered by the budget, though all are welcome to join. Please register your intention to attend that too.

This workshop is organised by Fenner Tanswell (St Andrews) and Josh Habgood-Coote (Bristol) .

We are grateful to the Social Machine of Mathematics at the University of Oxford, EPSCR and the Scots Philosophical Association for their financial support.

SCHEDULE

Saturday 7th April

9:30-10.45 Talk: Josh Habgood-Coote (Bristol) What is the point of authorship?

10.45-11.15 Coffee Break

11:15-12:30 Talk: Benedikt Loewe (Hamburg/Amsterdam) Training future researchers studying mathematical practices and cultures

12:30-1:30 LUNCH

1:30-2:00 Presentation: Kamilla Rekvenyi (St Andrews) Paul Erdős’s Mathematics as a Social Activity

2:00-2:10 Brief break

2:10-3:25 Talk: Stephen Crowley (Boise State) Does Collaboration make Mathematicians Virtuous?

3:25-3:50 Coffee Break

3:50-5:00 Panel Session on mathematical collaboration: Peter Cameron, Adam Dunn, Isobel Falconer, Louis Theran

7:00 Conference Dinner (Maisha)

Sunday 8th April

9:30-10.45 Talk: Colin Rittberg (VUB Brussels) & Fenner Tanswell (St Andrews) Epistemic Injustice in Mathematics (joint work with Jean Paul van Bendegem)

10.45-11.15 Coffee Break

11:15-12:30 Talk: Joe Corneli (Edinburgh) Argumentation theory for mathematical argument

12:30-1:30 LUNCH

1:30-2:45 Chris Kelp (Glasgow) Inquiry, Knowledge and Understanding

2:45-3:15 Coffee Break

3:15-4:15 Talk: Katie McCallum (Brighton) Situating Mathematical Communication: An Artist’s Ethnography of Research Mathematics

4:20-5:30 Talk: Ursula Martin (Oxford) Beyond inference, and towards impact: taking forward the study of mathematical collaboration.

ABSTRACTS

Title- What is the point of authorship?

Josh Habgood-Coote (Bristol)

Abstract. Getting to important results in mathematics often takes the intellectual efforts of many people, each offering different kinds of contribution, as we can see in the polymath project, the classification of finite simple groups, and everyday collaborations. When it comes to writing up collaborative work, the collaborators face the vexed question of who should be included on the author line. Researchers in a number of disciplines — most saliently high-energy physics and biomedicine — have worried about this question, putting forward various proposals for authorship attributions. In this paper, I will offer a different angle on this debate, thinking about the different functions played by authorship attributions, and suggesting that disciplines might do better by replacing the notion of authorship with a pluralist account that distinguishes contributors, writers and guarantors.

Title – Does Collaboration make Mathematicians Virtuous?

Stephen Crowley (Boise State University)

Abstract – The aim of this paper is to consider the ‘fit’ of two important recent views about knowledge making communities. On the one hand the importance of collaboration is becoming increasingly clear, on the other the notion of virtue is being appealed to more frequently as a way to understand the norms of practice of such communities. So far so good – but can we fit collaboration into a virtue based approach, and if not what follows? Mathematics, in addition to its intrinsic interest, is a great case study for thinking about this issue because i) its deeply collaborative and ii) its norms will be almost purely epistemic – no Human Subjects protocols to complicate things – as such a great deal of recent work from virtue epistemology can be ‘imported’ in a relatively straightforward fashion. I’ll suggest here that collaboration is a poor fit with the virtue framework and that the implications of this are that our thinking about the nature of knowledge making communities is still too individualistic.

Title: Inquiry, Knowledge and Understanding

Christoph Kelp (Glasgow)

Abstract: This paper connects two important debates in epistemology—to wit, on the goal of inquiry and on the nature of understanding—

and offers a unified knowledge-based account of both.

Title: Situating Mathematical Communication: An Artist’s Ethnography of Research Mathematics

Katie McCallum (Brighton University)

Abstract: Mathematics is often characterised as existing above and outside of our social and material world. Through ethnographic observation and creative and linguistic analysis I am undertaking to build up a picture of mathematical communication and even solo work as inextricably bound up with rich material and social resources, and its progress dependent on their successful deployment. Written analysis moves in parallel with creative sculptural experimentation in order to do justice to the material element emphasised in this research.

I will be talking about the results of my observations of nine mathematicians in the UK, USA and Europe, combining a cognitivist theory of communication with situated mind ideas in an effort to explain why it is that the study of mathematics takes the particular forms that it does in the world. These forms have developed and been maintained in dialogue with our limited, very human cognitive architecture, and understanding how this is the case might demonstrate that ideas about mind-environment systems have insight to offer in even the most ostensibly disembodied areas of human endeavour.

Title: Training future researchers studying mathematical practices and cultures

Benedikt Löwe

Abstract. The research field studying mathematical research practices and cultures (also known as “philosophy of mathematical practice”) uses methods from the empirical social sciences to study mathematical research practices and in particular cultural variations between different research practices and their effect on mathematics. Sociologists of science are well-equipped with an ample toolbox of methods to do studies like this, but traditionally, they have shown a “peculiar mixture of awe and lack of interest” in mathematics (Heintz, 2000). As a consequence, philosophers of mathematical practice have to follow in the footsteps of experimental philosophers and become empirical scientists themselves. In this talk, I report on a graduate-level course taught at the Universiteit van Amsterdam to train philosophers of logic, science, and mathematics for doing empirical research relevant for the philosophy of mathematical practice.

Title: Paul Erdős’s Mathematics as a Social Activity

Kamilla Rekvenyi (St Andrews)

Abstract: This presentation investigates the collaborative mathematical practice of Paul Erdős. It raises the question of whether communal mathematics, or mathematics as a social activity, can lead to individual success. It draws on new primary sources in both English and Hungarian.

I will look at Erdős’s social mathematics from several angles. Firstly, I will analyse his collaborations and heritage, and the ways he had for finding the ideal mathematician to work with him on each problem. Then I discuss two contrasting case studies: his influence on young mathematicians as exemplified by Kenneth Falconer; and the Erdős-Selberg collaboration on the elementary proof of the prime number theorem, which ended in dispute. Neither of these collaborations resulted in individual success for Erdős, but both furthered, what may have been his main aim: solving beautiful mathematical problems.

Title: Argumentation theory for mathematical argument (joint work with Ursula Martin, Dave Murray-Rust, Gabriela Rino Nesin, Alison Pease)

Joe Corneli (Edinburgh)

Abstract: To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. A paper recently submitted to the journal Argumentation introduces a framework with these properties, which has been applied to both mathematical dialogues and expository texts. (Preprint available: http://arxiv.org/abs/1803.06500 )

Title: Epistemic Injustice in Mathematics

Colin Rittberg (VUB) & Fenner Tanswell (St Andrews) joint work with Jean Paul van Bendegem (VUB)

Abstract: We investigate how epistemic injustice can manifest in mathematical practices. We do this as both asocial epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively – we show that folk theorems can be a source of epistemic injustice in mathematics – and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept to highlight a potential danger of intellectual enculturation. (Let me know if you’d like a copy of this paper.)