### Workshop, University of Oxford, 8th & 9th April 2017

Organisers: Fenner Stanley Tanswell, Lorenzo Lane, Josh Habgood-Coote & Sarah Baldwin

Part of the “Social Machine of Mathematics” project led by Prof Ursula Martin CBE, Department of Computer Science, University of Oxford.

Speakers include:-

- Patrick Allo (Oxford)
- Line E. Andersen (Aarhus)
- Catarina Dutilh Novaes (Groningen)
- S. Orestis Palermos (Edinburgh)
- Jeroen de Ridder (VU Amsterdam)

Location: Room 278 in the Oxford e-Research Centre, 7 Keble Road, Oxford ,OX1 3QG

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. The most famous example is the proof of the classification of finite simple groups, which relied on the work of scores of mathematicians. Likewise, the *polymath *project has shown the power of massive collaboration in mathematics at settling open problems and discovering mathematical proofs.

Nonetheless, the new questions that arise for specifically collaborative work on mathematics have received insufficient philosophical attention, unlike parallel questions about the importance of collaboration in science which have received significant attention. Social epistemology and work on group knowledge have in recent years made a great deal of progress on general issues surrounding epistemic cooperation. Similarly, sociological research on mathematical collaboration has revealed much of the everyday workings of mathematics in practice. In this workshop we aim to explore the social dimensions of mathematics, connecting new work in social epistemology, mathematical practice and sociology, in order to gain a better understanding of how collaboration in mathematics produces knowledge, proofs and understanding.

We will address the following questions:

- Is there distinctively social knowledge in mathematics?
- How can massive mathematical collaboration produce novel proofs and novel theorems?
- What are the epistemic benefits of collaboration and the division of cognitive labour in mathematical work?
- Can crowdsourcing and online collaboration produce genuine proofs of interesting theorems?
- Does it help to view massive collaboration as part of a “social machine” of mathematics?

**Registration**

Registration is free, but must be done in advance to have the lunches. There will also be a workshop dinner at Al-Shami on Saturday evening, at around £20. To register, please email Fenner.Tanswell [at] gmail.com including whether you would like to attend the workshop dinner and any dietary restrictions or further needs. Registration for lunch and the dinner will close on the 1st of April.

Any further enquiries can also be directed to Fenner by email: Fenner.Tanswell [at] gmail.com

# Programme

**S. Orestis Palermos**“Is Polymath a Social Machine?”

**Fenner Stanley Tanswell**“Proving Activities and Collaborative Mathematics”

**Patrick Allo**“Tracking common information and public announcements in Polymath: A data-driven and logically informed method”

**Catarina Dutilh Novaes**“Adversariality and Cooperation in Mathematical Proofs’

**Josh Habgood-Coote**“Collective Mathematical Knowledge”

**Line E. Andersen**“Acceptable Gaps in Mathematical Proofs”

**Lorenzo Lane**“Coordinating Visions: Documenting collaborative knowledge production at mathematics institutes”

**Jeroen de Ridder**“Beyond social knowledge”

The workshop will begin on Saturday at midday with lunch and registration, and the first talk will commence at 13:00. We will be done on Sunday by mid-to-late afternoon, currently planned for 15:30. This will allow people from nearby to travel on those days and only require one night of accommodation. A full programme will be added soon.

For college accommodation (£50+/night), we recommend using:

http://www.universityrooms.com/en/city/oxford/home

There are a number of rooms currently available in Keble college, which is just next door to the workshop. Most of the accommodation they offer will be within easy walking distance of us.

For budget accommodation (£25/night), we recommend the Oxford YHA youth hostel:

http://www.yha.org.uk/hostel/oxford

Again, this is not far from the workshop location.