# MathSoMac: the social machine of mathematics 2018-2023 (Extension)

MathSoMac: the social machine of mathematics 2018-2023 (outline)

**EPSRC Fellowship, the Social Machine of Mathematics**

The purpose of this UKRI/EPSRC Fellowship, 2014 - 2023, was to investigate cultures of mathematics viewed as a so-called "Social machine", an over-arching framework for considering human-machine collaboration. The resulting highly interdisciplinary portfolio of work drew on philosophy, social science, ethnography and history, alongside computer science research in artificial intelligence, argumentation theory and verification.

A particular focus was career development for postdocs, whose destinations included: Joe Corneli (Oxford Brookes), David Dunning (University of Pennsylvania), Chris Hollings (University of Oxford), Lorenzo Lane (UK government), Lee Macdonald (Greenwich Observatory), Jess Meagher (Royal Collection Trust), Alison Pease (University of Dundee), Gabriela Rino-Nesin (University of Brighton), Brigitte Stenhouse (University of Toronto), Máté Szabó (University of Greenwich), Fenner Tanswell (Technische Universität Berlin), Jacob Ward (University of Maastricht).

A landmark event was **Big Proof **, a major programme at the Cambridge Newton Institute in Summer 2017, which is credited with shifting the dial on how mathematicians think about using computation in proof. Other workshops included: **Group knowledge and mathematical collaboration ** 7-8 April 2017, Oxford Mathematics; **Enabling mathematical cultures ** 5-7 December 2017, Oxford Mathematics; Mathematical Collaboration II St Andrews 7-8 April 2018, and **Big Proof II ** 27-31 May 2019, ICMS Edinburgh.

### EPSRC Fellowship: Impact

**Mathematics policy and the impact of mathematics** We use materials submitted for the 2014 Research Excellence Framework as an evidence base to assess the mechanisms by which mathematics has impact, highlighting the importance of interdisciplinarity, relationship building and the long term view. The work was cited in a number of submissions to the 2017 HEFCE consultation on the REF, and in the 2019 Bond Review on Mathematics Knowledge Transfer, which led a substantial uplift in UK mathematics funding.

**Meagher,****Laura R.**and Martin, Ursula, 2017**Slightly dirty maths: The richly textured mechanisms of impact****Research Evaluation 26 (15-27)**- Widely disseminated through invited pieces in Times Higher, London Mathematical Society Newsletter, and IMA Mathematics Today magazine.

**Collaborations with Libraries and Museums** led to four public engagement projects, and a UKRI Impact Case Study, as described at the links:

**The mathematics of Ada Lovelace, 2015-2021**, including a popular book, highly cited journal papers, museum displays in the UK and USA, a conference, numerous public talks, and collaborations with composers. The work was submitted as an Impact Case Study for the 2021 UK Research Excellence Framework.**Oxford's female computing pioneers, 2020**, a series of oral history interviews by Georgina Ferry, archived in Oxford's Bodleian Library.**Imagining AI, 2022**, including a workshop, displays at the Bodleian Library and the History of Science Museum, and bespoke video of the Jevons "Reasoning piano". A much larger display had originally been planned, but could not go ahead because of the pandemic.**Archiving Babbage 2022**, the cataloguing, digitisation and dissemination of MSS Buxton, manuscripts of Charles Babbage collected by Harry Wilmot Buxton and now held in Oxford's History of Science Museum.

### EPSRC Fellowship: Main research themes

**Mathematical collaboration online ** Online collaboration captures informal processes that are normally not recorded. A variety of quantitative and qualitative techniques were used to investigate the PolyMath projects, and the MathOverflow Q&A site, to understand what's involved in developing a proof, and the fit with the model provided by social machines.

**Alison Pease, Ursula Martin, Fenner Stanley Tanswell, Andrew Aberdein 2020**,**Using crowdsourced mathematics to understand mathematical practice ZDM 52, 1087-1098**A capstone article, by invitation for a special issue, presenting our methods in the context of mathematical education**Martin, Ursula 2016 Computational logic and the social Journal of Logic and Computation, 26, 467-477**provides an overview in historical context.**Martin, Ursula and Pease, Alison 2015 Stumbling around in the dark: lessons from everyday mathematics Springer LNCS, 9195, 29 - 51**(invited plenary for 25 years of CADE, the major conference on automated deduction) looks at social machines in the context of formal proof and experimental mathematics**Martin, Ursula and Pease, Alison 2015, Hardy, Littlewood and Polymath**in**Mathematics, Substance and Surmise: Views on the Meaning and Ontology of Mathematics, ed Ernest Davis, Philip J. Davis, Springer**frames the polymath experiments in the context of G H Hardy's views of collaboration**Martin, Ursula and Pease, Alison 2013 What does mathoverflow tell us about the production of mathematics? SOHUMAN workshop at CHI 2013, Paris**is a preliminary study of the mathoverflow Q&A site for research mathematics, and provides a typology of questions and answers**Martin, Ursula and Pease, Alison 2013****Mathematical practice, crowdsourcing, and social machines****International Conference on Intelligent Computer Mathematics, Springer 7961, 98-119**(invited plenary) lays out the research agenda in the context of formal proof and social machines**Martin, Ursula and Pease, Alison 2012 Seventy four minutes of mathematics: An analysis of the third Mini-Polymath project****Proceedings of AISB/IACAP 2012, 52-105**, is a preliminary study of the mini-polymath experiments and provides a typology of the mathematical activities they exhibit - proof, examples, concept formation and the like.

**Modelling mathematical conversations with argumentation theory****y ** Social machines provide models for mathematical argument using argumentation theory and LSC - the lightweight social calculus.

**Joseph Corneli, Ursula Martin, Dave Murray-Rust, Gabriela Rino-Nesin, Alison Pease 2019****Argumentation theory for mathematical argument****Argumentation 33, 173-21**A prototype system for modelling mathematical arguments using Reed's argumentation calculus and Robertson's LSC**Joseph Corneli, Simon Holland, Alison Pease et al 2018, Patterns of design Proceedings of the 23rd European Conference on Pattern Languages of Programs, 1-11****Pease, Alison,**Corneli, Joseph et al, 2017 Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation Artificial Intelligence 246, 181–2192017 Towards mathematical AI via a model of the content and process of mathematical question and answer dialogues , in Intelligent Computer Mathematics, 10th International Conference, Edinburgh, UK**Corneli, Joseph,**Pease, Alison,**Martin, Ursula, Murray-Rust, Dave and****Corneli, Joseph; Martin, Ursula; Murray-Rust, Dave; Pease, Alison; Puzio, Raymond; Nesin, Gabriela Rino, 2017 Modelling the way mathematics is actually done, FARM 2017 - Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design, co-located with ICFP 2017**

**Philosophy and mathematical practice** The "Polymath" online mathematical collaborations were used as an evidence base for understanding mathematical practice, in particular to assess notions of explanation in mathematics. Fenner Tanswell works on the connection between formal and informal proofs

**Alison Pease, Andrew Aberdein, Ursula Martin, 2019, Explanation in mathematical conversations: An empirical investigation, Philosophical Transactions of the Royal Society A 377**Uses analysis of a polymath conversation as an evidence base to assess 9 hypotheses, drawn from the philosophical literature, about mathematical explanation**Lorenzo Lane, Ursula Martin et al, 2019, Journeys in mathematical landscapes: genius or craft? Proof Technology in Mathematics Research and Teaching (Springer) 197-212**Explores craft as a metaphor for creating mathematics**Fenner Tanswell 2018 Conceptual engineering for mathematical concepts Inquiry 61, 881-913****Fenner Tanswell 2017 Playing with LEGO® and Proving Theorems, LEGO® and Philosophy: Constructing Reality Brick by Brick, 217-226****Fenner Tanswell 2016 Saving proof from paradox: Gödel’s paradox and the inconsistency of informal mathematics , Logical Studies of Paraconsistent Reasoning in Science and Mathematics, 159-173****Fenner Tanswell 2015 A Problem with the Dependence of Informal Proofs on Formal Proofs Philosophia Mathematica 23, 295-310**

**The early roots of contemporary mathematical and computational practices **

**David Dunning, 2023, George Boole and the ‘Pure Analysis’ of the Syllogism. 2023 In Aristotle’s Syllogism and the Creation of Modern Logic: Between Tradition and Innovation, FGHI–FKLI, eds. Lukas M. Verburgt and Matteo Cosci. Bloomsbury Academic.****David Dunning, 2021, The Work of Writing Programs: Logic and Inscriptive Practice in the History of Computing, IEEE Annals of the History of Computing 25, 27-42****David Dunning, 2021, The Logician in the Archive: John Venn’s Diagrams and Victorian Historical Thinking. Journal of the History of Ideas 82, 593-614****David Dunning, 2020, Always Mixed Together’: Notation, Language, and the Pedagogy of Frege’s Begriffsschrift. Modern Intellectual History 17 (1099-1131)****Máté Szabó et al (2023). How Computers Entered the Classroom in Hungary: A Long Journey from the Late 1950s into the 1980s. In Flury C, Geiss M (Ed.), How Computers Entered the Classroom, 1960–2000: Historical Perspectives. Oldenbourg:De Gruyter****Máté Szabó (2021). Péter on Church’s Thesis, 17th Conference on Computability in Europe, CiE 2021, Springer (pp. 434-445).****Máté Szabó (2021). From the West to the East and Back Again: Hungary's Early Years in the Ryad. IEEE Xplore Digital Library,****Máté Szabó (2020). Alonzo Church Tihanyban. Érintö, Elektronikus Matematikai Lapok****Jacob Ward, 2020, Computer Models and Thatcherist Futures: From Monopolies to Markets in British Telecommunications, Technology and Culture 61 (843-870)**

**T****he nature of mathematical collaboration, an ethnographic appro****ach**** **These careful ethnographic studies at mathematics research institutes looked at the activities of mathematicians as they collaborated in person, and identified a variety of processes for generating shared knowledge

**Lane, Lorenzo****2017**Fixed performances in fluid publics, 5th Innovation in Information Infrastructures (III) Workshop**Lane, Lorenzo and Martin, Ursula****2015**Collaboration at the Isaac Newton Institute Report for the Isaac Newton Institute