Extension: MathSoMac: the social machine of mathematics

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Informatics

Abstract

This is an extension of the Fellowship: 'MathSoMac: the social machine of mathematics', which is an Established Career Fellowship, 2014-2018, EPSRC EP/K040251/2

Mathematics is recognized as a profound intellectual achievement, with impact on many aspects of wealth creation and quality of life, and as unique cultural capital, drawing crowds to exhibitions and public lectures. For centuries, the highest level of mathematics has been seen as an isolated creative activity, to produce a proof of a difficult theorem for review and acceptance by research peers. However, at a remarkable inflexion point, new technology is radically extending the power and limits of individuals.

Websites such as the polymath or mathoverflow sites allow researchers to collaborate with each other, and "show their working", so that others outside their specialist field can engage with their research and get early insight into things that might be useful. Now routinely used for verification of hardware and software designs, and in cyber-security, computer proof goes beyond symbolic computation, or numerical simulation, to generate mathematical arguments too complex for humans to grasp, and to check these chains of inference from first principles.

These phenomena have typically been viewed as distinct, linked only by their relationship to mathematics. Yet they have many common features, not least, as we showed in the original project, their dependence, ultimately, on human and social issues of mathematical judgement and creativity.

In this proposal, to extend our current research, we view these phenomena as a united whole, in which people and computer systems combine into a single problem-solving entity, where individuals interact with each other, and with computers which draw on a single "engine" of computer proof. We call this model of the production and application of mathematics the "social machine of mathematics" based on the new paradigm of "Social machines", identified by Berners-Lee about 20 years ago.

We focus on two research questions:
=== "Beyond Inference": how can we give human mathematicians the benefits of computer proof, while shielding them from its complexity?

=== " Towards impact: how can we evaluate the impact and cultural capital of foundational research?

Planned Impact

This is an extension of the Fellowship: 'MathSoMac: the social machine of mathematics'. This is an Established Career Fellowship, 2014-2018, EPSRC EP/K040251/2

By "Mathematics" we mean "Foundational research of a mathematical nature" - encompassing logic, theory of computing, statistics, and pure and applied mathematics, irrespective of administrative boundaries. Academic impact is described the previous section; non-academic impact is considerably overlapping.

"Beyond inference"
=== developers of computer verification and proof tools, as our work will contribute new techniques and understanding of the tools themselves, through extending their application, through the use of f-abstracts to bridge the gap between formal and informal proof.

=== mathematicians and users of mathematics will have access to tools that allow them to create and access new mathematics more quickly: specifically, our work on f-abstracts will contribute to developing new ways in which such users can access the benefits of computer proof, while being shielded from its complexity

=== mathematics educators, and those building tools for them will have new material and techniques for teaching proof, in particular we hope to deploy our techniques through our partnership with Maplesoft, with products and services used by more than 8000 educational institutions and other organisations, in over 90 countries.


Of "Towards impact"
=== researchers, and users, managers, and funders of research, who need to understand drivers for success, failure and impact of foundational research; track quantitative and qualitative whole-life indicators of promise and progress; develop resilient plans, responsive to such indicators as research proceeds; interpret impact to diverse audiences, to shape research strategy and practice; and, crucially, do this without impeding research quality and progress or increasing the burdens on researchers.

=== All those who communicate the impact of foundational research of a mathematical nature, either within or beyond their own community, or in professional settings such as museums, with a new framing as "Cultural capital" enabling broader thinking and assessment.

Publications

10 25 50
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Corneli J (2019) Argumentation Theory for Mathematical Argument in Argumentation

 
Description Major thread of public impact around nineteenth century science and the foundations of modern computing
Exploitation Route Wide variety of of impacts reported in the impacts section
Sectors Creative Economy,Digital/Communication/Information Technologies (including Software),Education,Culture, Heritage, Museums and Collections

URL https://people.maths.ox.ac.uk/martinu/
 
Description Wide variety of impacts on museums, music, cultural practice and education as reported in public engagement section
First Year Of Impact 2018
Sector Communities and Social Services/Policy,Creative Economy,Digital/Communication/Information Technologies (including Software),Education,Culture, Heritage, Museums and Collections
Impact Types Cultural

 
Description "Hay Levels" YouTube video 
Form Of Engagement Activity A broadcast e.g. TV/radio/film/podcast (other than news/press)
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Schools
Results and Impact A YouTube video of Ursula Martin's "Hay Levels" YouTube video, part of a Hay Festival series showing 'bite size answers to big questions'
Year(s) Of Engagement Activity 2018
URL https://youtu.be/g49Sy9T1BUg
 
Description Armadillo Magazine 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact Amadillo Magazine Children's books reviews, circa summer 2018
Year(s) Of Engagement Activity 2018
URL https://www.armadillomagazine.co.uk/non-fiction-1
 
Description BBC Radio Oxford Lilley Mitchell show 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Media (as a channel to the public)
Results and Impact 7 minute interview in between David Bowie and Queen
Year(s) Of Engagement Activity 2018
URL https://www.bbc.co.uk/programmes/p06dbvbb
 
Description Bodleian Libraries "Babel exhibition" 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Bodleian Libraries "Babel: adventures in translation" museum exhibition 15 February - 2 June 2019. Ursula Martin advised and wrote captions for programming related items, including Lovelace "first programme".
Year(s) Of Engagement Activity 2019
URL https://www.bodleian.ox.ac.uk/whatson/whats-on/current-exhibitions
 
Description Computer History Museum, Mounrtain View, California + Facebook live streaming 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Presentation on Ada Lovelace and her life and work.
Year(s) Of Engagement Activity 2019
URL http://www.computerhistory.org/events/upcoming/#ada-lovelace-making-computer-scientist
 
Description Edinburgh Book Festival with Darryl Cunningham 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact Presentation on Ada Lovelace and her life and work.
Year(s) Of Engagement Activity 2018
URL https://www.edbookfest.co.uk/the-festival/whats-on/darryl-cunningham-ursula-martin-12046
 
Description Erasmus Darwin House 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact Seminar day at Erasmus Darwin House Lichfield on "Lunar women". Presentation on Ada Lovelace and her life and work.
Year(s) Of Engagement Activity 2018
URL http://www.erasmusdarwin.org/event/seminar-day-lunar-women/
 
Description General talk on Lovelace's life and work, and our research 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Postgraduate students
Results and Impact Audience included the Oxford Mirzakhani Society and visiting female Cambridge maths students.
Year(s) Of Engagement Activity 2018
 
Description History of women philosophers event 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Lecture "Ada Lovelace 1815-1852: Logic and Computing Before the Computer" "The History of Logic: Women's Contributions", Paderborn, Germany.
Year(s) Of Engagement Activity 2018
URL https://historyofwomenphilosophers.org/event/the-history-of-logic-womens-contributions/
 
Description Lecture University of Kent 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Undergraduate students
Results and Impact "The scientific life of Ada Lovelace, and why computer scientists should care about history" by Ursula Martin at School of Computing, University of Kent 50 CS students and staff.
Year(s) Of Engagement Activity 2019
URL https://www.cs.kent.ac.uk/eventscalendar.html?view_by=upcoming&eid=37289
 
Description Lecture at Randolph-Macon College, Virginia 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact "Beyond the strength of a woman's physical power: Mathematics, Machines, and the Mind of Ada Lovelace" by Adrian Rice. Lecture was free and open to the public.
Year(s) Of Engagement Activity 2018
URL https://www.rmc.edu/news-and-calendar/current-news/2018/08/28/oct.-9-mathematics-professor-to-presen...
 
Description Lecture in the Philadelphia Area Seminar on the History of Mathematics, Villanova University, PA, USA. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact 'Ada Lovelace: The Making of a Computer Scientist' by Adrian Rice.
Year(s) Of Engagement Activity 2018
URL https://www1.villanova.edu/villanova/artsci/mathematics/newsevents/pashom.html
 
Description Leverhulme Centre for the future of Intelligence Cambridge 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Closed seminar, AI origin myths.
Year(s) Of Engagement Activity 2018
URL http://lcfi.ac.uk/events/origin-myths-artificial-intelligence-histories-tec/
 
Description Mathematics Today 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact 'Ada Lovelace, Mathematician' in Volume 51 Issue 6 (December), pp. 254-255.
Year(s) Of Engagement Activity 2018
URL https://ora.ox.ac.uk/objects/uuid:922e6961-dba6-4a50-a161-bf6cd2698752
 
Description Musuem of the History of Science Oxford 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Presentation on Ada Lovelace and her life and work. Repeated in Jan 2019 due to popular demand.
Year(s) Of Engagement Activity 2018,2019
URL https://hsm.ox.ac.uk/event/ada-lovelace-the-making-of-a-computer-scientist
 
Description New York Review of Books review 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact "Stepping out of Byron's Shadow" by Jenny Uglow. via Bodleian PR.
Year(s) Of Engagement Activity 2018
URL https://www.nybooks.com/articles/2018/11/22/ada-lovelace-byron-shadow/?sub_key=5bdd796816d47
 
Description New York Times website 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Article in NYT's interactive "Overlooked" Obituaries - on Ada Lovelace. Quotes Ursula Martin and other scholars/authors focused on Ada and her work. Links to Ursula Martin's "Research in Conversation"
Year(s) Of Engagement Activity 2018
URL https://www.nytimes.com/interactive/2018/obituaries/overlooked-ada-lovelace.html
 
Description Resolution of US Senate recognizing Ada Lovelace 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Ursula Martin advised on wording.
Year(s) Of Engagement Activity 2018
URL https://www.congress.gov/115/bills/sres592/BILLS-115sres592ats.pdf
 
Description Royal Holloway University of London 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Ursula Martin advised on Lovelace exhibition
Year(s) Of Engagement Activity 2018
URL https://www.royalholloway.ac.uk/research-and-teaching/departments-and-schools/computer-science/news/...
 
Description The Guardian 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Article on the sale of a copy of Ada's first edition algorithm, with Ursula Martin interview comments
Year(s) Of Engagement Activity 2018
 
Description The Oxford Scientist 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Undergraduate students
Results and Impact The Oxford Scientist #1, Hilary Term 2018. "The Oxford Scientist Interviews Prof Ursula Martin", pages 9-10. Really lovely interview with Ursula Martin where she talks a lot about Ada, and the book.
Year(s) Of Engagement Activity 2018
 
Description The School Librarian magazine, School Library Association 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Quarterly journal, circulation 4000 and readership 13300.
Year(s) Of Engagement Activity 2018
URL https://www.dropbox.com/s/ysqbqxgl8gt9b13/The%20School%20Librarian%201%20Oct%202018%20Review.pdf?dl=...
 
Description The Smithsonian 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Article again on the sale of Ada's first edition paper, picking up on Guardian article above with Ursula Martin comments
Year(s) Of Engagement Activity 2018
URL https://www.smithsonianmag.com/smart-news/sold-rare-copy-ada-lovelaces-groundbreaking-computer-algor...
 
Description Times Literary Supplement book review 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact 'Wild Spirits: Illustrating the Lives of Accomplished Women' by Corin Throsby. Review of our book and Miranda Seymour's 'In Byron's Wake'.
Year(s) Of Engagement Activity 2018
URL https://www.the-tls.co.uk/articles/private/wild-spirits/
 
Description UK Mathematics Trust, London Science Museum 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Schools
Results and Impact Lecture to circa 200 Math Olympiad competitors and families, later on YouTube.
Year(s) Of Engagement Activity 2018
URL https://www.youtube.com/watch?v=CNS4-6cS_AU&feature=youtu.be
 
Description University of Oxford AI podcast 
Form Of Engagement Activity A broadcast e.g. TV/radio/film/podcast (other than news/press)
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Podcast with Andrew Hodges and Jacob Ward on history of AI.
Year(s) Of Engagement Activity 2018
URL https://twitter.com/UniofOxford/status/1064428317292412928
 
Description University of Wyoming, Laramie, Wyoming USA 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Presentation on Ada Lovelace and her life and work as part of celebrations of 150 years of female suffrage in Wyoming, the first US state to offer women the vote
Year(s) Of Engagement Activity 2019