MathSoMac: the social machine of mathematics

Lead Research Organisation: University of Oxford
Department Name: Computer Science

Abstract

Mathematics is a profound intellectual achievement with impact on all aspects of business and society.

For centuries, the highest level of mathematics has been seen as an isolated creative activity, 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 that are just too long and complicated for any human to comprehend, using programs designed to verify hardware.

Yet these techniques are currently used in stand-alone fashion, lacking integration with each other or with human creativity or fallibility.

Social machines are new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity. Our long-term vision is to change mathematics, transforming the reach, pace, and impact of mathematics research, through creating a mathematics social machine: a combination of people, computers, and archives to create and apply mathematics.

Thus, for example, an industry researcher wanting to design a network with specific properties could quickly access diverse research skills and research; explore hypotheses; discuss possible solutions; obtain surety of correctness to a desired level; and create new mathematics that individual effort might never imagine or verify. Seamlessly integrated "under the hood" might be a mixture of diverse people and machines, formal and informal approaches, old and new mathematics, experiment and proof.

The obstacles to realising the vision are that
(i) We do not have a high level understanding of the production of mathematics by people and machines, integrating the current diverse research approaches
(ii) There is no shared view among the diverse re- search and user communities of what is and might be possible or desirable

The outcome of the fellowship will be a new vision of a mathematics social machine, transforming the reach, pace and impact of mathematics. It will deliver: analysis and experiment to understand current and future production of mathematics as a social machine; designs and prototypes; ownership among academic and industry stakeholders; a roadmap for delivery of the next generation of social machines; and an international team ready to make it a reality.

Planned Impact

Impact pervades our plans for research: WP 1.3 concerns the nature of the impact of mathematics research, WP 2 will consider impact in all aspects of Social Machines, with Open Innovation as a running example, and in WP3 we have deliberately chosen three timely Case Studies of relevance to needs of business and society: networks, security and energy. Thus we will ensure that our Social Machines meet the needs of users for impact, and so our task becomes that of ensuring that there is a likely take-up when they are built, beyond the end of the project.

The long-term overarching goal of the fellowship is to increase the reach, pace and impact of mathematics research, to benefit practitioners of, and potential users of, such research, in ICT, mathematics and other domains, whether in research labs, government or industry. New ways of working will enable practitioners and users to find more significant results more quickly, and to be able to access a broader range of researchers and research, with a greater degree of assurance of the results. In the lifetime of the project TCS researchers, and research users in security and networks, can engage through WP 3 above, which may provide immediate impacts. Longer term our work on design and roadmapping will be informed by working closely with our co-workers, partners and Advisers, so as to ensure that the tools that are eventually produced meet users needs and have impact.

The pathways to impact include work with stakeholders coordinated with project partners including two learned societies and the Industrial Mathematics Knowledge Transfer Network.

Related Projects

Project Reference Relationship Related To Start End Award Value
EP/K040251/1 01/01/2014 31/01/2014 £1,157,933
EP/K040251/2 Transfer EP/K040251/1 01/02/2014 30/06/2018 £1,146,391
 
Description Please note that this grant represents the first month of a four year grant, which after one month was transferred to another university. It is meaningless to report findings separately
Exploitation Route Please note that this grant represents the first month of a four year grant, which after one month was transferred to another university. It is meaningless to report findings separately
Sectors Creative Economy,Digital/Communication/Information Technologies (including Software),Education,Culture, Heritage, Museums and Collections
 
Description Major thread of public impact around nineteenth century science and the foundations of modern computing
First Year Of Impact 2015
Sector Creative Economy,Education,Culture, Heritage, Museums and Collections
Impact Types Cultural
 
Description Alison Pease: Social Creativity in Mathematics (ZiF, Bielefeld) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Social creativity is related to "framing" from the FACE model of creativity through connection with "explanation" in the production of mathematics. Hypotheses and empirical research on explanation were presented.
Year(s) Of Engagement Activity 2016
 
Description Fenner Tanswell: Conceptual Engineering for Mathematical Concepts (27th Novembertagung on the History of Mathematics) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Lecture to philosophers.
Year(s) Of Engagement Activity 2016
 
Description Fenner Tanswell: Conceptual Engineering for Mathematical Concepts (Friday Graduate Seminar, St Andrews, October 2016) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact A talk presented to an audience of philosophers
Year(s) Of Engagement Activity 2016
 
Description Fenner Tanswell: Proof, Rigour and Mathematical Virtues (Oxford Philosophy of Mathematics Seminar) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact An investigation the application of virtue epistemology to specically mathematical knowledge. The talk argued that this provides us with the tools to account for informal proofs and the nature of rigour as they are found in mathematical practice, overcoming obstacles that rule out the opposing formalist-reductionist approach. The talk included a case study of the ongoing difficulties with verifying the correctness of Mochizuki's proof of the abc conjecture.
Year(s) Of Engagement Activity 2016
 
Description Gabriela Asli Rino Nesin: Extending Inference Anchoring Theory for use with mathematical argumentation 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact Presentation on combining real-world data, argumentation theory research, and mathematical subject matter to understand mathematical practice in a way that neither pure socio-anthropological nor pure mathematical research would let us do.
Year(s) Of Engagement Activity 2016
 
Description Ursula Martin: Creativity and the Future of Proof (ZiF, Bielefeld) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact A description of the state of art of machine proof, social machines, and a perspective on human activity in mathematics using metaphors of landscape, journey, and craft.
Year(s) Of Engagement Activity 2016
 
Description Ursula Martin: The scientific life of Ada Lovelace (BCS Oxford, 13th Oct 2016) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Ada, Countess of Lovelace (1815-1852) is best known for a remarkable article about Babbage's unbuilt computer, the Analytical Engine. This not only presented the first documented computer program, but also, going well beyond Babbage's ideas of computers as manipulating numbers, outlined their creative possibilities and the limits of what they could do. Lovelace's contribution was highlighted in one of Alan Turing's most famous papers "Can a machine think?".

The comprehensive archive of Lovelace's papers preserved in Oxford's Bodleian Library displays Lovelace's wide scientific interests in everything from geology to acoustics to chemistry to mesmerism to photography; her exchanges with leading scientists such as Faraday, Babbage and Somerville; her correspondence course in mathematics with De Morgan, a leading mathematician of the day and pioneer in logic and algebra; and her grasp of the potential of mathematics whether to model a "calculus of the nervous system" or as a uniting link between the material and symbolic worlds.

In this talk we start to explore Lovelace, her background, her scientific ideas and her contemporary legacy.
Year(s) Of Engagement Activity 2016
URL http://www.bcs.org/content/conEvent/10595