MathSoMac: the social machine of mathematics

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.

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.