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.

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.

The acoustics industry contributes £4.6 billion to the UK's economy annually, employing more than 16,000 people, each generating over £65,000 in gross value added across over 750 companies nationwide. The productivity of acoustics industry is similar to that of other enabling technologies, for example the UK photonics industry (£62k per employee in 2014). Innovation through research in acoustics is a key to its industry success. The UK's acoustics industry and research feeds into many major global markets, including the $10 billion market for sound insulation materials in construction, $7.6 billion ultrasound equipment market and $31 billion market for voice recognition. This is before the vital role of acoustics in automotive, aerospace, marine and defence is taken into consideration, or that of the major UK industries that leverage acoustics expertise, or the indirect environmental and societal value of acoustics is considered. All the four Grand Challenges identified in the 2017 UK Industrial Strategy require acoustics innovation. The Industrial Strategy Challenge Fund (ISCF, https://www.ukri.org/innovation/industrial-strategychallenge-fund/) focuses on areas all of which need support from acoustics as an enabling technology. The future of acoustics research in the UK depends on its ability to contribute to the Four Grand Challenges. Numerous examples are emerging to demonstrate the central role of acoustics in addressing the four Grand Challenges and particularly through more focused research. The acoustics-related research base in the UK is internationally competitive, but it is important to continue to link this research directly to the four Grand Challenges. In this process, the role of UK Acoustics Network (UKAN) is very important. The Network unites over 870 members organised in 15 Special Interest Groups (www.acoustics.ac.uk) who represent industry, academia and various non-academic organisations which success relies on the quality of acoustics related research in the UK. UKAN was funded by the EPSRC as a standard Network grant with the explicit aim of pulling together the formerly disparate and disjoint acoustics community in the UK, across both industry and academia. UKAN has been remarkably successful. Its success is manifested in the large number of its members, numerous network events it has run since its inception in November 2017 and contribution it has made to the acoustics research community. Unfortunately, UKAN has not been in the position to fund new, pilot adventurous or translational projects nor has it any funding support for on-going research or knowledge transfer (KT) activities. The purpose of UKAN+ is to move beyond UKAN, create strategic connections between acoustics challenges and the Grand Challenges and to tackle these challenges through pilot studies leading in turn to full-scale grant proposals and systematic research and KT projects involving a wider acoustics community. There is a great opportunity for the future of the UK's acoustics related research to move on beyond this point, build upon the assembled critical mass and explore the trans-disciplinary work initiated by UKAN. Therefore, this proposal is for UKAN+ to take this community to the next stage, connect this Network more widely in the UK and internationally to contribute through coordinated research to the solution of Grand Challenges set by the government. UKAN+ will develop a new roadmap for acoustics research in the UK related to Grand Challenges, award exploratory (pilot) cross-disciplinary research projects to the wider community to support adventure research and knowledge transfer activities agreed in the roadmap and support the development of develop full-scale bids to the government research funding bodies which are aligned with the Grand Challenges. UKAN+ will also set up a National Centre or Coordination of Acoustics Research, achieve full sustainability and support best Equality, Diversity and Inclusion practices.