Resources for best practice in Knowledge Exchange in the Mathematical Sciences

The page is intended to be useful for all those engaged in the management and facilitation of knowledge exchange to and from the academic mathematical sciences in the UK. 

This web page has been curated as part of the Big Mathematics Initiative

This is a follow-up activity by the UK Council for the Mathematical Sciences to the Bond review of knowledge exchange in the mathematical sciences. 

There is no claim that this resource list is comprehensive, although we have attempted to be inclusive. It is intended to be a living document that will be updated by a group representing all of the UK Learned Societies in the Mathematical Sciences. If you have anything to suggest to be added, or have spotted an error, please let us know by sending an email to

  1. Commissioned reports and guides
  2. Knowledge Exchange Framework
  3. Case Studies and Think Pieces
  4. UK Government funding of Knowledge Exchange activity
  5. Other research funders supporting KE activity
  6. Dedicated KE brokers and KE events in mathematics
  7. Professional bodies
  8. UK Knowledge Exchange resources not specific to mathematics
  9. Sector-specific institutes and activities
  10. Mathematics KE institutes and centres at individual UK universities
  11. Commercial research
  12. Overseas exemplars

1. Commissioned reports and guides

First and foremost, there are plenty of examples of good practice and an extensive reference list in the Bond Review: The Era of Mathematics – an Independent Review of Knowledge Exchange in the Mathematical Sciences. Here is an alternative link.

  • The Deloitte report Measuring the Economic Benefits of Mathematical Science Research in the UK was published in November 2012.
  • A 2015 review sponsored by the Royal Academy of Engineering concerning UK knowledge exchange: Dowling Review of Business-University Collaborations.
  • The Royal Society report Dynamics of Data Science Skills looks at the current demand for data professionals, and how this varies across industrial sectors and UK regions.
    • This report is more focused on the skills pipeline than on knowledge exchange, but chapter 5 is concerned with movement of talent in both directions between academia and industry.
  • Blackett review of computational modelling (commissioned by Sir Mark Walport when he was Chief Government Scientific Advisor)
  • The Mathematical Sciences and the ISCF, a report by Matt Butchers of the KTN and Joanna Jordan (independent knowledge exchange consultant) summarising a February 2019 workshop exploring how mathematicians can engage with the UK government’s Industrial Strategy Challenge Fund.
  • There is a report on KE best practice that arose from the IMA Conference on Knowledge Exchange in Dec 2018. A full report will be available shortly, but an outline of the findings can be found at

2. Knowledge Exchange Framework

It is not specific to mathematics, but it will cover knowledge exchange between academia and industry across all domains. It may tilt the knowledge exchange landscape significantly for universities.

The detailed responses to UKRI’s consultation exercise on KEF are available via the above weblink.

There is a report from their pilot exercise and consultation here.

  • One of the two strands of KEF is “Metrics”. By measuring academic knowledge exchange more continuously than REF impact does, and in more diverse ways, the UK government hopes improve the incentives for UK universities to invest in knowledge exchange.  In the future the KEF may feed into the funding allocation mechanism for the Higher Education Innovation Fund (HEIF), though there are no current plans for this to happen.
  • The other strand of KEF is “Principles and good practice”, which means the development by UKRI and partners of good practice guidelines and resources for knowledge exchange.   This strand has already produced a report about good practice in commercialization of research and formation of spin-out companies.  Future activity in this strand may be particularly relevant to mathematics knowledge exchange, so keep an eye on the development of KEF.

3. Case Studies and Think Pieces

  • The impact case studies in the mathematical sciences from the 2014 UK Research Excellence Framework (REF) can be read and searched online.

There is also a book that presents some of these cases with extra commentary: UK Success Stories in Industrial Mathematics by Aston, Mulholland and Tant (Springer 2016).

  • A good resource on how maths can make a difference and how to get engaged is contained in the Maths Matters series, compiled by the Institute of Mathematics and its Applications (IMA). These are essentially expanded impact case studies that explain to a general audience how different areas of mathematics have made a difference in modern society.
  • There is also a worldwide resource currently maintained by the University of Oxford called Mathematics in Industry which contains links to all the reports from mathematical study groups with industry. It has recently been agreed that this resource will be curated by and updated by Cambridge University Press. The reports cover examples of KE in areas of applied mechanics, OR, statistics, network and data science and a whole range of other areas of mathematics. 
  • There is also a separate Council of Mathematical Sciences report on the value of the mathematics study groups with industry.
  • Newton Gateway case studies
  • Case studies describing outcomes of Industrial Mathematics Shorter Knowledge Transfer Partnerships, a scheme which closed in 2013.

4. UK Government funding of knowledge exchange activity

The Royal Society produced a fact-sheet in 2018 giving an overview of UK government investment in research and development (R&D), much of which concerns knowledge exchange funding.

A more detailed overview of the UK government’s knowledge exchange funding is given in the Research England Guide to research and knowledge exchange funding (2018) 

In particular it describes the Higher Education Innovation Fund (HEIF) which administers over £200 million p.a. of UK government funding in England for knowledge exchange between higher education institutions and business, public and third-sector organisations, community bodies and the wider public, of which £160 million is science and research funding.

Funding calls change all the time and the curators of this page do not have the capacity to maintain an up-to-date list. However, links to many current calls may be found on the following websites:

  • Innovate UK distributes government support for industrial and commercial R&D. Current Innovate UK calls are listed here.
  • The Knowledge Transfer Partnership (KTP) scheme is a UK government innovation scheme that has been running for over 40 years. It is funded through Innovate UK. Here is the Dowling report’s description: “The KTP scheme […] facilitates the formation of a partnership between a company or not-for-profit organisation and an academic institution for the formulation and delivery of an innovative, collaborative project. To manage and deliver the project, recently qualified individuals are recruited as KTP Associates. The average annual cost of a project is around £60k with SMEs contributing around a third of the project costs and large companies contributing around half. KTPs are particularly popular with SMEs: in 2013—14, 81% of KTPs involved SMEs. Projects can last between six months and three years.
  • EPSRC current calls
  • EPSRC CASE studentships
    Industrial Cooperative Awards in Science & Technology (CASE) provides funding for PhD studentships where businesses take the lead in arranging projects with an academic partner of their choice
  • UKRI is the umbrella organisation for the UK Research Councils and Research England. 

UKRI Impact Acceleration Accounts are a funding mechanism specifically designed to enable knowledge transfer based on research findings from UKRI-funded research. Here is information about EPSRC’s impact acceleration accounts:

5. Other research funders supporting KE activity

  • European Research Council:
    A current example of their KE funding is the MSCA-RISE call (Research and Innovation Staff Exchange).
  • The Royal Society has funding schemes for the life and physical sciences to support knowledge transfer in both directions between academia and industry.
  • The Clay Mathematics Institute is not particularly focused on KE, although its Dissemination Award is given in recognition of personal contributions to research in mathematics at the highest level as well as of distinction in explaining recent advances to the public at large. Through the Clay Millennium Problems, the CMI has contributed greatly to public interest in advanced mathematics research.

6. Dedicated KE Brokers and KE events in mathematics

“The Newton Gateway to Mathematics acts as a knowledge intermediary for the mathematical sciences. It is the impact initiative of the Isaac Newton Institute for Mathematical Sciences (INI). Supported by INI and the University of Cambridge, the Newton Gateway to Mathematics reaches out to and engages with the users of mathematics – in industry, business, public sector and other scientific disciplines. It helps to bridge the gap between those engaged in frontier mathematical research and those working in more applied areas, by stimulating the interchange of knowledge and ideas.

The Newton Gateway works as a delivery partner to facilitate the exchange, translation and dissemination of knowledge. Using effective communications and proven methodologies, it develops and runs activities such as workshops and meetings, bringing people and organisations together in order to share knowledge and stimulate further research and collaboration. With extensive access to multiple communities across the UK and globally, it can respond in an agile and flexible manner.”

  • International Centre for Mathematical Sciences (ICMS), Edinburgh
    ICMS hosts workshops in both pure and applied mathematics. One notable KE activity is the annual modelling camp to train students and early career mathematical science researchers to engage in study groups and similar activities.
  • European Consortium for Mathematics in Industry (ECMI)
    The European Consortium for Mathematics in Industry (ECMI) is a consortium of academic institutions and industrial companies that acts cooperatively with the following aims:
     – To promote and support the use of mathematical modelling, simulation, and optimization in any activity of social or economic importance.
     – To educate Industrial Mathematicians to meet the growing demand for such experts.
     – To operate on a European scale.
    More information:
    Annual report 2018:
    ECMI runs European study groups with industry:
  • Innovate UK’s Catapult Network. There are several Catapults dedicated to specific topics, for example “Digital” and “Connected Places”. Their purpose is to promote research through business-led collaboration with researchers.
  • IMA employers’ forums are an opportunity for employers to share best practice on topics such as recruitment, development and retention of mathematicians. These meetings provide networking opportunities between employers, universities and the IMA.
  • The Royal Society’s Creating Connections events
  • Virtual Forum for Knowledge Exchange in the Mathematical Sciences (V-KEMS) emerged in Spring 2020 as a result of the lock-down as a collaboration between the Isaac Newton Institute, ICMS, and the KTN to develop a virtual platform for engagement in the mathematical sciences.

7. Professional Bodies

8. UK Knowledge Exchange resources not specific to mathematics

  • Knowledge Transfer Network (KTN)
  • National Centre for Universities and Business (NCUB)
    The National Centre for Universities and Business is an independent and not-for-profit membership organisation that promotes, develops and supports university-business collaboration across the UK.
  • PraxisAuril                                                        
    PraxisAuril is a professional association for knowledge exchange practitioners. They annually host a large knowledge exchange conference, and it runs a training course “Foundations of Knowledge Exchange”.
  • ESRC Impact Toolkit                                                                                            Although this toolkit is aimed at social science researchers, it does feature useful advice for researchers in the mathematical sciences also.
  • Guidance on standardising the quantification of research impact, commissioned for the UK Research Excellence Framework (REF), is given in this report produced by RAND Europe.

9. Sector-specific institutes and activities

  • Actuarial Research Centre (ARC)
  • Alan Turing Institute (ATI)
    The Alan Turing Institute sits at the interface between the mathematical sciences, computer science, and industry. Much of its activity is mathematical.  ATI has its own Research Engineering team consisting mostly of data scientists with working experience in both academia and industry. They help to link academics in the Turing with problem owners in industry, facilitate data management and conduct research themselves. This role of acting as a conduit is very promising since many problems in achieving effective KE stem from communication difficulties of academics and practitioners. There are similarities to the concept behind the Fraunhofer Institutes in Germany that also may serve as a broker between users and academics.
  • Heilbronn Institute for Mathematical Research (HIMR)
    HIMR is a national institute funded by GCHQ.
    The HIMR website focuses on the institute’s public activities, both the academic research of its members and its financial support for UK mathematics research activity. The classified mathematical research of HIMR is led by a GCHQ mathematician. It is carried out by postdoctoral fellows on 50-50 contracts (mostly 3 years), permanent research fellows on 50-50 contracts, part-time and seconded consultants from academia, sponsored PhD students on summer internships, and collaboration with GCHQ’s own mathematicians.

Questions about HIMR should be addressed to

  • Scottish Financial Risk Academy
    The SFRA is an industry-academic partnership dedicated to improving the understanding of financial risk through a series of knowledge exchange activities. Founded in 2010 by a consortium led by Heriot-Watt University and the University of Edinburgh, the SFRA is now fully supported by member companies and universities. Membership is open to financial services companies or universities with links to Scotland.
  • Met Office Hadley Centre for Climate Science and Services 
  • Public Health England employs many statisticians. They are running an ambitious big data project to study 100,000 sequenced genomes to improve healthcare.

 10. Mathematics KE Institutes and Centres at Individual UK Universities

In this section we list some institutes and centres within individual UK universities that have been set up specifically to engage in mathematics knowledge exchange.   In this section we include EPSRC-funded Doctoral training centres (CDTs) that have a focus on industrial knowledge exchange.

11. Commercial research

  • Smith Institute
    The Smith Institute is a private mathematical modelling consultancy firm.
  • Oxford-Man Institute of Quantitative Finance
    This is a joint enterprise between investment management firm Man group plc and the University of Oxford. It is a centre for interdisciplinary research into the financial economy. Much of this research is mathematical. It is located in its own building in Oxford, which also houses Man group’s own researchers.
  • INQUIRE: Institute for Quantitative Investment Research                               Information for academics who want to engage can be found here.

12. Overseas exemplars

  • CERN is an interesting KE exemplar, even though it is an internationally state funded pure science project. Perhaps because of the large amount of funding it has received from governments and the fact that its main scientific goals are not obviously going to lead to near-term societal benefit, CERN puts a lot of effort into knowledge transfer and documenting its impact. Several technologies have been spun out of research done to meet CERN’s unique needs, most famously Tim Berners-Lee’s conception of the world wide web at CERN in 1989. CERN has a dedicated Knowledge Transfer website which includes many other success stories and information about how companies of all sizes can get involved in working with CERN. Most of the success stories are primarily physics-related but several are in data science.
  • Fraunhofer Institutes (Germany)
    There is a mathematics-specific Fraunhofer Institute in Industrial Mathematics in Kaiserslauten. Fraunhofer UK was started in Glasgow in 2012 and operates a photonics research centre but Fraunhofer is looking for opportunities to start other Fraunhofer research centres in the UK.
  • INRIA (National Institute for Research in Digital Science and Technology, France)
    INRIA is somewhat similar to the Alan Turing Institute but is larger and longer established, being over 50 years old. It has 9 research centres across France, employing 3500 researchers and engineers. Presumably it also gets income from its subsidiary companies, which under standard UK practice would have been spun out as independent companies in the UK rather than remaining in state ownership.
  • Microsoft Research is another interesting model of how a large corporation with deep pockets can look to fundamental science including mathematics in the search for future business opportuities. One Microsoft Research lab exists in the UK . It is not specifically focused on mathematics, but they do employ a significant number of mathematicians. The Microsoft Research labs operate similarly to the Heilbronn Institute in which part of the time of the researchers is devoted to open research and part to commercially sensitive research. Microsoft Research Redmond, (Seattle) and Microsoft Research New England (Cambridge, Massachusetts) have strong mathematics groups. Microsoft Research New England’s webpage notes that they had over 350 academic visitors in the last year.