Isaac Newton Institute for Mathematical Sciences

Lead Research Organisation: University of Cambridge
Department Name: Isaac Newton Institute (Math Science)


Mathematics, with its capacity for generality and abstract reasoning, is a subject that is unique in its ability to penetrate deep within other disciplines, to provide a common language for establishing communication channels between research communities, and in the longevity of its influence.

The Isaac Newton Institute (INI) is an international hub for supporting mathematical sciences research of the highest quality and impact. It attracts world leading researchers, in all areas of mathematics and cognate disciplines, who interact through a variety of long and short thematic programmes as well as associated workshops, follow-on meetings and a plethora of one-off events. Based in Cambridge, and benefiting from a bespoke and iconic building as well as many world-leading facilities of Cambridge University, INI is nevertheless an independent forum serving the whole of UK mathematical sciences. INI celebrates its 25th anniversary this year.

To the end of 2016 there had been 129 long-term programmes in total, and over 26,000 INI programme and workshop participants including 81 Rothschild Visiting Professors/Fellows, from Wolf Prize winner Vladimir Arnold in 1992 to Dijkstra Prize winning theoretical computer scientist Cynthia Dwork in 2016. Participants have also included 27 Fields Medalists, 13 Nobel Laureates, 12 Abel Prize winners, 25 Wolf Prize winners and over 50 Clay Senior Scholars as well as numerous winners of major prizes in other disciplines. This does not include unregistered participants, who are welcome to drop-in to events for a couple of days at a time.

INI gives UK researchers unparalleled opportunities to work with one another and with a critical mass of leading international figures in their field, unencumbered by teaching or administrative duties. It maximizes potential for knowledge exchange and the dissemination of UK research achievements, while exposing UK early career researchers to world leaders in their discipline.

A common strategic position of all Research Councils is to emphasise the importance of innovative mathematical and statistical methods to their science and in the training of young researchers. From its inception, INI's programmes and embedded workshops were demonstrably intra or interdisciplinary and conceived to accelerate research impact within the mathematical and sister sciences. Recently INI has broadened its remit to address fundamental questions in the social sciences, medicine etc. It has also concerned itself with the instigation of mechanisms to support diversity and gender equality in the sciences, and to nurture early career researchers so as to enlarge the people pipeline.

The Turing Gateway to Mathematics (TGM) was created in 2013 as the knowledge exchange arm of INI. Since then it has brought the mathematical sciences community together with an impressive range of over 700 partners in business, industry, commerce and government. It has a proven set of pathways to impact, and partners with a range of organisations to assist the whole of the mathematical sciences community.

Public engagement events are regularly hosted at INI, including its Rothschild Public Seminars. In addition to the 25th Anniversary events being held at the Institute, a highlight of which will be a discussion between Sir Andrew Wiles and his biographer Simon Singh, INI is organising a "road show" across the UK including talks by Keith Moore, Librarian at the Royal Society, and leading British space scientists.

INI is committed to the maintenance of a reputation for creativity and mathematical excellence. This will mean continuing to deliver ground-breaking research of the highest international standard, supporting the UK mathematical sciences community both in academe and beyond, and further extending the reach of mathematics into other disciplines and applications via TGM. Throughout it will strive to maintain the culture of creativity and achievement for which it is widely recognised.

Planned Impact

The Isaac Newton Institute provides underpinning support for research for the whole of the UK mathematical Sciences community. Its record of curiosity-led programming across the sciences has been substantial, but it also puts non-academic impact at the heart of much of its activity, in the areas of People, Economy and Society.

In the last few years INI's knowledge exchange role has expanded significantly, and now, through the Turing Gateway to Mathematics (TGM), it routinely facilitates this impact to an impressive list of over 700 stakeholder organisations, including as exemplars: Airbus Defence and Space, BAE Systems, Bank of England, Barclays, Deloitte, GCHQ, National Physical Laboratory, Telespazio Vega and Unilever. In total, they span the industrial, commercial, charitable and public sectors and have interacted with scientists in a wide variety of thematic areas including mathematics, statistics, big data, chemistry, climatology, computer science, cryptography, engineering, environmental science, energy, finance, healthcare, information technology, manufacturing, medical imaging, physics, security, space, uncertainty quantification. A typical meeting arranged by TGM was on the mathematical modelling of Algorithmic Trading, held in March 2017 at the Alan Turing Institute, London; it was heavily oversubscribed and attracted roughly an even split between academic and non-academic participants, which is common for such events.

As well as keeping stakeholders up-to-date with current mathematical and scientific technology, TGM can help broker long-term relationships which lead to significant impacts to both companies and individuals. Specific evidence for this is provided in the project partner letters. Similarly, long-term INI programmes, in pure or applied areas, can lead to impacts in highly current topics; for example models for the spread of infectious diseases developed at INI in 2013 are starting to directly influence policy in the prediction and planning for future human and animal virus outbreaks.

Associations forged at INI can often lead to new career opportunities for early career participants outside academe; for example, details are given elsewhere about two researchers who moved from academe to take up highly successful careers at Microsoft and Cryptomathic.

In regard to societal benefit, a recent INI programme on the Mathematics and Statistics of Forensic Science led to production of a set of guidelines "specifying conditions under which particular techniques can be used to provide results and reliability estimates that are sufficiently certain to be presented in court without the risk of being challenged on appeal". An associated TGM workshop to this programme was attended by leading judges and barristers, including David Kitchin the Lord Justice of Appeal.

A further example of INI's societal impact through TGM, raised by a project partner, is the 2013 workshop on Policy Support organised with the Department of Communities and Local Government. The meeting discussed policy issues related to business rates, national resilience and homelessness, and was the first time that a government department had engaged so closely and openly with the mathematical sciences community.

The other major beneficiaries of INI and TGM activity are the general public and especially school students. Public lectures are provided by the ever-changing array of world-renowned researchers to a packed audience, and mathematically oriented artwork and exhibitions are regularly on display for non-mathematicians to peruse. The Deputy Director and Director regularly talk to school students about the beauty, ubiquity and efficacy of mathematics, and the former is active in organising 'Girls in Maths' events. INI has bold ambitions to team up with other experts in mathematics communication to exploit the academic resource in the building in order to produce online, printed and broadcast material accessible to all.


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Bespalov A (2019) Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs in Computer Methods in Applied Mechanics and Engineering

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Chakraborty S (2019) Tracing cyclic homology pairings under twisting of graded algebras in Letters in Mathematical Physics

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