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The UK maths community came together during the pandemic as a working group to inform policy makers about covid measures. Reports from the Virtual Forum for Knowledge Exchange in the Mathematical Sciences, convened by the Newton Institute, include COVID-19 Safety in Large Events, Test Trace and Isolate for epidemic control and Aortic Stenosis Post-COVID-19: a Mathematical Model on Waiting Lists and Mortality and presented to SAGE meetings.

Professor Chris Dent, Dr Amy Wilson and Dr Stan Zachary’s research into energy generation and storage had a huge impact in improving energy supply. They used Extreme Value Theory to smooth data at extreme points and ensure that any estimates made are less sensitive to data fluctuations.

Mathematicians play a key role in our response to the challenges posted by climate change. Research by statisticians at Lancaster University has played a crucial role in building resilience to extreme flood events – the second largest natural hazard in the UK’s National Risk Register of Civil Emergencies (after pandemics). The team’s work on extreme value methods has produced a step-change in the quantification of spatial and multi-hazards for inland and coastal flood events, and is fundamental to government planning. •Auctions for carbon emissions: Pure

Pure-mathematician-turned economist Elizabeth Baldwin has applied algebraic geometry, an important set of ideas in pure mathematics, to micro-economics and in particular to constructing effective auctions for carbon emissions. Her work has been used by the Bank of England.

Operations Research (OR) is concerned with the application of advanced analytical methods to help make better decisions. Professor Bert De Reyck’s research at UCL has an impressive track record of using O.R. to deliver improvements in transport and travel including supporting Single European Sky (SES) initiative, a scheme to integrate air traffic management across Europe. Models developed to track passenger flow have been augmented to use machine learnings to deliver real time systems that have been able to manage passenger flow through airports post COVID.

The mathematics field of topology studies how shapes behave when they are twisted, stretched and contracted without breaking. Topological Data Analysis brings ideas in this field with information from all sorts of different sectors to reveal hidden patterns in data sets, with application in healthcare, finance, voting and beyond. As an example, researchers were discovered a new group of breast cancers which can provide more effective treatments.

Researchers at the University of Dundee used mathematical sciences based computational geometry to develop an automatic diagnostic tool that determines the best treatment practices and time to operate on children born with clefts of lip and palate. The innovation minimises human error, improves efficiency, and significantly improves patient experience and outcomes.

Machine-learning systems are already influencing several areas of clinical research. It can help with recruiting patients for clinical trials and allows researchers to reconstruct the underlying mechanisms of disease and help improve diagnostics.

Mathematicians and statisticians worked with the National Archives to build a tool to help understand the risks involved in digital preservation in 2020. The tool enabled the National Archives to develop a business case for a significant uplift in funding to protect digital archives.

Professor Andy White applies mathematics to understand and manage wildlife systems. Using mathematical modelling, Professor White discovered that red squirrels are being replaced by the invasive grey squirrels in England and Wales, in part due to the spread of the Squirrelpox Virus that is carried by grey squirrels and lethal to red squirrels. He has also used mathematics to design forest management plans to conserve and protect the remaining red squirrels in Scotland.

The creation of digital twins - software models that closely resemble the real-life counterpart they’re based on - allows us to harvest significant data analytics insights which are crucial to business. In 2020, the global digital twin market was valued at $3.1 billion and is expected to grow to more than $48 billion by 2026.

Research from the University of Edinburgh has provided tools for quantifying the value of evidence provided in courts with strong impact on the administration of justice.

Eric Lander led the Human Genome Project. He was the first named author on the first paper announcing the genomic sequence. Lander trained and initially worked as a mathematician (he did his PhD in the Mathematics Department in Oxford). He has gone on to make foundationally important contributions to genome medicine and the treatment of disease. For example, he led on the development of a molecular taxonomy for cancers. He leads a joint Harvard-MIT institute and was listed as number 2 on the list of the top 150 innovators and ideas from MIT. His work is strongly influenced by his mathematical background.

PRiSM is a dedicated centre co-established at the Royal Northern College of Music by composer Emily Howard. She was inspired by her collaboration with pure mathematicians at the University of Liverpool which led to seven of her critically acclaimed compositions, including pieces commissioned for the BBC Proms and by Simon Rattle for the London Symphony Orchestra.