Mathematics Matters

Contemporary mathematics research affects the daily lives of a very large number of people worldwide, yet most remain in almost total ignorance of this fact. More worrying, however, is that this ignorance also extends to that section of society which would otherwise consider itself well educated.

The industry and technology that surrounds us owes a great debt to modern mathematics research, yet this fact is perfectly hidden in its physical manifestation. The concern with this state of affairs is that what is unknown cannot be appreciated or valued.

This is not a simple matter to resolve since, although current mathematics significantly influences the familiar, the mathematics itself may seem impenetrable to the very people whose views we seek to influence. The Mathematics Matters case studies have been written to resolve this problem. Examples of contemporary research have been presented in a series of papers which describe the mathematics, without resort to technical detail but also without patronising over-simplification. In this way, policy makers can understand how mathematics research influences so many areas of modern life. However, in order to provide a satisfying level of detail to those with a more scientific training, each paper also includes a technical supplement, which describes the work in more detail, and includes references to published work which confirm the modern credentials of the research.

During the preparation of these case studies, it has become clear that there are many more topics upon which papers could have been written, and the series will continue with a second phase. The IMA wishes to engage with other organisations who may be aware of contemporary mathematical research affecting society today, or those who apply mathematics in new products or services and which could form the basis of a case study. In this case, please contact john.meeson@ima.org.uk

The first phase of case studies are available through this website; the balance of the papers will be uploaded as they are completed.

In preparing this work, the IMA is grateful for financial support from the EPSRC, and the help of a number of experts who have helped in the preparation of these papers and without whom they could not have been written.

Mathematics Matters Phase 2

To continue the success of the Mathematics Matters Research Case Studies, a second phase is now underway. The series will include a further 12 case studies, the first eleven can be found below.

As usual, the range of topics is very diverse, reflecting the pervasive nature of mathematics. Topics include using mathematics to tackle the stability of the plasma held within a fusion reactor, the application of Operational Research techniques to NATO operations and an exciting method to increase the yield of a novel hydrogen gas production technique. This is an energy source which is likely to become much more important in the future as we wean ourselves from fossil fuels.

The IMA wishes to acknowledge the support of the National HE STEM Programme in the second phase of this work.

Phase 2

• Exoplanets: the search for a second Earth

  Whether or not we share our galaxy with other intelligent life is a question that has been asked for centuries. Modern telescopes are finding planets beyond our solar system at an ever increasing rate, but it’s mathematics that tells us if those planets could be like the Earth.

• Following the crowd

  In order to minimise the risk as people gather together, mathematics is increasingly being used to model the situation and arm organisers with the tools they need to keep everyone safe.

• Fusion: fuelling the future

  With fossil fuels running out, the race is on to find the best power source for the future. Fusion, the process that powers the Sun, could be the answer and mathematics is crucial in designing the power stations that could copy it.

• Hydrogen: the fuel in water

  In the search for cleaner and greener sources of energy there are many options on the table. Mathematics is helping to develop a method which harnesses the power of the Sun to unlock the energy of the hydrogen that lies hidden in water.

• Internet shopping: stopping the scammers

  With ever more people purchasing things online, there is a greater potential reward for internet fraudsters. Mathematics helps make sure your money doesn’t end up in the wrong hands.

• Keeping an eye on diabetes

  Diabetes is on the rise in the UK, but current methods of directly measuring patients’ blood sugar levels have their drawbacks. Mathematics is playing a crucial role in finding a new, non-invasive, way to monitor the disease.

• Kosovo: mathematics on the front line

  It is crucial that as UK armed forces continue to deploy to destinations across the globe, they have the best tools at their disposal. As such, mathematical analysis is playing an increasingly important role alongside tanks and guns in their military arsenal.

• Quicker contact centres

  Contact centres pervade modern life, whether it is calling up your bank or utility providers. These companies are increasingly employing mathematical techniques to make sure you stay on the phone for as little time as possible.

• The Weak Link in the Fish Food Chain

  Cod stock numbers within the North Sea have already been depleted by decades of over fishing. Mathematical modelling now suggests that the North Sea population of cod and other commercial fish stocks could also feel the effects of a warming planet unless they can adapt fast enough.

• Train Delays: Staying on Track

  Catching a train is part of daily life for many, whether they are commuting to work or heading for a night out. Mathematics could help negotiate the minefield of delays that often accompanies train travel, reducing the risk of arriving late, and so reducing the stress of travel.

• Volcanic ash: air travel under a cloud

  The eruption of the Icelandic Eyjafjallajökull volcano in 2010 not only had newsreaders’ tongues in a twist but called a halt to air travel across much of Northern Europe. It was imperative to get planes safely back into the skies as swiftly as possible and mathematics was at the heart of the solution.

Phase 1

• Advancing the Digital Arts

  The computer animation industry relies on a steady stream of mathematics to produce the fantastic images found on our cinema and television screens. Advanced in mathematics also fuel developments in other areas of 3D modelling, such as car design.

• An Energy Evolution

  As oil supplies become harder and more expensive to reach, it’s essential that we maximise the yield from available reservoirs in any way possible. Mathematicians are contributing with a tool inspired by biological evolution that seeks out the best way to extract the oil.

• Building the Digital Society

  Computers and networks stuffed with ever-increasing amounts of data are transforming our society, creating a digital world with its own rules and behaviours. We need mathematicians who understand this new world and can turn data into useful information for the benefit of society as a whole.

• Danger: Rogue Waves

  Rogue waves appear without warning, towering high over ships and oil rigs. Traditional mathematical models couldn’t predict the occurrence of these dangerous waves, but the latest techniques let oceanographers make accurate forecasts. The research helps to protect our trade, energy and food supply routes.

• Faster Formula One

  Every second counts in the fast-paced world of Formula One, so race teams use advanced mathematics to squeeze the best performance out of their cars. Computational fluid dynamics lets car designers quickly test out new ideas before deploying them on the racetrack.

• Fighting Infections with Symmetry

  Many viruses have a symmetrical structure made from basic building blocks, and biologists have struggled to explain some of the more detailed shapes. Now, mathematicians are using complex theories of symmetry to reveal these viral structures, ultimately leading to new treatments for diseases.

• Go with the Industrial Flow

  Many industrial processes involve the complex moment of fluids, but predicting fluid behaviour can often be difficult. Mathematical models of fluid flow can help to improve manufacturing efficiency and reduce costs, while also enabling new applications of fluids within industry.

• Keeping Hearts Pumping

  Blood-related diseases can seriously harm patients’ quality of life and even lead to death. Many of these diseases are caused by problems with the flow of blood in the body, and using mathematical models to understand how and why these occur can help save lives.

• Modelling an Epidemic Emergency

  Epidemics can threaten the lives of both humans and animals, so it is essential that we react swiftly to any outbreaks. Mathematicians play a key role in assessing the risks of disease transmission and modelling the effects of vaccination programmes.

• Networking for the Future

  Modern society relies heavily on a variety of networks, but we don’t fully understand how they behave. Mathematical network theory lets us create models of our communication and transport networks, revealing new patterns and insights that will improve network capacity, reliability, and efficiency.

• Optical Fibres: The Hole Story

  The latest generation of optical fibres can be used for a wider range of applications, but their complicated internal structure makes them difficult to produce. A mathematical model of these new “holey fibres” promises to simplify the manufacturing process and reduce the cost of development.

• Picture Perfect Processing

  Mathematical image processing techniques make it possible for us to capture, transmit and store photographs and video. They also let us restore noisy or damaged images and extract useful information from visual data.

• Predicting Climate Change

  Our understanding of climate change draws on expertise from a variety of scientific disciplines, but climate models ultimately rely on advanced mathematical equations. Even the fastest computers in the world can struggle to solve these equations, so we need to deploy new mathematical techniques in the fight against global warming.

• Preserving Britain's Coastlines

  Much of the UK’s coastline is undergoing erosion, placing homes, businesses and other important coastal sites at risk. Mathematical modelling can enable us to understand both the short- and long-term processes that lead to erosion, and help protect the nation’s coast.

• Scans on the Brain

  Brain scans play a vital role in the treatment of many serious medical conditions, but decoding the signals inside our minds would not be possible without a variety of mathematical techniques.

• Smarter Phones for All

  The amount of information we can transmit though the air is limited by the laws of physics, but the mathematics of signal processing lets us squeeze more data into the same amount of space. As a result, we get better, cheaper and faster mobile phone calls.

• Statistically - Secure Identities

  It is essential that the biometric systems we depend on for national security can reliably identify individuals and aren’t easily deceived. A range of mathematical techniques ensure these systems work as intended, helping to keep the UK safe.

• Stats in Your Genes

  Sequencing the human genome was a fantastic achievement, but it was only the beginning. Now, statisticians are coming up with new methods to sift through large amounts of a genetic data and identify the differences in DNA that can lead to diseases.

• Taking decisions, not risks

  Risks are an unavoidable part of modern life, but mathematicians and statisticians have developed a variety of methods to help mitigate its effects. These techniques enable hospitals, banks and other organisations to make better decisions, based on evidence and facts.

• Unravelling the Genetic Code

  Understanding how to manipulate tangles of DNA could help us create new treatments for diseases, so mathematicians are working with biologists to explain how our genetic code becomes knotted. Their work combines the latest technology with a centuries-old branch of pure mathematics.