Mathematics Matters

Launching: Mathematics Matters

We are publishing this Mathematics Matters case study from 2010 as an illustration of how mathematical modelling has helped to protect society against epidemic diseases by informing public policy.  It does not describe the current COVID-19 outbreak, although we hope and believe that mathematics will make an equally valuable contribution in the current crisis.

As part of a Europe-wide endeavour to reduce carbon emissions and deploy sustainable energy sources, the UK government has set a series of targets. In particular, it has set the long term goal of reducing the UK’s greenhouse gas emissions by at least 80% compared to 1990 levels by 2050. However, this is likely to result in an increase in electricity consumption as consumers choose low carbon alternatives to heating and transport, for instance though electric vehicles and heat pumps. Additionally, although most power is generated in power stations, in the future there will be increased levels of local generation with up to 20% of our future energy coming from renewable, yet volatile, sources such as wind and solar power which are more dependent on weather and climate. The interaction between customers and such technologies will see the emergence of new types of energy usage behaviours and may drive potentially novel ways of mitigating high demands.

Cars are a ubiquitous part of modern life and the UK automotive industry is a key part of the UK economy, producing an average of 1.5 million cars and commercial vehicles every year. With 80% of these products exported overseas, the nation's car industry racks up an annual turnover of £50 billion.

Britain has a long and illustrious relationship with the sea. From the Spanish Armada and the Battle of Trafalgar, to Captain Cook's map-changing voyages around Australia and the merchants of the East India Company, Britannia is synonymous with the waves. But, nowadays, Britain has moved away from empire and exploration and is instead leading the maritime world in another way: by harnessing the power locked up in waves.

Work is under way on the largest engineering project in Europe: Crossrail. The project will connect 37 railway stations spanning the entire width of London. With the first sections planned to open in 2018, it is estimated that the service will ferry 200 million passengers across the capital every year. Current estimates place the economic benefit of Crossrail at £42 billion.

Modern warfare has never been more technological or more intricate. The average soldier carries equipment the cost of which runs into five figures. They operate machinery running to many times more. But with increased complexity comes an increased need for training, either on new equipment or for new theatres of warfare.

Mathematics is often viewed as an abstract subject. It has the touch of the ethereal about it, a quaintness derived from its use of unfamiliar symbols. Many grapple with the subject at school, pleased to leave it behind and perhaps quipping that they'll never use maths in “real life” anyway. And yet, in today's modern, technological society, they're using it even if they don't realise it. Mathematics has never been more important or in such wide use. In short, it plays a fundamental role in underpinning UK PLC. A recent report by audit, tax, consultancy and corporate finance firm Deloitte found that 10 per cent of British jobs stem from research in the mathematical sciences. Thanks to mathematics, the country's coffers are boosted to the tune of £208 billion annually.

Air travel in the UK is on the rise again following a post-recession dip. In the first quarter of 2012 alone, almost 45 million passengers arrived in or departed the country aboard 420,000 flights. Yet when getting on a plane we rarely think about the intricate air-traffic control system keeping us safe in the sky.

Cycling in the UK has seen somewhat of a revival over the past few years. With Bradley Wiggins's maiden Tour de France victory sandwiched between outstanding Olympic cycling medal hauls in Beijing and London, the sport is riding high.

How many tablets have you taken this week? Whether it is for pain relief, high blood pressure or diabetes, Britons are taking more medicines than ever before - in 2012 over one billion prescription items were dispensed, many of them in tablet form. Coupled with over-the-counter medicines, it is estimated that the average person will swallow 40,000 pills over their lifetime, an average of more than one a day. It is also big business - the pharmaceutical industry ranks second only to finance in terms of its contribution to the UK economy. Mathematical pharmaceutical research alone added £16 billion to the country's coffers in 2010.

The UK is home to Europe's noisiest airport. Heathrow has picked up this unwanted accolade thanks in part to the sheer number of people living under its flight path. Those residents of south-west London are regularly exposed to jet noise in excess of 57 decibels. With the number of flights set to almost double by 2050, residents and jet manufacturers alike are keen to reduce the noise generated by aircraft, not just at Heathrow but across Britain and around the world.

In the information age the computer chip is key — the average person will probably utilise the power of many integrated circuits several times before they even leave the house each day. With worldwide demand for their wares, the work of computer chip designers is big business. But, with the cost of making the first prototype of a chip running into the millions, getting it wrong can be an expensive mistake.

From Vulcan to Krypton, Alderaan to Gallifrey, alien worlds have been a fixture of science fiction for decades. Science fiction became science fact in 1995 when a team of astronomers revealed the presence of a planet orbiting a star other than the sun - the first extrasolar planet, or exoplanet, to be discovered.

Football matches, pilgrimages and political protests all have one thing in common: people. Lots of them. Whenever people gather in large numbers, whether it's to pray to sporting deities or wailing walls, there is always the potential of danger. The main aim of the organisers in such situations is to keep people safe.

On a crisp, dark evening it is possible to see three thousand stars twinkling across the sky. Far from far-off specks of light, they are cosmic nuclear reactors busy devouring the matter in their cores to produce the energy we see as starlight. Bringing their method of energy production, called fusion, down to Earth would go a long way to solving the planet's growing energy crisis.

It is the ultimate source of energy for the Earth. Trees and plants lock its rays into their leaves before passing that energy up the food chain. The coal, gas and oil we currently rely on to power our planet were formed when that organic material was trapped deep under the weight of the world’s water. Without the Sun, life would be impossible.

The internet has revolutionised the way we shop. Customers can order goods and services without the need to leave the house. Weekly shopping no longer requires an actual visit to the supermarket, films can arrive through your letterbox, you can even send a birthday card without ever seeing it.

It costs the NHS £1 million an hour to treat the UK’s 2.8 million diabetics. It is estimated a further 850,000 people are unaware they are living with the condition. With the number of UK diabetics expected to smash the four million mark by 2025, mathematics is underpinning a new technique which might help to monitor patients using something unexpected: their eyes.

Of all the places you'd expect to find a mathematician, the theatre of active warfare probably doesn't feature very high on the list. However, a group of UK mathematicians have played a key role on the front line for over two decades.

"Your call is currently in a queue” - seven words to strike fear into the heart of any caller. Most people will have experienced being told that their call is important, followed by inordinate renditions of music like Greensleeves. Estimates place the amount of money UK consumers spend on contact centres, including the cost of phone bills and lost time, at around £15 billion a year.

Getting fish from the sea to your stomach is big business: Britain consumes £5.65 billion worth of seafood every year. A consistent member of the country's top three seafood staples is cod - of all the cod eaten on the planet, a third of it ends up on British plates. However, cod stocks around Britain's coastlines, particularly in the North Sea, have dwindled in recent decades under the strain of over-fishing.

Every year more than a billion journeys take place on Britain’s railways. Together, UK train passengers annually travel a combined distance of over 50 billion kilometres - enough to take you on five return trips to Pluto. However, 1 in 10 trains do not arrive on time.

On 14 April 2010 the Eyjafjallajökull volcano erupted under a sheet of Icelandic glacial ice for the second time in a matter of weeks. The ice shattered the magma into fine glass and ash which climbed into the sky with the rising volcanic plume. Fearful of its effect on aircraft engines, UK airspace was closed the following day, as the ash cloud headed south, marking the beginning of the largest shut-down of air traffic since the Second World War.

Duelling wizards, alien invaders and fairytale monsters have little need for proofs and equations, but advanced mathematics is essential to the computer animation and visual effects industry that creates them. The UK is a market leader in this sector, generating annual sales of around £375 million, and many of Hollywood's biggest releases are brought to life by visual effects generated in UK post

Oil is one of the most valuable commodities on the planet, and even though use of renewable sources is increasing, it still provides a large proportion of the world’s energy. Our dependency on oil looks set to continue in the near future, but the past 150 years of oil drilling have left many reservoirs depleted and gaining access to those that remain is becoming increasingly difficult. Thankfully, mathematicians are helping to keep the oil flowing with models that map these buried reservoirs and techniques for boosting efficiency that are inspired by biological evolution.

The past few decades have seen the rapid growth of digital technology in every area of life, enhancing our society in ways that were previously impossible. Now that we've all come to rely on ultra-fast communication, instant access to the world's information, online shopping and more, the nation's digital infrastructure is as essential as our waterworks or roads.

Sailors have always told tales of rogue waves, describing encounters with gigantic walls of water that appear without warning and drag ships to the depths below. Until recently, oceanographers dismissed these accounts as nonsense, no more real than sea monsters or mermaids, because mathematical models predicted that such an immense wave was almost impossible. That all changed on New Year’s Day 1995, when measuring instruments aboard the Draupner oil platform in the North Sea detected a wave nearly 26 metres high: the first verifiable rogue wave.

With more than half a billion television viewers across the globe and annual revenues of around $4 billion (£2.5 billion), Formula One is among the most popular sports in the world. It is a highly competitive field where even a fraction of a second can mean the difference between first or second place, so Formula One teams will do whatever it takes to gain an advantage. In the past ten years, that's increasingly meant relying on performance boosts through advanced mathematics.

Viruses are responsible for a variety of illnesses, ranging from the common cold to more serious conditions such as AIDS and some types of cancer, but their methods of infection are always similar. Once a virus has entered a host's body, it hijacks the replicating mechanisms within the host's cells and starts pumping out copies of itself. Viruses can only do this by concealing their genomic material within a protein shell, or capsid, which allows them to slip inside the host's body like a Trojan horse. These capsid shells often have complex symmetrical structures, so mathematicians are investigating their shapes in the hope of discovering new treatments for viral infections.

Fluids play a vital role in a wide variety of industries, from packaging manufacturers to pharmaceutical companies. Understanding how to best manage the use of fluids is important for companies wishing to remain efficient and competitive, and many have partnered with mathematicians such as Mark Wilson at the University of Leeds to help solve their problems.

Our bodies contain thousands of miles of blood vessels, from millions of tiny capillaries each ten times thinner than a human hair, to the 3 cm-wide aorta connecting the heart to the lower body. The passage of blood through this dense circulatory system is a complex process, but one that mathematical modelling can make easier to understand. Learning more about how our blood flows and what can cause flows to change is an important part of understanding many blood-related diseases.

Networks are all about making connections. The global internet and telephony networks form the largest and most complex machine the human race has ever constructed, allowing billions of people to exchange vital information in the blink of an eye. Equally important is the global transport network, which enables the mass movement of people and goods by land, air and sea. Understanding how these connections work is essential if we want to improve them, and only the mathematics of network theory can get the job done.

Optical fibres have a wide range of applications, such as transmitting data around the globe, letting doctors peer inside their patients and even brightening up Christmas in the form of tree lights. These kind of fibres have been in use for decades, but the latest optical fibres are far more advanced and producing them is more difficult. Thankfully, manufacturers can use mathematical models to simplify the process.

Our world is full of cameras and other imaging sensors producing millions of photographs, video clips and digital 3D models every single day. Imaging technology is constantly evolving, with new products and applications launched each year, and the rate of change is so fast that the digital cameras found in modern mobile phones now provide better quality images than the top-of-the-range digital cameras of the late 1990s.

Increasing global temperatures, rising sea levels and the disruption of fragile ecosystems: climate change is one of the greatest challenges humanity has ever faced, and could potentially affect billions of lives in the coming century. Scientists around the world are working to tackle the problem with detailed models of our changing climate, and mathematicians are at the heart of these models, solving the difficult equations that no one else can. Researchers in meteorology, physics, geography and a host of other fields all contribute their expertise, but mathematics is the unifying language that enables this diverse group of people to implement their ideas in climate models.

Coastal erosion is a serious problem in the UK and currently occurs along 17% of the country’s coastline. The problem is worst in England, where 30% of the coastline is eroding, partly due to sea levels rising by 3 millimetres in each year since 1992. Erosion places homes at risk and can wash away sites of strategic and scientific importance, so understanding the processes at work is essential if we are to protect our coastline. Mathematicians such as Vanesa Magar and others at the School of Marine Science and Engineering at the University of Plymouth create models of these processes and use them to predict how erosion might occur and what effect introducing coastal defences will have.

Medical imaging techniques let us peer inside the human mind, furthering our understanding of how the brain works and offering the possibility of combating devastating conditions such as Alzheimer’s disease and schizophrenia. Mathematical research is at the heart of these techniques, working together with technological advancement to create enormous benefits for society.

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.

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.

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.

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.

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.