Mathematics Matters: Synoptic Paper

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.

The benefits are not just financial. Lift the lid of any corner of modern living and you’ll find mathematics beating away at the very heart of it. Whether that’s increasingly ubiquitous technology like smart phones1 or the cutting edge animation in the latest Hollywood blockbuster2. Numbers and equations also help forecast the weather, with Britain a leading international hub for meteorology – the Met Office employs over 2,000 mathematicians alone. In April 2010, their work on modelling the volcanic ash cloud from the Eyjafjallajokull eruption returned aircraft to the skies as swiftly as possible, minimising the economic catastrophe of a grounded fleet over much of Europe3. The aviation industry as whole is also underpinned by mathematics research. Maths is used to reduce the noise created by aircraft4, as well as test air traffic control radar to ensure they meet rigorous safety standards5.

The pervasive nature of mathematics continues in areas as diverse as architecture and defence. Numbers are crunched to create comfortable environments in buildings such as railway stations and schools6, as well as to find the best ways to succeed on the front line7. The ability of mathematics to help defend ourselves is not limited to physical warfare, however. Cyber-security is increasingly making its way up the list of defence priorities. Mathematics has a crucial role to play in encrypting sensitive information from prying eyes, with similar techniques used to keep your credit card details safe online8.

One the biggest industries in the world – pharmaceuticals – is also dominated by mathematics. UK companies employ many mathematicians and statisticians across every aspect of drug manufacture, from the initial design to final product9. In fact, the UK pharmaceutical industry spent £4.6 billion on research and development in 2010 – 29% of all UK R&D spend and more than any other country in Europe. Mathematics is also helping to save lives by pioneering non-invasive tests for diabetes10, understanding blood flow11 and modelling the outbreak of disease12. It is also tackling our growing need for stable energy by maximising yields from current oil sources13, along with striving for greener technology such as harnessing the power of nuclear fusion14 or unlocking the hidden energy in water15.

The mathematical techniques deployed across this vast array of areas vary considerably. They can, however, be grouped into three broad categories: data analysis, modelling and optimisation.

Today’s world is awash with data – a 2013 estimate suggests that 90% of existing data had only been created in the previous two years. If an HD movie took up as much digital storage space as all the data in the world today, it would take 47 million years to watch. It is only set to increase: some have predicted that data production will be 44 times greater in 2020 than it was in 2009. This flood of ones and zeroes is a rich source of information, and one that requires mathematical techniques to harness. These vast amounts of data are too large for humans to trawl for patterns and trends. Instead, mathematical algorithms are deployed to farm the data sets for useful insights. This can include sifting huge amount of genetic data to open a window on DNA differences that lead to disease16, or building more efficient electricity grids17.

When faced with a real-world problem, it is often prohibitively expensive and time consuming to try out a variety of solutions in practice. This is often the case in engineering. One particular example is in car design where stringent safety criteria have to be met, and that’s where modelling comes in. Designers can construct a mathematical model of parts of the vehicle, such as the bonnet, and manipulate its size and shape to see how its performance varies18. Only then would they build for real. Modelling can also help peer into the future. By constructing a model of an environment or situation and plugging in current data, mathematics can be used to hit the fast-forward button and see what might happen at a later date. This is particularly useful in environmental science where it has been used to model climate change19 and fish stocks in the North Sea20.

Sometimes you already know how to do something, you just want to do it better. That could be faster, cheaper or both. In these situations the mathematics of optimisation can help. Turning the process into a string of numbers and symbols and calculating when that function is maximum can provide powerful insights into realms as disparate as call centres21, railway journeys22 or computer chips23.

So whether it is on land, sea or air, online or on the front line, mathematics underpins every nook and cranny of modern life. Far from a quaint subject to be forgotten upon leaving school, it is the glue that holds modern life together and significantly boosts our economy.


  1. Smarter phones for all
  2. Advancing the Digital Arts
  3. Volcanic ash: Air travel under a cloud
  4. Aircraft noise (Phase III – to come)
  5. On the radar- calibrating air traffic control antennas
  6. Keeping it cool- controlling the climate in railway stations
  7. Kosovo: Mathematics on the front line
  8. Internet shopping: stopping the scammers
  9. Pfizer (Phase III – to come)
  10. Keeping an eye on diabetes
  11. Keeping hearts pumping
  12. Modelling an epidemic emergency
  13. An energy evolution
  14. Fusion: fuelling the future
  15. Hydrogen: the fuel in water
  16. Stats in your genes
  17. Next generation local electricity networks
  18. All aflutter- reducing car bonnet vibration
  19. Predicting climate change
  20. The Weak Link the Fish Food Chain
  21. Quicker contact centres
  22. Train delays: staying on track
  23. Predicting Performance – Mathematical Verification of Chips

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