Encryption, medicine, Formula One, and energy optimisation: The essential nature of maths to industry and the economy

By Zubin Siganporia

Nearly everyone learns maths at school. Despite that, the proportion of people who continue to study the subject at a higher level, and who then go on to develop and apply mathematics as a key part of their careers, is very small.

This could be unfortunate for many reasons. From a national perspective, there is overwhelming evidence that increasing the work in mathematical sciences adds enormously to a country’s economic standing, security, and ability to solve challenging technological problems. At a personal level, many individuals have a negative experience of maths at school, and are put off long before they might otherwise have had the opportunity to see the appeal of the subject first-hand. Mathematics can be intimidating, and we need to do as much as possible to make it both inclusive and interesting during learning at school and beyond. Whilst effective maths education is essential, it's not the primary focus of this short blog post. Instead, we want to give some short examples to highlight the essential nature of maths to industry and the economy.

You’re probably reading this article on a device connected to the internet. When we send and receive sensitive information over the internet, we rely on cryptography, specifically the mathematics of encryption and decryption, to secure our transactions and messages. The design of many cryptographic schemes is based on difficult underlying mathematical problems that aim to provide security against a malicious eavesdropper. To give a specific topical example of cryptographic research, mathematicians have developed approaches in recent years that allow potentially untrusted third-parties (such as cloud computing services) to carry out useful sensitive computations for individuals (such as analysing their medical data). This can be done in such a way that the third-party is never able to actually see the data or the calculation, instead just providing the user an encrypted answer at the end. Secure computation will be extremely useful for many applications, not least in healthcare and genetics.

Medicine has already benefitted hugely from completely different areas of mathematics, and there continue to be important developments in medical data science today. Machine learning is a very large and general area of mathematics concerned with extracting patterns from datasets, and then using them to inform predictions or decisions without a human having to program the logic explicitly. There are many instances of machine learning improving upon the previous state-of-the-art medical imaging analysis, leading to better detection and interpretation of findings. A significant area of current research involves understanding the three-dimensional structure of molecules that are important to biological processes, and which are formed out of smaller building blocks called amino acids. The overall three-dimensional shape is often critical to the function of these molecules, but determining this in advance just from the knowledge of the smaller amino acid building blocks is a very challenging problem. Machine learning has helped to address this challenge, which in turn provides better opportunities to design more effective medicine.

Perhaps a more surprising use of mathematics has been completely outside science and technology, and instead in the world of sport. Mathematical modelling has been crucial in a large number of sports, including Formula One racing. Simulating the airflow around a racing car has led to engineers constructing car bodies that reduce drag along the straights, and that also exert downward pressure onto the tyres to allow the car to move faster around corners. Separate probability models greatly help teams with their strategies during races, and inform decisions made in response to competitors. Mathematically optimising race decisions has been applied successfully in other sports, including both sailing and rowing. Olympic medal winning rowing squads have also made use of mathematical simulations of athletes and boat motion in order to improve their training before races.

Although there are a huge number of other examples, we’ll highlight one final instance of the power of mathematical modelling and optimisation by referring to the global energy network. When countries attempt to organise their energy supplies, and when multinational companies distribute sources of energy, they need to solve very complicated network problems in order to accurately balance supply and demand as efficiently as possible, often in the context of geopolitical challenges. Optimising energy scheduling and transportation can be worth hundreds of billions of pounds to a country. A closely related example of mathematical scheduling is the famous Travelling Salesman Problem (TSP), which seeks to find the most efficient route that visits a number of locations and returns back to the origin. Mathematicians have made large progress on the TSP, which often allows us to find extremely good practical solutions, but the question of finding a complete and general solution is widely believed to be intractable. If anyone were to solve the TSP in its purest sense, then it would have implications far beyond logistics, and there are reasons to believe that it could fundamentally change whole areas of science.

In more immediate and tangible terms, there is a need to improve links between the mathematical community and business, industry and policymaking. Mathematicians will increasingly need to communicate potentially complicated ideas that underpin a huge range of technologies used in daily life by millions of people, whilst appreciating that the subject may be intimidating to those outside their field. Policymakers will need to be given the ability to understand the value of mathematical sciences, not just abstractly, but in practical terms.

Clearly, there will be a requirement to have resources for initiatives that promote and encourage mathematical work. This is a large topic in its own right, but with the concrete steps and objectives identified by the Protect Pure Maths campaign, as well as those in ‘The Bond Review: The Era of Mathematics’, we have an excellent place to begin. Mathematics is vital to industry, the economy, and people’s lives more generally, and we can’t afford it to be undervalued.

Zubin Siganporia is Director of QED Analytics. He is also Visiting Research Fellow at the Oxford Mathematical Institute and a lecturer and tutor of pure mathematics at St Catherine’s College, Oxford.