Mathematics for data processing

Spain leads pioneering initiatives in mathematical research and model development, thanks to the work of universities and the CSIC. However, the importance of mathematics in our economy is still far below that of other European countries.

Mathematics is a seemingly invisible science. Although we do not see it, it is behind millions of everyday things, such as checking our e-mails or weather forecasts. A commitment to mathematics guarantees economic development and growth. They are key to accelerating innovation. The European Commission wants to encourage the development of new algorithms and mathematical models for member states to lead the digital transformation, the design of new diagnostic tools and new cryptographic methods, which can help us face possible security attacks carried out from quantum computers.

Mathematics studies the properties of numbers, symbols and geometric figures. At first glance, it is difficult to understand the importance of this science in our daily lives, but in reality, it is fundamental for economic development. In particular, Manuel de León, research professor at the CSIC and former director of the Institute of Mathematical Sciences, highlights three ways in which mathematics directly benefits society. Firstly, they allow us to rationalise, analyse and interpret data - from weather forecasts to the results of an MRI scan - which amounts to a better understanding of the world. They also enable a more secure society thanks to algorithms and cryptography, which protect our communications, our bank accounts and our data. Finally, mathematics facilitates the development of models to minimise uncertainty and predict the evolution of complex phenomena, such as the COVID-19 pandemic. Some of these systems, for example, calculate the need for beds in intensive care units using both complex mathematical equations and artificial intelligence technologies. In short, the different branches of mathematics are key to society, and continued investment in research and development ensures a positive impact on the economy.

By 2030, there will be twice as many devices connected to the internet as there are now, according to Statista. These figures would be impossible without the contributions of mathematics to telecommunications, which allow us to compress and decompress information efficiently and securely. Much of this work is based on studies developed in the 18th and 19th centuries by the French mathematician Joseph Fourier. His formulas allow us to decompose complex mathematical signals and functions into simpler expressions known as 'series'. Moreover, these transformations are reversible. Therefore, they also make it possible to recompose the fragments and decompress the information. These processes allow signals to be handled and interpreted as they travel through electrical and electronic devices. Information of zeros and ones is transformed into electromagnetic pulses and vice versa.

These mathematical advances have also enabled the development of digital formats that store information efficiently. A classic example is JPEG algorithms, which use successive Fourier transforms to compress the information in an image. Once compressed, JPEG images contain less information than an original photograph, but are much lighter and allow us to store six to ten times more data in the same space. Today, data storage is one of the most polluting industries on the planet, responsible for a carbon footprint comparable to all air travel. According to some estimates, by 2025 data centres will consume 20% of all electricity generated and, by 2040, will be responsible for 15% of greenhouse gas emissions; comparable to US emissions today.

Interestingly, the man who discovered the mathematical tools that will help us mitigate the impact of our massive data consumption, Joseph Fourier, was the first scientist to observe the greenhouse effect. After studying heat transfer for years, he observed that the temperature of our planet was much higher than his models predicted and suggested that the atmosphere was somehow responsible for keeping the Earth warm.