The MATH+ excellence cluster enables visitors to the HU exhibition at the Humboldt Forum to delve deep into the world of mathematics

How do we ensure that there is less congestion on the roads? How can we put to use the data that we generate daily? And how do we ensure that electricity is available exactly where it is required? Mathematics helps us find solutions to problems that affect us in everyday life. “We live in a world of mathematics without being aware of it,” says Dr. Gorch Pieken, curator of the exhibition in which the Humboldt-Universität zu Berlin (HU) presents itself at the Humboldt Forum.

The grand foyer features the Berlin universities’ clusters of excellence that are funded by the excellence strategy of the federal and state governments. One of them is the MATH+ Berlin mathematics research centre, with the Technische Universität (TU) as its representative institution and the Freie Universität (FU), the Humboldt-Universität (HU), the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) and the Zuse-Institut Berlin (ZIB) as participating facilities.

Gazing into the black box with MATH+

Mathematical issues and applied solutions will permeate the Humboldt-Universität’s exhibition at the Humboldt Forum, says its curator, starting with the virtual shoal of fish projected onto a gigantic theatre curtain in the entrance area that reacts to movements by visitors. It took maths to make this shoal of fish possible just as it did for many other visual representations of scientific research at the exhibition. They are activated by, inter alia, computers or smartphones that would not exist were it not for mathematics. “It nonetheless remains a mystery for many people,” says curator Gorch Pieken. “That is why we would like to gaze into the black box with the MATH+ cluster,” he says.

Traffic is a vivid example of its use. Many motorists use navigation devices to get from A to B quickly. Different variables are involved in calculating the suggested routes. Where is there a road closure, where is the road clear? “What lies behind it is a mathematical algorithm that can handle lots of data,” explains Martin Skutella, Professor of Mathematics and Computer Science at the Technische Universität (TU) Berlin and MATH+ spokesman. “Our aim is to guide traffic in such a way that there are as few traffic jams as possible. Mathematical network optimization helps us to achieve it,” he says. In future it will also be a matter of guiding self-driving cars around the city.

All of Berlin’s mathematics under one roof

The prerequisite for developments of this kind is the ever-increasing quantities of data that are available in all areas of life and research. “No individual can cope with the gigantic amounts of data that find their way into our lives. That is where mathematics is required,” the cluster’s spokesman says. One of the core tasks of mathematics is to develop algorithms that can analyse and interpret large quantities of data in order to solve specific problems. “At MATH+ we now face the challenge of taking the mathematical methods required forward decisively,” Professor Skutella says. To do so the cluster aims to unite under one roof all of Berlin’s mathematics, including around 100 mathematical research groups.

Mathematicians will also be needed in the course of the transition to renewables - an important topic in the exhibition - to help with network optimisation. If, say, the weather is calm or it is night time and there is no wind or solar power, gas-fired power stations can be fired up to ensure that energy supplies are available. MATH+ cluster research scientists are also engaged in managing the gas network across Europe.

Robot sheep at the Humboldt Lab?

Since the beginning of 2019 the cluster has also been funded by the German Research Foundation (DFG), and in May it was officially inaugurated. Its top-flight research scientists collaborate not only with engineering science partners but also with partners in life sciences, the humanities and social sciences. In one project they are working with archaeologists to find out how wool sheep spread around Europe. In the course of evolution sheep developed longer coats and only then could humans start to use their wool to make clothes. Excavations reveal where this innovation was already established, Professor Skutella says, but mathematical models then help us to understand how the sheep spread.

Will there be robot sheep to see at the Humboldt Forum along with the virtual fish? Who knows? The inaugural exhibition is modular in design and can be changed or added to at any time. There is no lack of examples of mathematical use cases. From energy supplies to public transport, the Anthropocene, the age in which human activity has predominated, has numerous challenges at the ready. “We will need to fundamentally think further on many issues. For our future it will not be enough to imagine it only as an optimised present. And that is where mathematics will be especially important,” says Gorch Pieken.