Research | WIAS | 18-04-2023

Mathematics – the universal science

Like no other scientific discipline, mathematics stands out for its universal language and applicability. It allows people from different cultures to easily work together on solving problems.

Clip from the video "Weierstrass Institute for Applied Analysis and Stochastics"

Mathematics is not always thought of as the easiest subject in school. Its formal language, concepts and construct of ideas are complex and follow strict logic. Yet those very qualities make it a valuable form of training for the human mind. And, as far as disciplines go, mathematics is quite accessible because it doesn’t take much to do it: all you need is pencil and paper, or blackboard and chalk – maybe a couple of well-sorted bookshelves and an Internet connection – and you’re all set to do mathematics at an advanced level.

If you compare that with the amount of equipment that many scientific disciplines require, the initial material hurdle to getting into mathematics is utterly tiny. It takes little more than aptitude and diligence to succeed in maths. Once you have overcome the initial barrier of understanding the formalism, you then choose your own field of specialization.

That allows people from all over the world to work together on solving mathematical problems. “I find it wonderful that the universality of mathematics is reflected not only in the general applicability of its concepts and implications, but also in the internationality of our workgroups,” says Professor Michael Hintermüller, Director of the Weierstrass Institute for Applied Analysis and Stochastics (WIAS).

Mathematics forges international connections

The universality of mathematics as a science can be seen in the fact that it is the archetype of an abstract science. Once a mathematical proof is established and a theory is proven, the resulting methods can be applied to all problems and areas whose systems can be represented by that mathematical structure. Many times over in history, for example, a mathematical method first developed to answer a question in physics has ultimately found new applications in entirely different fields, such as manufacture, engineering or medicine.

Furthermore, mathematics stands out for clearing the way for researchers from all countries and cultures of this world to work unhindered on solving the same problems. “Of course, you do encounter material hurdles sometimes, like when you need a supercomputer to calculate certain systems of equations,” Hintermüller points out. Researchers from developing countries often have no access to these kinds of resources. “But in most cases, such equipment is not critically important for our work,” the mathematician explains.

Much more important is the ability to express the intellectual concepts in all terminological rigor with the help of mathematical symbols. “Having gone to distant countries for conferences, I have been in situations where not all participants could communicate equally well in English,” Hintermüller relates. “But then, it was through the universal, formal language of mathematics that, despite the other language barriers, we could follow the content of the lectures very well.”

Lingua franca of modern science

No other science allows such rigorous, logic-based understanding across language barriers. And if the formalized areas of the natural sciences – such as theoretical physics and chemistry – can also do this to some extent, then it is precisely because they use the language of mathematics. That makes the universal, formal language of mathematics effectively the lingua franca of modern science – indeed since the very beginning, as pondered in the reflections of a certain Galileo Galilei.

The universal accessibility of mathematics is also reflected in the composition of the staff at WIAS. Over the years, it has continually become more international. “Today, we have 46 scientists from abroad. They come from 24 countries and nearly all continents,” Hintermüller reports. “That is almost half of our scientific workforce.” And this development will likely continue.

The alignment of the Institute certainly plays a role in this development. The institute for applied mathematics is, after all, primarily interested in researchers who want to solve concrete problems. The methods enabling them do so, which are being developed at the Weierstrass Institute, naturally
have the general applicability typical of mathematics. Therefore, the researchers from their respective countries can also apply and teach these advanced problem solving methods in their homelands when they return. And ultimately, because mathematics does not require big, expensive equipment, it is easy to pass on the knowledge.

Text: Dr. Dirk Eidemüller

The article was published in Verbundjournal 119 | 2022 with the focus on "30 years of FVB."

Video / Science Clip