People Don’t See Equations. They See Results

What do artificial intelligence, modern medicine, and pure mathematics have in common? More than one might think. Finding answers to questions like these is at the heart of Professor Marek Galewski’s research at Lodz University of Technology. For almost a decade, he has been returning to the Department of Mathematics at the Faculty of Electrical Engineering and Communication (FEEC), Brno University of Technology, where he and Professor Josef Diblík have built a collaboration that has resulted in numerous joint publications and new research findings. During this year’s visit, we spoke about mathematics whose equations most of us will never see, yet whose results influence the technologies around us.

Professor Marek Galewski serves as Vice Dean of the Faculty of Technical Physics, Information Technology and Applied Mathematics at Lodz University of Technology. However, his visits to the Department of Mathematics at FEEC are about much more than delivering lectures. Over the past decade, Brno has become one of the places where part of his scientific work takes shape. Together with Professor Josef Diblík and Associate Professor Zdeněk Šmarda, he has developed research that connects experts from Brno and Łódź and brings new results in mathematical analysis.

“People do not see the equations themselves. They see the results. Yet mathematics lies behind treatment optimisation, algorithms, and artificial intelligence,” says Professor Galewski. According to Professor Galewski, few people realise that without fundamental mathematical research many of the technologies we now take for granted would never exist. Modern medicine, optimisation algorithms, and today’s rapid development of artificial intelligence all rely on mathematical models that were created long before they found practical applications.

From a Conference in Poznań to a Decade of Collaboration

The story of this joint research began in 2015 at a conference in Poznań, Poland, where Professor Galewski first met Professor Josef Diblík from the Department of Mathematics at FEEC. What started as a professional meeting gradually evolved into a collaboration that continues to this day. The result has been joint publications, regular research visits, and collaborative projects linking Brno and Łódź.

“We initiated this research during one of my visits to Brno. Afterwards, we continued working on it remotely and prepared the results for publication,” recalls Professor Galewski. Throughout the interview, Professor Galewski emphasized that although mathematics is often viewed as an individual discipline, good research is above all the result of collaboration. “Every country develops its own expertise. When we bring those experiences together, new ideas emerge that would never have arisen otherwise,” explains Professor Galewski.

Looking back on their years of collaboration, Professor Josef Diblík speaks not only about publications and scientific achievements. Above all, he highlights the mutual trust and open discussion without which such cooperation could not exist: “Professor Galewski and I have worked together for many years. Each of us brings a slightly different perspective to solving problems, and that diversity is precisely the strength of our collaboration. It is not only about joint publications, but above all about long-term scientific discussion and mutual trust,” says Professor Josef Diblík.

Professor Marek Galewski of Lodz University of Technology during his lecture at FEEC BUT. | Author: UMAT, FEEC

Good Science Begins with People

Professor Galewski speaks about collaboration with warmth and humour. One story, in particular, illustrates how important personal relationships are in science. While looking for a research partner for a stay in Portugal, he had to choose among mathematicians he had never met in person. In the end, an unexpected resemblance influenced his decision.

“I was looking through photographs of potential colleagues, and one of them reminded me of Josef—dark hair, a moustache, and glasses. I thought that if he looked like Josef, he might be just as good a colleague,” Professor Galewski says with a smile. His intuition proved correct. What began as a chance decision developed into another long-term scientific collaboration.

He has many similar stories. In one of them, he recalls receiving a phone call while out for a run, urging him to return to the hotel immediately because Professor Diblík had just arrived and it would be a shame to miss the opportunity for discussion. “That was probably one of my fastest runs,” he laughs. According to Professor Galewski, such informal moments often lead to new research ideas.

Artificial Intelligence Will Need Mathematicians

A large part of our conversation focused on the rapid development of artificial intelligence. Professor Galewski is convinced that AI will not reduce the importance of mathematics – quite the opposite: “Artificial intelligence can already write a simple computer program. That means we will need even more people who understand complex systems, create new models, and develop original solutions. That is exactly what mathematics teaches students.”

In his view, technical universities across Europe face the same challenge: attracting talented students to mathematics and motivating them to pursue research careers. Mathematics is about much more than calculations. Above all, it develops abstract thinking, the ability to recognise patterns, and problem-solving skills. That is why mathematicians find careers not only in research, but also in computer science, economics, and law.

Whenever He Is in Brno, He Runs through Lužánky Park

Professor Galewski is as passionate about sport as he is about mathematics. He enjoys running, swimming, and cycling to work. Lodz University of Technology even has its own university swimming pool. “Sometimes we go swimming with colleagues before a seminar,” he says with a smile. During his stays in Brno, he follows another favourite routine – running in Lužánky Park. He thinks that it is the best way to relax after a day’s work.

At the end of our interview, Professor Galewski summed up the significance of mathematics in a sentence that, in his view, applies equally to research, technology, and everyday life.

“Mathematics helps people understand the world. The world is becoming increasingly complex, and mathematics enables us to simplify and understand those complex systems.”

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During his visit to FEEC, Professor Marek Galewski delivered the lecture *On the Existence and Uniqueness of Homoclinic Solutions for Non-Variational Discrete Problems*. He presented the results of joint research on discrete boundary value problems that cannot be solved using standard variational methods. The research team therefore employed the Browder–Minty theorem (a mathematical theorem used to prove the existence and uniqueness of solutions to certain classes of nonlinear problems, editor’s note). The study also involves the p-Laplacian operator (a nonlinear generalisation of the classical Laplace operator used to model nonlinear phenomena in mathematics and physics, editor’s note).

Author: Zdeňka Koubová