# Mathematics: science or art?

- Interview

** First publication date:**
08/06/2023

The conference on Finite and Residually Finite Groups will be taking place in Bilbao from June 20-23. It is jointly organised by the University of the Basque Country (UPV/EHU), the University of Brasilia and the University of Padua to honour Professor Pavel Shumyatsky, currently visiting lecturer at the UPV/EHU, and will feature a large international group of speakers highly experienced in group theory. Apart from the academic papers, on Tuesday, 20 June, the prestigious mathematician Efim Zelmanov, winner of the Fields Medal, an international award for outstanding discoveries in mathematics, will be delivering a lecture entitled “What is Mathematics?” It is geared towards the general public and in it he will be discussing whether mathematics is a science or an art.

On the occasion of the conference, Iker de las Heras, researcher in the UPV/EHU’s Department of Mathematics, 2022 Reinhold Baer Prize winner and holder of a Marie Curie scholarship, interviewed none other than Pavel Shumyatsky, professor of the University of Brasilia; he is an international reference in the area of group theory and de las Heras has been collaborating closely with him. Professor Efim Zelmanov, professor of the Southern University of Science and Technology in China (SUSTech) and one of the world's leading researchers in the area of group theory was interviewed together with Shumyatsky.

When asked how long they had known each other, the two professors from the former Soviet Union laugh knowingly: “Since always,” they reply. They actually met in the late 1980s at a lecture on the restricted Burnside problem given by Zelmanov when Shumyatsky was still a pre-doctoral student.

### Relationship with mathematics during childhood

Shumyatsky does not remember having a particular preference for mathematics during his childhood, “although I used to play chess, a game considered to be mathematical. So I have probably always been secretly in love with mathematics”. Zelmanov, however, admits that for a long time he has liked thinking about difficult mathematical problems. “I was lucky to have a very good maths teacher who encouraged and helped me. What is more, in the former Soviet Union, being a mathematics or physics teacher was the most prestigious option, ahead of being an actor or a sportsperson.”

### Influence on their careers as mathematicians

Zelmanov remembers his teachers Shirshov and Bokut of the former Soviet Union. However, “I never met Malcev, but he also had a great influence on my work. And in the United States, I would say Jacobson. Jacobson was a colossus in our area of mathematics. I later became his official successor at Yale University. I moved into his study.” Shumyatsky admits that his teachers were not famous mathematicians, “but they were good teachers. One of the mathematicians who really influenced me was Brian Hartley, at that time a great expert in group theory. Now I reckon people probably won’t know much about his work. Efim's work has made quite an impact on me. My mathematical interests are very closely related to that.”

### Choice of subjects to investigate

The two professors agree that everyone has “a list of difficult problems that accompany us throughout our lives”, but that, nevertheless, they cannot work on all of them “because the question is whether I have any possibilities”. Zelmanov stresses that “it is very important to choose a problem”, and underlines the importance of attending conferences like these. “At every conference, we listen to talks given by others, and perhaps unconsciously, we weigh them up, to see whether or not they can help us with the problems on our lists. We see what everyone else is interested in. Somehow, the interactions seem to find common interests. Sometimes it's also about personal chemistry: I like the talk, I like the person and I want to work with him/her”.

### The future of mathematics

Zelmanov says, “Mathematics has never affected our daily lives as much as it does now. In a sense, we are entering the information revolution, which has its roots in mathematics and which emerged out of mathematics. Everyone understands this, which is why all students are required to take mathematics courses. So welcome to the bright future of mathematics”.