In July 2022, mathematician Prof. Maryna Viazovska received a Fields Medal, a prestigious honour often described as the ‘Nobel Prize of Mathematics’. The 37-year-old professor, who works at the Swiss Federal Institute of Technology in Lausanne, is the second woman to receive this prestigious award in the 86-year history of the prize. We spoke to her about academic freedom, her love of science, and its role in times of war in her homeland, Ukraine.
Prof. Viazovska, born in Kyiv, Ukraine, was awarded the Fields Medal for her work on the sphere-packing problem. As she explains in a video posted on the International Mathematical Union YouTube channel, sphere-packing formulas can be used to solve geometric questions such as how best to stack cannonballs in a ship or arrange oranges in a supermarket. Her formula shows the solution for this problem for spaces of 8 and 24 dimensions.
The Fields Medal comes a few years after you announced the solution to the sphere-packing problem in 8 and 24 dimensions. How long was the road to your formula?
Maryna Viazovska: I had already known about this problem for some time, and I was also familiar with the work of Noam Elkies and Henry Cohn. But it’s only been in the last few years, when I worked in Berlin, that I mostly worked on this problem.
I have been doing mathematics since childhood – we all study maths at school. Then I got involved in maths competitions. But at these competitions you solve problems that have already been solved. My first research experience was in 2004 when I wrote a short paper about approximation theory.
Why did you focus on the sphere-packing problem? What are the practical implications of your formula?
Maryna Viazovska: I think that, at the moment, this work is mainly theoretical. That is to say, I am not looking for practical implications because I am a pure mathematician. For me the application is the new approach to geometrical optimisation problems. Of course, in all areas where optimisation problems are important it is possible to try to apply these special types of functions that I have found. This could help people find optimal solutions and speed up computations in practical situations. But I am not an applied mathematician and I don’t work on the implementation side. For me what is interesting is the theoretical result.
Do you think STEM education (science, technology, engineering and mathematics) is important? How could we get more children interested?
Maryna Viazovska: That’s a very good question. I know from my own experience what made me interested in maths: ‘mathletics’ and maths circles, solving puzzles and small mathematical mysteries. At the same time, I realise that this approach doesn’t work for all kids, so maybe it’s not something universal. I think there’s basically no short-cut, you have to work with children and communicate with them. Of course, nowadays children like computers and computer games, so maybe this opens up ways to teach them about programming or about different types of experiments. I think that one of the nicest things about STEM is the many discoveries that children themselves can make. So maybe the best way is to let kids explore and not just instruct them, to let them find out things for themselves.
Can science bring hope and help people overcome difficulties and look to the future?
Maryna Viazovska: I hope so. On the one hand, we see at the moment that in these trying times science is probably not top priority. But, of course, we do see applied science helping people. It’s sad, but now we are seeing that science is important with all the challenges war presents us; the practical aspects of science become visible in many ways. It’s sad to see that science plays a role in many military applications.
On top of this, many people now understand – I hope – that we have not been working fast enough and have not dedicated enough attention to our energy problems. For issues of this kind, I think science is and should be the solution. Many energy-related research projects are often delayed for years, struggle to get enough funding, and so on. I hope people now realise that in these ‘happy’ past 10 to 20 years we should have done more.
I recently visited Ukraine and while talking to my colleagues there, I had to remind myself that science and pure maths also provide a refuge for our souls from the terrible things that are happening around us. In this respect, I think science is inspiring and I really hope that it can help people save themselves from despair and disbelief and help them psychologically until the war ends. That is crucial because science is a dream of the future and it’s important to keep this dream alive.
What kind of support is best for the Ukrainian research community these days?
Maryna Viazovska: Right now the best support for Ukraine is military and political support so that the war will be over as soon as possible and people can get back to normal. This is what many people, even scientists, tell me. Of course, they have pressing needs but the most important thing is for the war to be over and this is the best way to help.
There are, of course, other practical things that could help, but when I spoke to people, nobody really asked for things for themselves.
It is clear that Ukrainian education and science are now under enormous pressure as many people have left as they had to flee. In terms of budgets, many institutions that are not directly related to practical applications have seen their budgets cut, so they have financial problems to solve. Cooperation with European institutions offers them a way to stay afloat.
For scientists themselves it helps a lot if they can join educational teams and institutions in the countries they have fled to, but for the scientific institutions in Ukraine the loss of staff and students could be difficult. For those who really want to help, the best way is to stay in direct contact with Ukrainian universities and institutions and ask them personally what they need and how best to help them.
Your nation is defending its freedom and as a scientist you need academic freedom too. Have you ever felt that your freedom as a scientist was challenged? How do you think it should be protected in Europe and elsewhere?
Maryna Viazovska: I personally have not felt that, fortunately; I have never felt pressure on me about how I have to do my research. But I am a pure mathematician and maybe that makes it easier for me. I imagine people working on some more sensitive topics, such as climate change or some aspects of ethics, might feel pressured. Also in the social sciences, I could imagine many more challenges to that freedom.
In mathematics, no one would tell me not to do something because it is ‘wrong’ or pressure me to do something because it is ‘right’. I have the privilege of working with very abstract notions. But academic freedom is a fundamental right and it is vital that we protect it and do not forget about it. Probably a big question is how we deal with countries where it is a problem, but I don’t have an answer to that.
What is the next challenge in mathematics for you?
Maryna Viazovska: It’s best not to tell you about the precise task because there is a lot of competition and maybe it would be bad luck to talk about it right now, but I am still working on geometric optimisation problems. In the area of sphere packing, there are many open questions and one of my favourites is what happens in very big dimensions. This is an important theoretical question, as it could tell us how much space we have. There is a huge gap in our knowledge when it comes to this and a complete answer to this question is still out of reach, but I hope to at least move things forward in order to understand the question better.