Portrait of Marina Biazovska

    Number theorist Marina Wiazowska was awarded the Fields Medal for her work on sphere packing.Credit: EPFL/Fred Mertz

    On July 5, Ukrainian mathematician Marina Byazovska became the second woman in history to win the Fields Medal, one of the field’s highest awards. Based at the Swiss Federal Institute of Technology (EPFL) in Lausanne, Biazowska is most famous for solving the problem of how to pack spheres in an eight-dimensional space in the most efficient way.

    Nature He spoke to Wiazowska about the importance of the prize and her vision for mathematics.

    How does it feel to win the Fields Medal?

    Of course, very few people win this award, so I am very happy and honored. I’ve actually known about it for some time. Carlos Kenig, president of the International Mathematical Union, contacted me and told me the news in January.

    What made you interested in the sphere packing problem?

    This is a very natural, very good geometric problem — a very simple formulation problem and often very difficult to solve. There are still many open issues surrounding it. Also interested in the dimension 8 and dimension 24 filling problem was, of course, the work of Henry Cohn and his Noam Elkies, who proposed a solution to it and came very close to solving it. As such, it seemed like an easily available fruit. Even now that it’s solved, there are countless dimensions where the problem is still open and the same method doesn’t work. There are still many discoveries to be made.

    Given that your work has been hailed as a major breakthrough, calling it something easily accomplished sounds very understated.

    Yes, but perhaps the nature of mathematics requires us to pursue easily achievable achievements in order to achieve major breakthroughs. In mathematics, when we think of unsolved problems, we often don’t think in terms of months or years to solve them, but in terms of decades or centuries.

    Does the award have a special meaning for the Ukrainian people in such a difficult time?

    i hope so. Maybe this news made someone’s day better. But compared to what we are currently losing, of course it is not comparable.

    I was named the winner before the Russian invasion of Ukraine began in February. I believe this decision is about mathematics and nothing else. It should be.

    Is it also an important victory for women in mathematics?

    My dream is that winning a big award for a woman becomes an everyday occurrence rather than a special occasion. The award may have a positive effect on young women, but what is more important is what happens early in school: the hard daily work done by parents, teachers, and university professors.

    Mathematics is one of the fields where we can enjoy diversity. Diversity is an advantage, not a problem.

    How does diversity enrich the math community?

    Everything we do is connected to our everyday experience in a very indirect way. People with different backgrounds, even in very abstract fields, have different work habits and, although not directly related to mathematics, important cores that can influence how we approach problems. may have beliefs.

    How would you describe your math style?

    I prefer to work on concrete examples rather than big abstract theories. My view of mathematics is that of a pioneer discovering uncharted lands. So rather than trying to build a castle, I go into the jungle and follow a path, hoping that this path will lead me to new, undiscovered lands.

    How is mathematics research evolving? Do you see any particular trends?

    On the one hand, mathematics, at least pure mathematics, is very conservative and goes its own way. But now we live in this exciting time when technology is changing our lives. Of course, technology is changing mathematicians and mathematicians. We get a lot of our input from the outside rather than from within mathematics.

    A topic that is receiving increasing attention is the mathematical side of machine learning. There are many directions. What interests me is how I can use these new and exciting tools in my own research. to create a theory. When can you fail and when can you expect good results?

    Also, the idea of ​​quantum computing comes with a number of interesting mathematical problems.

    Does mathematics play a big role in quantum error correction, which is essential for quantum computers to work?

    The study of sphere packing is in some respects very close to the problem of error correction. Many approaches and methods translate from one to the other.

    As a mathematician, I can’t build a quantum computer, but I might be motivated by its possible existence to prove some interesting and meaningful theorem.

    This interview has been edited for length and clarity.

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