On 5 July, Ukrainian mathematician Maryna Viazovska grew to become the second lady in historical past to earn a Fields Medal, one of many high prizes within the discipline. Viazovska, who is predicated on the Swiss Federal Institute of Expertise in Lausanne (EPFL), is most well-known for fixing the issue of the way to pack spheres in essentially the most environment friendly manner in an area with eight dimensions.
Nature spoke to Viazovska concerning the award’s significance, and her imaginative and prescient for arithmetic.
How does it really feel to be one of many winners of the Fields Medal?
After all, I used to be extraordinarily pleased and honoured, as a result of only a few individuals get this award. I’ve really recognized about it for some time: Carlos Kenig, the president of the Worldwide Mathematical Union, contacted me and advised me the information in January.
Why did you change into fascinated about the issue of sphere packing?
It’s a really pure, very good geometric drawback — an issue with a quite simple formulation, and infrequently very tough to resolve. There are nonetheless many open questions surrounding it. Additionally, what made me within the packing drawback in dimensions 8 and 24 was, in fact, the work by Henry Cohn and Noam Elkies, the place they proposed the way to resolve it, and got here very near an answer. So it appeared like low-hanging fruit. Even now, after it’s solved, we nonetheless have infinitely many dimensions for which the issue remains to be open and the identical strategies don’t work. There are nonetheless so many discoveries to be made.
Calling it low-hanging fruit sounds very modest, given how your work has been hailed as an enormous breakthrough.
Sure, nevertheless it’s perhaps within the nature of arithmetic that to make an enormous breakthrough, you must chase low-hanging fruit — and a few of our low-hanging fruits are nonetheless fairly excessive! In arithmetic, after we consider open issues, we don’t assume when it comes to months and years to resolve them — typically, we expect when it comes to a long time and centuries.
Does the prize have a particular significance at such a tough time for the Ukrainian nation?
I hope so. Possibly this information made any person’s day higher. However in comparison with how a lot we’re dropping proper now, in fact it’s not comparable.
I used to be chosen as a winner earlier than the Russian invasion of Ukraine started in February. I consider that this determination is about arithmetic and never about anything — that’s the way it needs to be.
And it’s additionally an vital win for ladies in arithmetic?
My dream is that girls getting main prizes will likely be a routine occasion, not an important day. It shouldn’t be. Possibly this prize might have a constructive impact on younger ladies, however what’s far more vital is what occurs early in school — the arduous, on a regular basis work that’s finished by dad and mom, academics, college professors.
Arithmetic is without doubt one of the fields the place we will simply get pleasure from our variety — the place it’s not an issue however a bonus.
How does variety enrich the mathematical group?
All the pieces we do is in some very oblique manner linked to our on a regular basis expertise. Even in a really summary discipline, individuals with totally different backgrounds may need totally different working habits, or vital core beliefs that aren’t instantly associated to arithmetic however can affect the way in which they assault issues.
How would you describe your model of doing arithmetic?
I desire engaged on concrete examples, not on large, summary theories. My view of arithmetic is that I’m like a pioneer discovering an unknown land. So, I don’t attempt to construct castles, however relatively I’m going right into a jungle and comply with a path, and hope that this path will lead me to new, undiscovered land.
How is arithmetic analysis evolving? Do you see any specific tendencies?
On the one hand, arithmetic — a minimum of, pure arithmetic — may be very conservative and does go its personal manner. However now we reside on this thrilling time when know-how is altering our lives, and, in fact, it’s altering mathematicians and arithmetic. We get a whole lot of enter not from inside arithmetic however from exterior.
A subject that’s attracting increasingly more consideration is mathematical points of machine studying. There are numerous instructions; one which pursuits me is how I might use a few of these new thrilling instruments in my very own analysis. One other very formidable and noble purpose is to create a mathematical idea of machine studying. When does it fail, and after we can we hope for good outcomes?
Additionally, the thought of quantum computing comes with an enormous variety of fascinating mathematical issues.
Is there an enormous function for arithmetic in quantum error correction, which is essential to creating quantum computer systems work?
Finding out sphere packing may be very shut in some methods to the issue of error correction — many approaches and strategies translate from one to the opposite.
As mathematicians, we can not construct a quantum pc, however perhaps, motivated by the opportunity of its existence, we will show fascinating, significant theorems.
This interview has been edited for size and readability.