The 2022 recipients of the Fields Medal, arguably the highest honor in the field of research mathematics, have been announced by the International Mathematical Union, as part of the quadrennial International Congress of Mathematicians, which this year is being held in Helsinki, Finland.

This year’s award recipients are interestingly diverse. One was raised in Ukraine, and grieves over her childhood city being bombed in the current military activity; one is known for his passionately independent approach to both life and mathematics; one is very active athletically, and has often found key insights while engaged in these activities; and one dropped of high school, wanted to be a poet and only became seriously interested in mathematics in the last year of his six-year undergraduate studies. Here is some background on each of the four recipients:

**Maryna Viazovska**. Maryna Viazovska, a native of Kyiv, Ukraine, is only the second woman to receive a Fields Medal in the 86-year history of the award. In February, just after she was officially notified that she was a recipient, Kyiv was invaded, so her two sisters, a young niece and a young nephew fled to Slovakia and then joined Viazovska in Switzerland, where Viazovska now lives. She notes with great sadness that the ongoing military conflict has destroyed much of what she remembers growing up there. For example, In March, an airstrike leveled the aircraft factory where her father had once worked.Viazovska was interested in mathematics from an early age. She recalls that in the first grade, “In reading, I was too slow. In writing, I was too messy. But with math, I was kind of quick.” Later she attended Kyiv University, where she collaborated on her first major research. This culminated in a 2011 paper, published in the prestigious journal

*Annals of Mathematics*, on the topic of “spherical t-designs,” which are closely related to the sphere-packing problem, namely what is the most efficient way to pack spheres in d-dimensional space.Within hours after this paper first appeared, mathematicians worldwide were marveling at it. Peter Sarnak of Princeton’s Institute for Advanced Study, called the paper “stunning,” adding that it is “one of these papers you pick up, [and] you don’t put down before you’ve read the whole thing.” Henry Cohn, a mathematician at Microsoft Research and the Massachusetts Institute of Technology, recalls saying to himself when he first read the paper, “Wow, what a fantastic paper.” Numerous conferences and meetings have been convened to discuss this paper and its techniques.

Viazovska is proud of her native Ukraine, but is very saddened by the recent cataclysmic turn of events there. She explains, “[T]yrants cannot stop us from doing mathematics. There is at least something they cannot take away from us.” For additional background and details, see this Quanta article by Erica Klarreich, this NY Times article by Kenneth Chang and this New Scientist article by Matthew Sparkes.

**James Maynard**. James Maynard has always had an independent streak. When he was three years old, a health official came to his home to administer a standard battery of tests to measure his development. But Maynard thought the tests were stupid, so, for example, when given a shape-sorting task, he intentionally put the shapes in a different order, explaining why his solution was more interesting than the one expected.In 2013, Maynard, a fresh doctoral graduate of Oxford University, was working hard on a very difficult problem, namely to establish some bounds on the gaps between prime numbers. Unbeknown to Maynard, another mathematician, Yitang Zhang, had also worked on the problem, and published a result that there are infinitely many gaps of size at most 70,000,000. Maynard then proved a significant improvement, by a completely different approach, lowering the bound to 600. As it turns out, this result, which was a tour-de-force for a young mathematician, was also independently proved (by a different method) by the well-known Fields Medalist Terence Tao of UCLA. Tao graciously deferred announcing his result, so as to not eclipse Maynard’s result.

Undeterred, Maynard continued his work at the forefront number theory. His most notable recent work is a three-paper series (A, B and C) on the distribution of prime numbers.

Another startling result is his 2019 proof that there are infinitely many primes that do not have any 7s (or any other decimal digit) in their decimal expansion. While primes lacking some given digit are plentiful among small primes, they are extremely rare among primes say with 1,000 or more digits. The result is much easier for large number bases, so Maynard started with base 1,000,000, then reduced to 5,000 and then to 100. After being stuck at base 12 for some time, he was finally able, with more sophisticated methods, to reduce to base 10. He explained, “I was very happy to just about drag myself over the line and then declare victory.”

For additional details, see this Quanta article by Erica Klarreich, this NY Times article by Kenneth Chang and this New Scientist article by Matthew Sparkes.

**Hugo Duminil-Copin**. Hugo Duminil-Copin is known as a very energetic and enthusiastic mathematician. He is also quite athletic — he rides bicycles, swims and climbs mountains, and reports that often his best ideas come to him as he is engaging in one of these activities. While growing up, he says that mathematics was not his primary interest — his father was a gym teacher and his mother was a dancer before becoming an elementary school teacher. He enrolled in a Paris high school that focused on mathematics and science, but recalls that while he was reasonably good at mathematics, others were better.Ultimately Duminil-Copin gravitated to research at the interface of mathematics and physics, in particular analyzing fluids flowing through porous models, known as “percolation models.” They have application in epidemiology, social media and, recently, in analyses of forest fires. Jordana Cepelewicz describes his work in these terms:

To understand mathematical percolation, imagine an infinite grid of points connected by edges so that they form a checkerboard. For each possible edge, flip a weighted coin. If it lands on heads — which might happen with a probability of 1% or 20% or 80%, depending on how the coin is weighted — color the edge black. Otherwise, leave it alone. (In physical percolation, a black edge means the fluid can flow through that part of the system.) Mathematicians want to understand how clusters of connected black edges, called connected components, can materialize on the original lattice.

As you slowly raise the probability that any two points will be connected by a black edge, a phase transition occurs. That is, the overall behavior of the system changes abruptly, in much the same way that water freezes when the temperature dips below zero degrees Celsius. (In fact, “most systems actually undergo a phase transition,” Duminil-Copin said.) In this case, if you gradually increase the probability that the coin will land on heads, the system passes some critical value: Below that value, there is practically no chance that there will be an infinitely long connected component, and so our fluid will get stuck. Above it, there will be an infinite, continuous path through the system, and our fluid will flow.

For additional details, see this Quanta article by Jordana Cepelewicz, this NY Times article by Kenneth Chang and this New Scientist article by Matthew Sparkes.

**June Huh**. June Huh was born in California, but when he was two years old, his family moved to Seoul, South Korea. His father taught statistics, while his mother taught Russian literature. Huh recalls that school was “excruciating” — he had difficulty focusing in class, and avoided mathematics. But on his own he was an avid reader — in elementary school, he read all ten volumes of an encyclopedia on living things. When he was just 16 years old, he decided to drop out and write poetry, focusing on nature and his own experiences.Huh attended Seoul National University, but required six years to graduate. In his final year, he enrolled in a mathematics class on algebraic geometry and singularity theory taught by the Japanese Fields Medalist Heisuke Hironaka. Huh was transfixed. He applied to doctoral programs in the U.S., but because of his checkered undergraduate experience, most of these applications were rejected. But he was admitted to the University of Illinois, Urbana-Champaign. There he proved a conjecture in graph theory, known as Read’s conjecture that had been open for 40 years.

Read’s conjecture concerns polynomials that are connected to graphs. If one wishes to color the vertices of a graph so that no two adjacent vertices have the same color, the total number of possibilities can be calculated using what is known as the “chromatic polynomial.” Researchers had observed that the coefficients of chromatic polynomials are unimodal, meaning that they first increase and then decrease, and are also “log concave,” meaning that the square of the central number is always at least as large as the product of the coefficients on either side. His solution “stunned” the mathematics community; the University of Michigan, which had earlier rejected him, recruited him to their graduate program.

In another research effort, Huh and his collaborator Botong Wang, a mathematician at the University of Wisconsin, Madison resolved the Dowling-Wilson “top-heavy” conjecture. In a 2-dimensional plane, this says that the number of lines connecting a set of points must always be greater than the number of points (unless all points are collinear). In higher dimensions, the situation is more interesting. In 3-D space, for instance, a set of four noncollinear points is connected with six lines and four planes; five points are connected by 10 lines and 10 planes. Hugh and Wang proved the Dowling-Wilson conjecture, in particular that this pattern always holds, in a certain set of spaces with appropriate conditions.

When asked if he would ever return to being an artist and writing poetry, Huh shrugged, “Maybe. But I don’t know. … I’m very much into something else.” For additional details, see this Quanta article by Jordana Cepelewicz, this NY Times article by Kenneth Chang and this New Scientist article by Matthew Sparkes.

Congratulations again to the 2022 Fields Medalists!