Maryna Viazovska

Maryna Viazovska
Viazovska in 2013 at Oberwolfach
Maryna Viazovska
Born	Maryna Sergiivna Viazovska 2 12, 1984
Birthplace	Kyiv, Ukrainian SSR, Soviet Union
Nationality	Ukrainian
Occupation	Mathematician
Title	Full Professor and Chair of Number Theory
Employer	École Polytechnique Fédérale de Lausanne (EPFL)
Known for	Sphere packing in dimensions 8 and 24
Education	PhD in Mathematics
Awards	Fields Medal (2022), Clay Research Award (2017), Salem Prize (2016)
Website	[https://people.epfl.ch/maryna.viazovska Official site]

Maryna Sergiivna Viazovska (Template:Lang-uk; born 2 December 1984) is a Ukrainian mathematician whose work on the sphere-packing problem in higher dimensions brought her international recognition and some of the most distinguished honors in the field of mathematics. In 2016, she proved that the E8 lattice provides the densest packing of spheres in eight-dimensional space, a result that had eluded mathematicians for decades. Shortly thereafter, working with a team of collaborators, she extended this result to prove that the Leech lattice achieves the densest sphere packing in 24 dimensions. These breakthroughs resolved longstanding open problems at the intersection of number theory, harmonic analysis, and geometry. In July 2022, Viazovska was awarded the Fields Medal, becoming the second woman in the 86-year history of the prize to receive the honor. She holds the position of Full Professor and Chair of Number Theory at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland. In 2025, she was elected as an international member of the United States National Academy of Sciences.

Early Life

Maryna Sergiivna Viazovska was born on 2 December 1984 in Kyiv, then part of the Ukrainian Soviet Socialist Republic within the Soviet Union. She grew up in Ukraine during a period of significant political and economic transformation following the dissolution of the Soviet Union in 1991. Viazovska demonstrated mathematical aptitude from a young age and became involved in mathematical competitions during her school years.

As a university student, Viazovska participated in the International Mathematics Competition for University Students (IMC), where she achieved notable results over several consecutive years. In 2002, she competed in the IMC and earned recognition among the top participants. She continued her participation in 2003, 2004, and 2005, building a strong record in international mathematical competition.

Education

Viazovska received her undergraduate education in Ukraine. She subsequently pursued doctoral studies in mathematics in Germany and completed her PhD dissertation. Her doctoral research focused on topics in number theory and modular forms, areas that would later prove foundational to her groundbreaking work on sphere packing. She developed expertise in the theory of automorphic forms and their applications to problems in discrete geometry and optimization, a combination of mathematical fields that positioned her to make significant contributions.

Career

Early Academic Career

Following the completion of her doctoral studies, Viazovska held research positions in Europe, building her expertise in number theory and related areas of mathematics. Her research focused on modular forms, spherical designs, and optimization problems, and she developed a growing reputation within the mathematical community for her technical skill and originality. In 2013, she received the Vasil A. Popov Prize, which is awarded for distinguished contributions to approximation theory.

Sphere Packing Breakthrough

The sphere-packing problem — the question of how to arrange identical spheres to fill as much space as possible — is one of the oldest and most fundamental problems in mathematics and geometry. The problem was first posed in three dimensions by Johannes Kepler in 1611, when he conjectured that the familiar pyramid arrangement used to stack cannonballs and oranges is the most efficient packing possible. This conjecture was not proven until 1998, when Thomas Hales produced a lengthy computer-assisted proof. In higher dimensions, however, the problem remained largely open.

In March 2016, Viazovska posted a preprint proving that the E8 lattice provides the densest packing of spheres in eight-dimensional space. The E8 lattice packing fills approximately 25.37 percent of eight-dimensional space. While mathematicians had long suspected that E8 was the optimal packing in eight dimensions, no one had been able to prove it. Viazovska's proof was celebrated for its elegance and relative conciseness — in contrast to the Hales proof in three dimensions, which had required extensive computation and ran to hundreds of pages, her argument was comparatively short and relied on the construction of a special auxiliary function using modular forms.

The key insight of Viazovska's proof involved constructing a "magic function" — a radial function whose properties, when combined with techniques from linear programming bounds developed by Henry Cohn and Noam Elkies, could be used to establish the optimality of the E8 packing. The challenge of finding such a function had been recognized by experts for years, and Viazovska's identification and construction of this function represented the critical step that previous researchers had been unable to achieve.

Within a week of her initial result, Viazovska collaborated with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko to extend the method and prove that the Leech lattice gives the densest sphere packing in 24 dimensions. The Leech lattice packing fills approximately 0.19 percent of 24-dimensional space — a figure that, while seemingly small, represents the optimal density achievable in that dimension. The speed with which the 24-dimensional result followed the 8-dimensional proof reflected the power and flexibility of Viazovska's approach; once the method for constructing the magic function was established, it could be adapted to the 24-dimensional case relatively quickly.

The sphere-packing results were covered extensively in the scientific and popular press. Writing for Forbes, Kevin Knudson explained the significance of the result in terms accessible to a general audience, describing the problem of "stacking cannonballs in 8 dimensions." The German newspaper Die Zeit also covered the work. Frank Morgan, writing for the Huffington Post, discussed the mathematical significance of sphere packing in higher dimensions.

The importance of dimensions 8 and 24 in mathematics extends well beyond the sphere-packing problem. These dimensions are connected to deep structures in algebra, number theory, and mathematical physics. The E8 lattice and the Leech lattice are exceptional algebraic objects with symmetries that appear in diverse areas of mathematics, and Viazovska's proofs reinforced the special status of these structures.

Professorship at EPFL

Viazovska joined the faculty of the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland, where she was subsequently promoted to the rank of Full Professor. She holds the Chair of Number Theory at the Institute of Mathematics. At EPFL, she has continued her research on topics at the intersection of number theory, harmonic analysis, and discrete geometry.

In May 2025, Viazovska delivered a three-day lecture series as part of the Simons Lecture Series at the Massachusetts Institute of Technology, presenting her work on sphere packing. Her lectures, titled to reflect the journey "from cannonballs to magic functions," traced the historical development of the sphere-packing problem from Kepler's conjecture through to her own results in dimensions 8 and 24.

Contributions to the Broader Mathematical Community

Viazovska's work has had a catalyzing effect on research in sphere packing and related optimization problems. Her methods, particularly the construction of auxiliary functions using modular forms, opened new avenues for research in discrete geometry and analytic number theory. The technique of using linear programming bounds, combined with appropriately constructed functions, has been further developed by other mathematicians building on her approach.

Beyond her technical contributions, Viazovska's achievements have drawn attention to the contributions of Ukrainian mathematicians and women in mathematics more broadly. As the second woman to receive the Fields Medal — following Maryam Mirzakhani, who received the award in 2014 — her recognition has been noted in discussions about representation in mathematics at the highest levels.

Personal Life

Viazovska was born and raised in Kyiv, Ukraine. She has maintained connections to her country of origin throughout her career, and her Ukrainian identity has been noted prominently in coverage of her achievements, particularly following the Russian invasion of Ukraine in 2022. She resides in Switzerland, where she works at EPFL. In a 2022 interview with Nature, she described mathematics as "an unknown land," reflecting on the process of mathematical discovery and the experience of working on problems whose solutions are not guaranteed.

Recognition

Viazovska has received numerous awards and honors for her mathematical work. In 2013, she was awarded the Vasil A. Popov Prize for her contributions to approximation theory.

In 2016, she was awarded the Salem Prize by the Société Mathématique de France for her work on sphere packing and harmonic analysis.

In 2017, she received the Clay Research Award from the Clay Mathematics Institute, one of the most prominent awards in mathematics, in recognition of her solution to the sphere-packing problem in dimensions 8 and 24.

Also in 2017, Viazovska was awarded the SASTRA Ramanujan Prize, which is given annually to young mathematicians for outstanding contributions to areas of mathematics influenced by Srinivasa Ramanujan.

In 2020, she received the New Horizons in Mathematics Prize, part of the Breakthrough Prize family of awards.

In July 2022, Viazovska was awarded the Fields Medal at the International Congress of Mathematicians. She became the second woman in the history of the prize to receive this honor, after Maryam Mirzakhani in 2014. The Fields Medal, often described as the Nobel Prize of mathematics, is awarded every four years to mathematicians under the age of 40 for outstanding mathematical achievements. Nature profiled her on the occasion of the award, describing her mathematical contributions and their significance.

In the same year, Time magazine named Viazovska to its TIME100 Next list, which highlights emerging leaders across various fields.

In May 2025, Viazovska was elected as an international member of the United States National Academy of Sciences, one of the highest honors for scientists. She was among two Ukrainians elected that year, the other being climate scientist Svitlana Krakovska.

Legacy

Viazovska's solution to the sphere-packing problem in dimensions 8 and 24 is considered one of the major mathematical achievements of the 21st century. The problem of sphere packing has a history stretching back more than 400 years to Kepler's conjecture, and while the three-dimensional case required a massive computer-assisted proof, Viazovska's approach in higher dimensions was noted for its mathematical elegance and the way it drew together ideas from number theory, harmonic analysis, and optimization.

Her work demonstrated the power of modular forms as tools for solving problems in discrete geometry, reinforcing deep connections between seemingly disparate branches of mathematics. The "magic functions" she constructed have become objects of study in their own right, and her methods have inspired further research into optimal configurations in various dimensions and related extremal problems.

As the second woman to receive the Fields Medal, Viazovska's recognition has served as a landmark in the representation of women in mathematics. Her achievement, coming eight years after Maryam Mirzakhani's Fields Medal and following Mirzakhani's death in 2017, was noted by commentators as evidence that the highest levels of mathematical achievement are not limited by gender, even as significant disparities in representation persist in the mathematical sciences.

Viazovska's Ukrainian heritage has also been a prominent element of her public profile, particularly given the timing of her Fields Medal award in 2022, during the Russian invasion of Ukraine. Her achievements have been a source of recognition for the Ukrainian scientific and mathematical tradition, and her election to the National Academy of Sciences in 2025 further cemented her international standing.

Her ongoing work at EPFL, combined with her public lectures such as the 2025 Simons Lecture Series at MIT, continues to shape the direction of research in number theory and discrete geometry. Through both her published results and her role as a leading figure in contemporary mathematics, Viazovska has established a body of work whose influence extends across multiple mathematical disciplines.