Maryna Sergiivna Viazovska was born on 2 December 1984 in Kyiv, then part of the Ukrainian Soviet Socialist Republic. She is the oldest of three sisters. Her father worked as a chemist at the Antonov aircraft factory, and her mother was an engineer. She showed an early talent for mathematics, attended a selective school with strong science teaching, the Kyiv Natural Science Lyceum No. 145, and later studied at Taras Shevchenko National University of Kyiv, where she earned a bachelor’s degree in mathematics around 2005 and competed successfully in student olympiads.
She continued her training in Germany. In 2007 she received a master’s degree from the University of Kaiserslautern. She then completed doctoral work connected with the Institute of Mathematics of the National Academy of Sciences of Ukraine and, in 2013, a doctorate from the University of Bonn. Her Bonn thesis, Modular Functions and Special Cycles, was supervised by Don Zagier and Werner Müller. The subject of that thesis, modular forms—functions with a high degree of symmetry that arise in number theory—later became the technical key to her most famous result. After the doctorate she held research positions that included time at the University of Cologne, the Institut des Hautes Études Scientifiques, and the Berlin Mathematical School at Humboldt University.
The problem that made her name is centuries old in spirit, even if its higher-dimensional versions are modern. How densely can one pack equal spheres into space so that they do not overlap? In two dimensions the answer is the familiar hexagonal arrangement of circles. In three dimensions Johannes Kepler conjectured in 1611 that the pyramid stacking used for cannonballs and oranges is best. Thomas Hales proved that conjecture only in the late 1990s, with a long argument that relied heavily on computer assistance. Beyond three dimensions the problem is harder still, because intuition fails and the number of possible arrangements grows rapidly. Two lattices had long been suspected of being optimal: the E8 lattice in eight dimensions and the Leech lattice in twenty-four dimensions. Both are exceptionally symmetrical, and both appear in other parts of mathematics, but a proof that no denser packing exists had remained out of reach.
A promising approach came from work of Henry Cohn and Noam Elkies. They showed that if one could find certain “magic” functions—functions whose values and Fourier transforms satisfy strict sign conditions—then those functions would prove an upper bound on packing density. Matching that bound to the density of a known lattice would settle the problem. For years no one could construct the required functions in the dimensions that mattered. Viazovska kept returning to the question after earlier collaborations on related ideas had moved on. In 2016, while a postdoctoral researcher in Berlin, she found the missing function for eight dimensions. The construction drew on modular forms, the subject of her doctoral work, and produced a function with exactly the properties the Cohn–Elkies method demanded. The argument showed that no packing of equal spheres in eight-dimensional Euclidean space can be denser than the E8 lattice packing. The optimal density is Ï€⁴/384, a little over one quarter of the volume of space.
The eight-dimensional proof appeared quickly and was short by the standards of earlier sphere-packing arguments. Within about a week, Viazovska, Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko adapted the method to twenty-four dimensions and proved that the Leech lattice is optimal there. Radchenko later described that stretch of work as one of the most intense weeks of his life. The two papers transformed a problem that had looked intractable into a pair of completed theorems, and they did so with tools from number theory and Fourier analysis rather than exhaustive computer search.
Recognition followed at once. She received the Salem Prize in 2016, the Clay Research Award and the SASTRA Ramanujan Prize in 2017, the New Horizons in Mathematics Prize in 2018, the Fermat Prize and the Ruth Lyttle Satter Prize in 2019, and the European Mathematical Society Prize in 2020, among other honors. In late 2016 she accepted a tenure-track assistant professorship at the École Polytechnique Fédérale de Lausanne. She was promoted to full professor in 2018 and holds the Chair of Number Theory there. She is married to the physicist Daniil Evtushinsky and has two children.
In July 2022 the International Mathematical Union awarded her the Fields Medal, given every four years to mathematicians under forty. The citation recognized the proof that the E8 lattice gives the densest packing of identical spheres in eight dimensions, together with further contributions to related extremal problems and interpolation problems in Fourier analysis. She was the second woman to receive the medal, after Maryam Mirzakhani in 2014, and the first recipient to have earned a degree from a Ukrainian university. The award came months after Russia’s full-scale invasion of Ukraine. The International Congress of Mathematicians, planned for Saint Petersburg, was moved online, and the medal ceremony was held in Helsinki. Viazovska has spoken of the difficulty of celebrating a personal honor while her home country was at war, and she has used the attention that followed to speak about Ukrainian science and colleagues who remained in the country.
Her later work has continued in the same circle of ideas: optimal point configurations, Fourier interpolation, energy minimization, and the analytic properties of functions that control geometric bounds. The sphere-packing theorems are not mainly about stacking fruit. High-dimensional packings and related codes appear in digital communications, crystallography, and theoretical computer science, and the modular-form techniques she introduced have influenced other extremal problems. She has described herself as a theoretical mathematician and has been cautious about claiming immediate applications, while noting that the same symmetry and analysis that solved the packing problem keep generating new questions.
What stands out in accounts of the discovery is the combination of persistence and a change of tools. Many mathematicians had looked for the magic functions. Viazovska found them by importing a class of objects from number theory that did not, at first glance, belong to the geometry of packings. The resulting proofs are often praised for their clarity as well as their depth: once the right function is written down, the inequalities fall into place. In that sense the work is both a solution to a classical problem and an example of how a method from one field can close a question in another. At EPFL she continues to teach and supervise research in number theory, and the eight- and twenty-four-dimensional theorems remain the results for which she is best known.
CONCLUSION
Mathematician set an example for other mathematicians.