In 1611, the German astronomer Johannes Kepler wondered how to best stack bullets, like oranges in a greengrocer or bullets in a cannon, so that they take up as little space as possible. The scientist, famous for his description of the movement of the planets around the Sun, suggested that the ideal is the formation of a pyramid, but his hypothesis was not proven until 1998. Ukrainian mathematician Maryna Viazovska, who was 31 at the time, went beyond space to three dimensions in 2016, solving the problem in eight and 24 dimensions. This Tuesday, Viazovska won the Fields Medal, one of the most prestigious awards in mathematics, along with three other brilliant colleagues: British James Maynard, French Hugo Duminil-Copin and American June Huh.

The Fields Medals are awarded every four years at the International Congress of Mathematicians. This year it was supposed to be held in the Russian city of Saint Petersburg, but the organizer, the International Mathematical Union, decided to move the headquarters to Helsinki (Finland) as punishment for the invasion of Ukraine by Vladimir Putin’s army. Ukrainian Maryna Viazovska, born 37 years ago in Kyiv, was already a favorite in the previous edition in 2018, but her recognition this year takes on a new dimension, beating the Russian authorities who were barred from Congress became. The winner received a moving ovation.

The Ukrainian researcher, a professor at the Federal Polytechnic School in Lausanne (Switzerland), has commemorated in a video her young compatriot Julia Zdanowska, a 21-year-old mathematician who was killed in a Russian missile attack in the city of Kharkiv at the beginning of the war. “My life changed in February,” lamented Viazovska, whose parents and sisters usually live in Kyiv.

Still from a video showing mathematician Maryna Viazovska stacking oranges at the Swiss Federal Polytechnic School in Lausanne, Switzerland FRED MERZ / EPFL

Spanish mathematician Eva Miranda emphasizes that Viazovska is the second woman to win a Fields Medal since these awards were introduced in 1936, after Iranian mathematician Maryam Mirzajani, who won it in 2014. Around 60 men have won the award during this time. The medal is awarded every four years to one or more mathematicians under the age of 40. “This prize brings a breath of fresh air to all of us and is a recognition for all female mathematicians. Maryna Viazovska does not climb the podium alone,” praises Miranda, professor at the Polytechnic University of Catalonia.

The sphere packing problem isn’t just a hobby for greengrocers, it’s also essential in disciplines like crystallography and big data processing, Miranda explains. His colleague Pablo Hidalgo from the Institute of Mathematical Sciences (ICMAT) has explained in detail that this math for stacking oranges beyond three dimensions is used to correct codes. “If we treat each message of (at most) 20 bits in length as the vertex of a 20-dimensional cube, we can use the good packing of spheres in dimension 20 to correct erroneous messages,” Hidalgo explained in the newspaper two months ago. “If we receive a message that doesn’t fit into our list of allowed messages – either because it doesn’t make sense or because we have a predefined list of messages that we think are allowed – it could mean that an error has occurred in the communication channel and in such a case it would be nice to be able to correct it,” he stressed.

This prize is a recognition for all women mathematicians

Eva Miranda, mathematician

The other three Fields Medal winners are also luminaries in their disciplines. The Brit James Maynard, from the University of Oxford, has shed light on the distribution of prime numbers divisible only by one and by itself: 2, 3, 5, 7, 11, 13, 17… When two consecutive prime numbers are separated by two units, like 5 and 7, are called twin primes. The twin prime conjecture states that there are infinitely many pairs of these numbers. Maynard, who was born 35 years ago in Chelmsford, England, and other colleagues have shown that there are infinitely many pairs of prime numbers that are less than 246 units apart.

Frenchman Hugo Duminil-Copin of the University of Geneva, Switzerland, has received the Fields Medal for his work in statistical physics, a branch that uses mathematical tools to solve physical problems. Duminil-Copin, born near Paris 36 years ago, has focused on so-called phase changes, i.e. transitions in complex systems, such as the melting of ice into liquid water. “What we mathematicians do is understand how these phase changes occur, through mathematical caricatures of the physical phenomenon,” the Frenchman explained to the University of Cambridge’s Plus Magazine.

Eva Miranda compares Duminil-Copin to a goldsmith. “His job is to find properties of a huge system by analyzing the interactions between its small components. His theory is related to the theory of percolation: how a liquid flows through a porous medium,” explains the Spanish researcher.

Researcher June Huh from Princeton University (USA) does not fit the stereotype of mathematical genius. As a teenager, he was bored and preferred poetry. Today, Huh, who was born in Stanford 39 years ago, is a reference in combinatorics, the branch that makes it possible, for example, to calculate how many ways there are to order a deck of cards. The complexity of his work is devilish, as Javier Aramayona, also of ICMAT, suggests: “June Huh found an unexpected bridge between two areas of mathematics that were a priori quite distant from each other, applying techniques of algebraic geometry to solve problems to solve in the combinatorics that existed remained open for decades.”

The Fields Medals compete with the Abel Prize, awarded by the Norwegian Academy of Sciences and considered the equivalent of a Nobel Prize in mathematics. The Abel is annual, has no age limit and is accompanied at around €775,000 compared to just €11,000 for the Fields Medal. American mathematician Karen Uhlenbeck, 2019 laureate, is the only woman to have won the Abel Prize against 24 men. In a 1997 book, Cleveland-born Uhlenbeck, born 79 years ago, describes the difficulties young mathematicians have historically encountered: “I’ve been told that nobody hires women because women should be at home and let you drink.”

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