Ukraine's Maryna Viazovska paid tribute to those suffering in her war-torn country on Tuesday as she became the second woman to be awarded the Fields medal, known as the Nobel prize for mathematics.
Viazovska, a 37-year-old Kyiv-born math professor, received the prestigious award alongside three other winners at a ceremony in Helsinki.
"My life changed forever" when Moscow invaded Ukraine in February, she said in a video displayed at the ceremony, adding that her sisters had been evacuated from Kyiv.
"Right now Ukrainians are really paying the highest price for our beliefs and our freedom," she said.
The International Congress of Mathematicians, where the prize is awarded, was initially scheduled to be held in Russia's second city Saint Petersburg -- and opened by President Vladimir Putin.
Earlier in the year hundreds of mathematicians signed an open letter protesting the choice of the host city, and after Moscow invaded Ukraine in late February the event was moved to the Finnish capital.
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The other Fields winners were France's Hugo Duminil-Copin of the University of Geneva, Britain's James Maynard of Oxford University and June Huh of Princeton in the United States.
The medal, along with $15,000 Canadian dollars ($11,600), is awarded every four years to between two to four candidates under the age of 40 for "outstanding mathematical achievement".
'Tour de force'
Viazovska was born in 1984 in Ukraine, then still part of the Soviet Union, and has been a professor at the Ecole Polytechnique Federale de Lausanne in Switzerland since 2017.
At the ceremony she paid tribute to Yulia Zdanovska, a young mathematician who studied under the same teachers she had in Kyiv, who was killed by a Russian missile attack on the Ukrainian city of Kharkiv in March.
"Yulia was a person filled with light, and her big dream was teaching mathematics to kids in Ukraine," Viazovska said.
"When someone like her dies, it's like the future dies."
In a decision made before the war in Ukraine began, Viazovska was awarded for her work in sphere packing -- a problem first posed by German astronomer and mathematician Johannes Kepler nearly 400 years ago.
In what is called the Kepler conjecture, he proposed that the most compact way to pack spheres was in a pyramid, like oranges at a supermarket.
But it was such a complex problem that it was not considered proved correct until 1998 via intense computer number-crunching.
Then in 2016, Viazovska solved the problem in the eighth dimension, using what is called an E8 lattice.
Marcus du Sautoy, a British mathematics professor at Oxford University, told AFP it was a surprise when Viazovska came up with such "slick proof" compared to the "tortuous proof needed in three dimensions".
Renaud Coulangeon of Bordeaux University told AFP the solution was a "tour de force".
The only previous female laureate in the prize's more than 80-year history was Iranian mathematician Maryam Mirzakhani, who died of breast cancer in 2017 just three years after winning the award.
Du Sautoy said he hopes Viazovska's win "will contribute to inspiring more women to choose mathematics as a career."
'Express the inexpressible'
Duminil-Copin, born in France in 1985, is a professor at the Institut des Hautes Etudes Scientifiques, focusing on the mathematical branch of statistical physics.
He was honoured for solving "long-standing problems in the probabilistic theory of phase transitions", which, according to the jury, has opened up several new research directions.
Maynard, 35, received the medal "for contributions to analytic number theory, which have led to major advances in the understanding in the structure of prime numbers," Kenig said.
"His work is highly ingenious, often leading to surprising breakthroughs on important problems that seemed to be inaccessible by current techniques," the International Mathematical Union said in a statement.
June Huh, 39, was given the award for "transforming" the field of geometric combinatorics, "using methods of Hodge theory, tropical geometry and singularity theory", the jury said.
He is a rare Fields winner who did not focus on mathematics in his teen years, after a bad elementary school test score convinced him he didn't have a talent for it, he told Quanta Magazine.
"When I was young, math was like a faraway land, surrounded by giant walls that I could not climb," Huh said in his video.
"I grew up in Korea and I dreamed of becoming a poet, to express the inexpressible. I eventually learned that mathematics is a way of doing that."