In Ukraine, Mathematics Offers Strength in Numbers

On a Saturday evening in August, two Ukrainian mathematicians, Maryna Viazovska and Masha Vlasenko, set out on a 19-hour train trip from Warsaw to Kyiv. They were en route to a conference titled “Numbers in the Universe: Recent Advances in Number Theory and Its Applications.” Symbolically, the journey served to plant a flag.

The event marked the opening of the International Center for Mathematics in Ukraine, or I.C.M.U., which was established on paper in November. “The goal is to bring the world of mathematics to Ukraine and open, or reopen, Ukrainian science for the world,” said Dr. Viazovska, of the Swiss Federal Institute of Technology in Lausanne. She won a Fields Medal in 2022 and serves as scientific lead on the center’s coordination committee.

“Making this investment is of course meaningful from a strictly scientific point of view,” said Jean-Pierre Bourguignon, the chair of the center’s supervisory board and a former president of the European Research Council, “but also in terms of how Ukraine can redevelop after the end of the war in a way which is meaningful economically. Highly trained mathematical people are going to be a key factor.”

The center’s first major donor, XTX Markets, an algorithmic trading company in London, promised to match funds raised up to one million euros for a year. So far, the French government has contributed 200,000 euros.

The center’s inaugural conference drew 75 participants at the Kyiv School of Economics, a venue chosen for its bomb shelter, which was suitable for lectures and equipped with whiteboards, backup power and internet. (The search is on for a permanent home in the city.) Simultaneously, via live video, the conference proceeded in Warsaw, at the Stefan Banach International Mathematical Center, where 110 participants attended. The parallel locations were necessary since martial law prevented adult Ukrainian men ages 18 to 60 from traveling outside the country, and the organizers were hesitant to invite foreign participants into a war zone.

No Such Place Until Now

Dr. Vlasenko, from the Institute of Mathematics of the Polish Academy of Sciences in Warsaw and a member of the I.C.M.U. coordination committee, had long dreamed of creating a mathematics research institute in Ukraine. The catalyst was the war, she said, coupled with Dr. Viazovska’s Fields Medal. On the way to the conference — while waiting for a midnight connecting train at the station in Chelm, Poland — the two scholars had coffee with a few more conference-bound mathematicians and discussed growing up in Ukraine studying mathematics.

“The generations change, but they have the same feeling,” Dr. Vlasenko said. There is a deep tradition of science and math in the country, but in the last several decades, in part due to underfunding, there has been a massive brain drain, she said, as students and researchers feel they must go elsewhere to advance.

Masha Vlasenko, originally from Kyiv, is a professor at the Institute of Mathematics of the Polish Academy of Sciences.Credit…Brendan Hoffman for The New York Times

Dr. Viazovska, who is originally from Kyiv, attended the Technical University of Kaiserslautern in Germany for her master’s studies. “I was very young, and it felt like an adventure,” she said. “I had the idea I will go there, I will study, and then I will come back. I didn’t realize that it was very difficult to come back.” She went on to do her Ph.D. at the University of Bonn in Germany.

Dr. Vlasenko, who is also from Kyiv, received her Ph.D. from the Institute of Mathematics of the National Academy of Sciences of Ukraine and then was a postdoc at the Max Planck Institute for Mathematics in Bonn. When she first saw the library there, “it turned my world upside down,” she said. “There is no such place in Ukraine.” She added, “There is no such place until now.”

About three-quarters of the conference participants were students and young mathematicians, and a series of multilecture courses and problem-solving sessions was directed at them. In Kyiv, Dr. Viazovska delivered four lectures on sphere packing. From Warsaw, Terence Tao, of the University of California, Los Angeles, and a 2006 Fields medalist, taught a course on prime numbers and related topics.

“It was a surprisingly pleasant and normal mathematics conference,” Dr. Tao noted in an email afterward. The focus was not the war but the mathematics, he said, and the two sites shared lighthearted banter: “‘Kyiv, do you have any questions?’ No, Kyiv understood everything. ‘Warsaw, do you have any questions?’”

Yulia’s Dream

The conference’s youngest participants were two students from Yulia’s Dream, a new online enrichment program for Ukrainian high schoolers who excel in math.

The program is named in memory of Yulia Zdanovska, a talented mathematician and computer scientist, and a teacher with Teach for Ukraine, who was killed in March 2022 at the age of 21 during Russian shelling in her home city of Kharkiv. Yulia’s Dream is organized through the mathematics department at the Massachusetts Institute of Technology, as an offshoot of a similar program for American students, the Program for Research in Mathematics, Engineering and Science for High School Students, or PRIMES.

The goal is to expose students to the world community of research mathematics by, for instance, connecting them with early-career mentors in the United States and Europe. “Mathematics is often misunderstood as a solitary endeavor,” said Slava Gerovitch, a historian of science at M.I.T. and the director and a co-founder of PRIMES. “One cannot be a successful mathematician without being integrated into these international networks for the exchange of knowledge.”

Attendees of the “Numbers in the Universe” conference on Aug. 10.Credit…Brendan Hoffman for The New York Times

From 260 applicants to Yulia’s Dream last year, 48 students were selected. They worked in small groups on reading studies; some did nine-month group research projects and wrote papers for submission to math journals.

“Now I understand better what real mathematicians do,” said Maryna Spektrova, 15, of Kharkiv. Ms. Spektrova, who was a spare for the Ukrainian team at the International Mathematical Olympiad this year, observed that while such contests entail solving a problem in hours, research problems can take months or years.

Ivan Balashov, 16, from Dnipro, found that during the war, opportunities like the olympiad and Yulia’s Dream were important for a student’s sense of achievement and confidence. “Self-realization is one of the main concepts which makes the person freer,” he said in an email. “After all, it is what we are fighting for — freedom.”

Yehor Avdieiev, 18, said that the program helped him cope. Finishing a long, hard problem was “the best feeling in the world,” Mr. Avdieiev said last fall from his apartment in Berlin. (He noted that math had long been a passion of his; at age 4, he liked to add license plate numbers.)

As the war began, he was making plans to attend V.N. Karazin Kharkiv National University, which suffered extensive damage from Russian missiles in March 2022. “All my plans were ruined,” he said. He relocated on his own to continue his mathematical education; that he might be required to serve in the military was also a factor in the decision. This year he is at the University of Bonn and studying remotely at Karazin University, pursuing two mathematics degrees.

Dmytro Antonovych, 18, of Chernivtsi, is now at Minerva University in San Francisco, where he intends to study mathematics and data science. He attended the meetings on Zoom, at least twice weekly, from his dorm room at Ipswich School in the U.K. Mr. Antonovych found the program meaningful, he said, because “it gave me a vision of how I could use my knowledge in mathematics.” And he appreciated the advice on how to succeed in mathematical research provided by Pavel Etingof, a mathematician at M.I.T. and the chief research adviser and a co-founder of PRIMES. One of the tips Mr. Antonovych especially liked: “Listen to your heart. As in all important things in life, what you want and what you dream about is the most essential.”

‘An Opera House for Math’

Dr. Viazovska discussed the sphere packing constant during her lecture.Credit…Brendan Hoffman for The New York Times

On Wednesday afternoon in Kyiv, the conference began in a fifth-floor lecture room with a view of the city. During a special session dedicated to the opening of the center, an air-raid alert sent the attendees, including several dignitaries, into the basement bomb shelter. A City Council member in attendance arranged a meeting the following day with the mayor, Vitali Klitschko, a former world boxing champion with a Ph.D. in sports science. Mr. Klitschko pledged his support for the project.

“He said that his mission is to make Kyiv so beautiful that people come back, because many people have left during the war,” said Dr. Vlasenko, who attended the meeting along with a group representing the center. She had described the center to the mayor as “an opera house for math.”

The conference atmosphere was “total excitement,” Dr. Vlasenko recalled. “One could feel it.” Every talk prompted so many questions afterward — “we let all questions go until there were no more questions,” she said — that every day the schedule ran two hours over. Even the problem-solving sessions went late, fueled by the energy of the students.

“It was very inspiring to see how first-year bachelor students are solving problems in advanced topics in mathematics,” said Olha Kharchenko, 23, who is in the second year of a master’s program at the University of Duisburg-Essen in Germany. The conference was her first time back in Ukraine since the war started.

Most of Ms. Kharchenko’s family is still in the Russian-occupied city of Kakhovka, where a major dam was destroyed in June. She already had hopes of returning to Ukraine for her career; the new center makes it feel feasible. Eventually, postdoctoral and long-term visiting positions would allow Ukrainian mathematicians like her to split their time between the I.C.M.U. and other institutions.

During the conference, Ms. Kharchenko also began thinking about returning sooner rather than later, before starting her Ph.D. She felt an urgency “to be present in Kyiv,” she said, “to understand what is happening there and to make my small impact to the education in Ukraine.” Maybe she would teach undergraduate students or children — things were changing in the country so fast, she said, it was difficult to foresee what the situation would be a year or so from now.

“It’s just my plan,” Ms. Kharchenko said. “I don’t know what will be there.”

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