From Village Dreamer to Fields Medalist

Years ago, as a young mathematics student at Tehran University, Caucher Birkar would often gaze at the photographs of the Fields Medal winners displayed on the wall of the university's math club. "I would look at them and think, 'Would I ever meet any of them?'," he said in an interview.

Today, Professor Birkar, the 2018 Fields Medal recipient, has not only met some of those legendary figures but joined their ranks, showing how far he has come from that quiet moment of wondering.

A new chapter

In 2021, he began a new chapter in Beijing, starting his full-time academic career at Tsinghua University.

The decision to move to China came quickly — just two months after receiving the formal invitation in 2019 — but it was rooted in long-standing connections. "Even before the offer, I had close academic ties with Tsinghua," Birkar explained. "Choosing to join (it) was natural. Tsinghua is an outstanding university, and Chinese mathematics is growing stronger every year."

Beyond academic excellence, he was also drawn by a desire for cultural exploration. "I wanted to experience a different way of life," he said. "China offers a rich history, diverse cultures, and vast geography. Every time I visit, I see more and learn more. I still have much to discover."

He sees strong parallels between Tsinghua and Cambridge. "As the top university in China, Tsinghua attracts the best students, just as Cambridge does in the UK," he said. "But what truly stands out is the support for researchers. The university provides excellent resources and infrastructure, allowing scholars to focus fully on their work without unnecessary distractions. That kind of environment is invaluable for deep, meaningful research."

Beauty of mathematics

Birkar's passion for mathematics began in elementary school in a small village in Iranian Kurdistan. Inspired by his older brother, who had a keen interest in science and technology, he started learning math at an early age. "At first, I followed his lead," he said. "Then I began reading math books on my own. The more I learned, the more I realized how fascinating and full of mystery mathematics truly is." For him, math is a source of deep personal joy: "Some people love sports or music. For me, solving problems and exploring ideas in math brings real happiness."

He says the value of mathematics operates on two levels. On a personal level, it's about passion and meaning. "If you love what you do, it gives your life purpose and fulfillment. That inner drive is essential for success in any field, especially mathematics." Also, math is foundational on a social level. It underpins nearly every modern scientific and technological advance, from physics and engineering to economics and medicine. The more humanity progresses, the more it relies on mathematical insight.

Of course, the path of a mathematician is not without challenges. "You face problems you can't solve, ideas that don't work, and sometimes even lack of funding," Birkar admitted. "You have to learn to deal with failure and keep going."

To explain his work in birational geometry, a field central to algebraic geometry, he uses a simple analogy: "Think of polynomial equations, like the ones you learn in high school. We don't just look for solutions. We study the space of all possible solutions. Just as you might classify people by age, gender, or income, we classify geometric spaces using certain mathematical parameters. My work helped develop tools to organize and understand these spaces systematically, leading to breakthroughs in classification and structure."

To advance human knowledge

Winning the Fields Medal, recognized as the highest honor in mathematics, has changed Birkar's life in profound ways. The award opened doors. However, he views it as a platform to contribute more deeply to the mathematical community. While it has increased his visibility and responsibilities, he remains focused on research, mentorship, and fostering a culture of curiosity.

He firmly believes that becoming a mathematician is not reserved for the "genius" few. Creativity, hard work, patience, and courage are far more important than innate talent. A deep love for the subject, combined with persistence, is what enables progress. Anyone who earns a degree or completes a PhD in mathematics, he argues, has already demonstrated the capacity to contribute meaningfully. The goal, he insists, is not to be the best in the world, but to grow, understand, and advance human knowledge.

Looking at China's mathematical future, Birkar is optimistic. The country possesses vast intellectual talent and increasing financial resources, creating ideal conditions for scientific advancement. With a long tradition of scholarship and a growing commitment to research, Chinese mathematics has made remarkable progress in recent decades. Interdisciplinary work in areas like cryptography, computer science, and theoretical physics is already underway, and Birkar sees even greater potential ahead.

This is an edited version of the original Chinese article by GUO Lili and ZHAN Meng from Tsinghua University.

Source: Science and Technology Daily