“The Math Olympics led me to IMPA,” says Artur Avila

19/08/2024

IMPA researcher extraordinaire and professor at the University of Zurich, Artur Avila, welcomed IMPA Tech students to kick off the academic activities of the second term of the degree in Mathematics of Technology and Innovation. On Monday (19), in the auditorium of the Port Maravalley, the Fields Medal winner showed how students can begin to interact with mathematics at a more advanced level, based on personal and academic events in his career, such as his experiences at the Mathematical Olympiads and his master’s and doctorate at IMPA.

At a young age, Avila went to the institute for the first time to receive a bronze medal from the OBM (Brazilian Math Olympics). The visit opened the door to a future career in mathematics. “The mathematical olympiads, just as they brought many of you here, brought me to IMPA,” he said.

The researcher also spoke about the evolution of the discipline over the years and how the notion of what it means to do mathematics is changing. “The mathematics of the 17th century is still useful. It’s been built up since the beginning. The Greeks already used mathematics and these fundamentals are still applied today from elementary school onwards,” he added.

Marcelo Viana, director-general of IMPA, took part in the meeting and explained to the students the importance of the Fields medal for Brazilian mathematics. Viana was Avila’s teacher during his master’s degree and the two share the same area of research, dynamic systems.

“When I did my master’s, I tried to learn a bit of everything and, little by little, I noticed small differences in understanding and affinity with the disciplines. Dynamical systems is an area that intersects many things and includes notions of fractal objects. It was an opportunity that attracted me,” said Ávila.

The researcher encouraged undergraduate students, who are still starting out on the path to advanced mathematics. “Don’t be afraid to make mistakes. Your ideas will almost always fail, with exceptions. All the stages of failure will build the final understanding of a piece of research. With dedication, things get better. Not just the mathematical tools, but also the psychological preparation.”

Alongside Avila, Viana reinforced the social value of mathematics, from the pleasure that Olympiad students feel in developing challenges, to the application of mathematics in the economy, medicine, among other benefits.

Avila added the importance of collaborative work and the need to spread mathematical knowledge. “I have a vision of how science ideally works, which involves wanting to solve questions to solve useful problems, be they technological, biological, etc. Mathematics can be used for many things. Mathematical knowledge doesn’t remain isolated where it was discovered, it spreads.”

Taina Queiroz, an undergraduate student, found the meeting motivating and was excited about the start of her second term classes. “Seeing someone of Avila’s stature, a graduate of IMPA, gives us a very good insight into IMPA Tech. We are graduating from an institution that trained a Fields medal winner,” she said.

At the end of the chat, the researcher answered questions from undergraduates and gave tips to future professionals. “Don’t point directly at the most difficult problem. I recommend working laterally on more interesting issues, because it’s through a more general analysis that ideas and possibilities emerge to apply to central issues,” concluded Avila.

Suelen Luiz, who is also a Mathematics of Technology and Innovation student, also left the meeting motivated. “It’s great to see Artur’s example. Even after all this time, he’s still passionate about the research area and manages to pass this on to us,” she said.

Read more: Marcelo Viana debates innovation and technology at Rio Innovation Week
See also: IMPA Tech student approved at 8 universities in 4 Brazilian states