IMPA Tech students share their knowledge at FestMat
How can mathematics be used to surprise and delight an audience? And how does linguistics relate to the exact sciences? These questions were explored by IMPA Tech students on stage at the Wednesdays National Mathematics Festival, held at Axia Marina da Glória this Saturday (29). Organized by IMPA, this free event aims to bring mathematics closer to the general public and demystify the subject.
The extension project “Mate-maravilhando”, coordinated by IMPA professor and researcher Milton Jara, brought to the Festival stage presentations that demonstrate how advanced mathematical concepts can be transformed into experiences capable of surprising and delighting the audience. The students presented the activities “Monte Carlo Method,” “Baby Hummer Magic Trick,” and “Brachistochrone and Its Properties,” exploring interdisciplinary concepts in a playful way.
The audience was able to witness card tricks based on group action invariants, geometric drawings inspired by representation theory, and group dynamics based on principles of probability. The goal is to show that sophisticated mathematical concepts can also be presented in a visual, interactive, and accessible way.
The students’ experience at the Festival also revealed other ways to connect mathematics with different fields of knowledge. While in “Mate-maravilhando” mathematical concepts come to life through tricks, drawings, and experiments, in the Xenolinguistics Project this connection is evident in the very structure of language itself.
Paula Pires, a student at IMPA Tech, said she was delighted with the event’s concept. “I’d never attended a fair focused solely on math before. The experience is surreal—all the interactive activities and educational games bring math closer to people. Seeing my college classmates present their work makes me proud. IMPA Tech is one big family, so it’s like watching my siblings showcase their research—and that’s incredible!”
The Activity “Lenão’s Dialogue: A Story That Escaped the Comics” brought the Xenolinguistics Project to the festival stage. The project involves creating a hypothetical language with a syntax similar to that of human languages, as a way to develop tools for learning grammar.
As part of the IMPA Tech curriculum, the project is integrated into the “Linguistic Skills” course, taught by Professor Cilene Rodrigues, which approaches language as a cognitive and combinatorial system.
Pedro Henrique dos Santos, a teaching assistant for the course and a Ph.D. candidate in Linguistics at UFRJ, participated in the presentation alongside the undergraduate students. “It was really cool to bring the project to FestMat. Although I was a little nervous about speaking on stage, it was great to show that the boundaries of knowledge aren’t so rigid and that different fields are closely interconnected. By creating a new language, we were able to apply theoretical concepts in practice—while having fun—and fulfill the purpose of science, which is to produce knowledge,” he said.
Languages can also be understood in terms of mathematical structures. They operate with a few dozen basic elements, such as sounds and signals, which can be combined to form thousands of morphemes and, from these, a potentially infinite set of sentences.
Participation in the Festival also exposed the students to the challenge of communicating mathematics to different audiences. Through projects that combine creativity, interdisciplinary approaches, and scientific rigor, the undergraduates demonstrated that mathematical concepts can take on different forms and interact with fields such as magic, geometry, probability, and language.
Another highlight of the main stage was the presentation by IMPA Tech professor Asla Sá, a member of the Festival’s academic committee, on the topic Pop Math: Pop Mathematics. The researcher explored mathematical myths, infinity as an object of formal investigation, the probability of victory, a tie, and defeat in soccer games, mathematical language, and many other topics.
“There is a latent mathematical dimension to everyday practices: in economic and financial organization; in estimating times and trajectories; in game strategies; and so on. Pop Math is a language that engages with people to bridge these worlds a little, showing how we act mathematically in various real-world situations.”