15/10/2019

'Mathematics leads people to logical thinking,' says Ramos.

Cecilia Manzoni

From a young age, Vinicius Gripp B. Ramos possessed a characteristic that would guide his life: a desire to expand his knowledge. His morning school schedule left hours to be filled in the afternoon, which Vinicius used to deepen his mathematical understanding. He devoured textbooks from the library of the Colégio de Aplicação of the Federal University of Rio de Janeiro (CAP-UFRJ), without envisioning where this academic vigor would lead him. Interest was his only motivation.

At 30 years old, this Rio de Janeiro native joins the IMPA research group after a meteoric rise in his studies. His talent for the discipline was discovered in his teens by one of his teachers in high school.

Raised in Tijuca and Flamengo (Rio de Janeiro), Vinicius independently traveled around the city by bus as part of his studies. Noticing this ease and an insatiable interest in mathematics, Professor Ionilde, who occasionally participated in grading exams for UFRJ (Federal University of Rio de Janeiro), arranged for the student to be contacted by the university.

At the invitation of Felipe Acker, from the Applied Mathematics department at UFRJ, Vinicius began attending the analysis course at the federal university. "He talked to me and saw that I knew more math than was taught in high school and was a little demotivated by that," says Vinicius.

At the end of his undergraduate studies, he was invited to join the master's program at the age of 16. He accepted the challenge without hesitation and transferred to a private school while pursuing his master's degree at UFRJ. For bureaucratic purposes, he passed the entrance exam for a bachelor's degree in Mathematics, which he completed in record time: one year.

In three years, Vinicius completed high school, a master's degree, and a bachelor's degree in Mathematics. At 18, he packed his bags and moved to the United States to pursue a doctorate at the University of California, Berkeley. “I wanted to leave the country and research a different topic. I knew that many areas of Mathematics were still in their infancy in Brazil. And one advantage of American universities is that during a doctorate, it's possible to take many courses without going straight into research. I wanted to learn about as many subjects as possible before choosing a specific area,” he reveals.

On a personal level, the changes were also intense. Known for bringing together students from all over the world, Berkeley's environment changed Vinicius's perception of several countries. “I started to better understand the culture of places we hear little about in Brazil, and where we have a stereotypical view. When you start having Chinese, Indian, Korean, Thai friends, you begin to understand places differently.”

There, he adopted the bicycle as an ally. “Here, for me, the bicycle was for leisure. I would never have thought of using a bicycle to get around. And there I saw how it was a wonderful form of transportation,” says the Rio native, who every day climbs the long hills of Horto on his bicycle to get to IMPA.

After six years enjoying the open culture and fertile academic environment of the American West Coast, it was time to try something different once again. The old continent seemed like a good choice. “I wanted to live in Europe. I noticed that people researching the same topic were going to the University of Nantes (France) and I considered it a good option.”

Besides indulging in the cheeses, breads, and wines of the Brittany region, it was during his postdoctoral studies that Vinicius experienced his immersion in symplectic geometry. With historical roots in the geometric formulation of 19th-century classical mechanics, known as "Hamiltonian formalism," symplectic geometry has intimate relationships with diverse areas of mathematics, including contemporary topology, dynamics, and complex geometry; and mathematical physics.

One of his greatest desires is to explore the relationship between symplectic diving and billiards studies. And that is what he has dedicated himself to since arriving at IMPA, first for his postdoctoral research in 2015, and now as a researcher.

"What's interesting about this area is the many surprises. The results have profound meanings and often reveal something unexpected. It's common to study a problem without having any idea what the answer will be, which is rarer in many areas of mathematics. Sometimes you go all the way to the end of the calculations, and in the final moments you still don't know 'who's going to win the game.'"

Still in its infancy in Brazil, symplectic geometry has a community of fewer than 30 mathematicians in the country. For studies on symplectic embeddings, this number is considerably smaller. Naturally, Vinicius, whose project was awarded R$ 1 million by the Serrapilheira Institute's scientific research support program, views innovative mathematical research proposals favorably.

“In science, in general, it’s important to think outside the box. Of course, you can always repeat other studies, slightly changing the initial conditions, and arrive at new results that are already expected, and end up not being so relevant. The most relevant research is the unexpected or very difficult kind, in which you either propose a problem that hasn’t been addressed much, or you answer a problem that’s already been ‘tested’ with an unexpected solution.”

To do this, you need stamina. In Vinicius's view, one of the biggest challenges of his project stems from a basic premise: the fact that mathematics is "very difficult." Another is the need to make choices. "You can spend a lot of time thinking about one point and end up banging your head against the wall. At the beginning of the research, you don't know anything yet, it's difficult to map out the project and know if you have the time and the necessary techniques to answer the question. You need discernment to identify if you are trying something too difficult and won't succeed, to switch to simpler questions, with more certainty that you can conclude them, because, in the end, it's important to publish articles," he explains.

Vinicius has achieved several successes in his endeavor. Among his publications, he highlights an article published during his doctoral studies, with two collaborators, on asymptotic behavior in a set of abilities; and another more recent article, from 2017, where he used the relationship between billiards and symplectic geometry to prove new results in symplectic diving.

With his recent promotion to associate researcher at the institute in August, new responsibilities arose. This year, Vinicius is part of the organizing committee for the thematic semester in symplectic geometry, which aims to promote collaborations between national and international researchers in the field and encourage the training of master's and doctoral students.

"So far, the results are very positive. We've had several events, seminars, lectures, and other activities. There are many people studying symplectic geometry at other universities in Rio, such as UFRJ, UFF, and PUC, so we're trying to mobilize everyone to participate and organize events. It's important to keep the symplectic community in Rio cohesive."

For the mathematician, joining the scientific body of IMPA carries a gratifying feeling of giving back to Brazilian research. “My first steps in Mathematics were taken in Brazil, so it’s very good to be able to give back. Furthermore, IMPA is a great institution, with excellent working conditions. Everything works well, the infrastructure is high quality, and the students are great.”

Vinicius acknowledges the practical value of Applied Mathematics, which he considers "essential for the development of technology," but endorses the importance of Pure Mathematics for the advancement of humanity. "Logical mathematical thinking starts from the principle of truth. When you discover something in this area, you're talking about truths that won't be disproven in 50 or 100 years. The search for truth is something very noble," he adds.

In his view, mathematical thinking brings great benefits to the general population. “Mathematics leads people to logical thinking, something fundamental to any field, important even for sustaining a conversation. It saddens me to see how commonly mathematics is taught not as a tool for thinking and a way to stimulate the brain, but as a way to repeat procedures. What is the point of doing something that, nowadays, a computer does for you?”