04/04/2023

'Mathematics is a big train,' says João Pereira.

It was at the age of 13, during the 7th grade of elementary school, in the city of Leiria, Portugal, that IMPA researcher João Pereira began to strengthen his relationship with mathematics. At the time, the young man dedicated himself to proving the Pythagorean Theorem, a mathematical expression that relates the sides of a right triangle called legs and hypotenuse. The motivation to explain the theorem stemmed from a mistaken piece of information he received from his father.

“I asked what a theorem was, which is nothing more than a mathematical result, but at the time, my father said it was a result that everyone thought was true, but no one had proven. I found that very interesting and I tried to undertake a theorem. I worked on it and found a proof. I was overjoyed, and only later did I learn that I hadn't discovered anything new. The theorem already had more than 1,000 proofs,” he recalled, laughing.

Despite the mistake, João's father maintained a good relationship with the subject. In fact, when he was younger, he had been a finalist in one of the Portuguese mathematics olympiads – which inspired his son to also venture into the competition. "If my father could do it, I can too," the student thought.

João never imagined that he would become a professional in the field of applied mathematics, much less the first researcher hired for an industrial mathematics position at IMPA – an institute more than 7,400 km from Portugal.

At the time, the concern was to repeat his father's achievement – an objective that was successfully reached in various scientific competitions. In 2006, in the 9th grade of elementary school, he won a silver medal in the Portuguese Olympiad and, later, a gold medal. This result led to the student being invited to participate in Delfos – a Portuguese project dedicated to students with an aptitude for mathematics and solving complex problems.

In 2009, while still in high school, the young man also won a bronze medal at the IMO (International Mathematical Olympiad).

João, 31, an adjunct researcher at IMPA since June 2022, recalls that his participation in Delfos was decisive in his choice of mathematics as a career.

“If it weren’t for this program, I wouldn’t have studied mathematics. At school, we learn many formulas, and in this program, we learn to do mathematics differently. It was a project that taught me a lot. Several successful [Portuguese] mathematicians also went through Delfos. It’s very important work that has greatly improved Portugal’s results in the Olympiads.”

At the time, the researcher had the encouragement of his parents to remain at Delfos. “The project teaches advanced mathematics. I remember the first editions. In the beginning, it's very difficult to follow these classes, I was quite confused, the first few times were very complicated, and I remember my parents encouraging me: 'keep going, it will do you a lot of good,' and it did.”

Passes through IMPA

It was through the mathematics olympiad that João had his first opportunity to get to know IMPA. In 2012, when he was still a high school student, the Portuguese mathematics team received an invitation to study with the Brazilian group, led by the institute.

“It was my first time in Brazil. We spent a week in Rio de Janeiro, and I remember Gugu [Carlos Gustavo Moreira, senior researcher at IMPA] giving a class on bodies. I also remember meeting Tábata Amaral, before she became the figure she is today [federal deputy; OBMEP medalist].”

The application to the institute would only occur 13 years later. Before arriving at the Botanical Garden in Rio de Janeiro, João Pereira earned a bachelor's degree in mathematics from the University of Coimbra and completed his master's degree at the same university in Portugal. His doctorate was from Princeton University, where he was supervised by Emmanuel Abbe and Amit Singer. During his postdoctoral studies, the researcher worked with Vahid Tarokh at Duke University and with Joe Kileel and Rachel Ward at the University of Texas at Austin.

It was also in the United States that João met his wife, a Brazilian lawyer who was on an exchange program at the time. The two got married in 2016 and had a daughter, who is now 3 years old. The new family was an extra incentive for the mathematician to apply for a research position at IMPA.

"IMPA was the only institute that was hiring even during the [Covid-19] pandemic. I knew the institute not only for organizing the mathematics olympiads, but also for recognizing it as very advanced in mathematics, making Brazil a very strong country in the field."

Work in Brazil

The first researcher hired for a position in applied industrial mathematics, João Pereira compares mathematics to a large train, or a "train," as they say in Portugal. According to him, the most important thing to succeed in the discipline is not to derail.

“Mathematics is like a train. For example, if we don't fully understand Ancient Greece, that doesn't prevent us from understanding Modern History. It's not like that in mathematics. If we don't know variables, we won't be able to solve systems of equations; if we don't know how to solve systems of equations, we won't learn how to solve differential equations. If we fail to learn one topic, we compromise the entire learning process – which doesn't happen as much in other areas.”

After eight years in the US, the mathematician arrived at IMPA last year. He is part of the Pi Center (IMPA's Center for Projects and Innovation) team , which aims to intensify the transfer of knowledge to the national productive sector. "The idea is to help the Pi Center grow," he emphasized.

At the Pi Center, the researcher, with a background in machine learning, multilinear algebra, and information theory, is participating in the development of a solution for Hurb – the largest online travel agency based in Brazil. The goal is to create an algorithm capable of improving the pricing system for travel packages offered by the company.

"We have some really cool ideas for addressing the problem, I think we're going to achieve something quite interesting, a finished product for Hurb with a theoretical application," the researcher concluded.

Reunião que detalhou projeto do IMPA com Hurb