15/04/2021

Maurício Peixoto, the mathematician of infinite inspiration.

When he was nearing 90 years old, Maurício Peixoto (1921-2019), one of the founders of IMPA and an emeritus researcher, was urged by Marcelo Viana, the institute's director-general, to participate in a book that would bring together all his works. He declined. The reason, confessed shortly afterward, proved surprising. Even after publishing more than 40 articles and changing the course of Brazilian and world mathematics with groundbreaking discoveries in the field of dynamical systems, the prolific researcher continued to do mathematics and believed that the high point of his work was yet to come.

Besides highlighting the enthusiasm with which Peixoto, already in his advanced age, approached research, the example leads us to imagine what other contributions the mathematician could have made to science until he reached 100 years of age. The round date is this Thursday (15). Deceased in April 2019, the Ceará-born researcher had his talent recognized by important distinctions, such as the Moinho Santista Prize (1969), the Mathematics Prize of the World Academy of Sciences (1987) and the Grand Cross and Commendation of the National Order of Scientific Merit.

Physicist Carlos Alberto Aragão de Carvalho Filho, from the Federal University of Rio de Janeiro (UFRJ), collaborated with Peixoto on his last works and witnessed the scientific vigor that the researcher maintained. “Maurício had fantastic lucidity. Part of his genius was being able to explain complex things in a very simple way. He presented his ideas clearly and went to the heart of the problems to solve them, not just getting bogged down in technique,” he says.

For mathematician Alciléa Augusto, Peixoto's widow, her husband's insatiable curiosity partly explains his long academic productivity. "He had a genuine enthusiasm for knowledge. At 94, he was still spending nights poring over a publication he was preparing."

According to Alciléa, to achieve the successful results that earned him international renown, he relied on a keen intuition. "It was evident not only in research, but also in other areas, such as his relationships with people. I remember that at the beginning of Maurício's studies on focal decomposition, he had to do very complicated calculations, but he went ahead because he knew the results would be correct."

History

The son of the governor of Ceará, José Carlos de Matos Peixoto, Peixoto was born on April 15, 1921, in Fortaleza. He moved with his family to Rio de Janeiro in his childhood. After failing mathematics at Colégio Pedro II in Rio, he began to take an interest in the subject. As a career in mathematics did not exist, he went to the School of Engineering at the University of Brazil. There, he befriended his classmates Leopoldo Nachbin (1922-1993), also a founder of IMPA, and Marília de Magalhães Chaves (1921-1961), whom he would marry in 1946. The two were important influences in his becoming a mathematician.

Despite graduating in civil engineering, he never practiced the profession. He pursued mathematics, and at the same institution, he passed the competitive examination for Associate Professor of Rational Mechanics in 1947, and for the Chair of the same discipline in 1952.

Maurício Peixoto, Steven Smale e Jacob Palis

Also in 1952, Maurício founded IMPA, alongside Lélio Gama (1892-1981) and Leopoldo Nachbin. Initially, the institute was temporarily located in a room at the headquarters of the Brazilian Center for Physics Research (CBPF), in Praia Vermelha, in the southern zone of Rio de Janeiro. The first scientific unit of the National Research Council (CNPq), IMPA was created with the objective of stimulating scientific research in Mathematics, training researchers, and disseminating and improving mathematical culture in Brazil.

Although he visited IMPA less frequently in the last years of his life, Peixoto had a special affection for the institute. “Every time he came back from IMPA he would say, ‘that place is my home.’ He loved spending hours in the library. He would stay there more than in his own office. He would even forget to have lunch,” recalls his widow.

Pioneering

His work on structural stability is considered a landmark for the consolidation of dynamical systems, an area of specialization for some of the best Brazilian mathematicians, such as Artur Avila, winner of the Fields Medal in 2014. Peixoto's first contact with the concept was in 1955, during forays into the then newly created IMPA library.

A year after focusing on the subject, Peixoto reported on the progress he had made in correspondence with the American Solomon Lefschetz (1884-1972). He was then invited to spend time at Princeton University in the United States. At the American institution, the Brazilian completed the manuscript of his first article on structural stability.

His studies on the subject made him a "pioneer in the field of dynamical systems in Brazil," says Jacob Palis, emeritus researcher at IMPA, who even did an internship with Peixoto early in his career. "His enthusiasm for mathematics and the certainty that the problems that arose always had a solution, which he diligently sought, distinguished him as a researcher," he praises.

According to Carlos Aragão, Peixoto's discovery opened up new avenues in the field, which is rare in science. “The impact of the discovery was enormous. Peixoto's theorem was obtained for two-dimensional systems, but it was later generalized by Steven Smale (an American mathematician who won the Fields Medal in 1966). It has applications in physics and other areas, and many theses and works have originated from this discovery,” assesses the professor from UFRJ.

Maurício Peixoto e Artur Avila em uma de suas últimas visitas ao IMPA

Personal life

Described by friends and relatives as an intelligent, modest, and good-humored man—in short, an extremely pleasant companion—Peixoto turned several colleagues into personal friends. He befriended peers he met during his presidency of CNPq, the Brazilian Academy of Sciences (ABC), and the Brazilian Mathematical Society (SBM). This was the case with Lindolpho de Carvalho Dias, former director-general of IMPA, who witnessed various moments in the career of the researcher from Ceará.

Dias, who is the godfather of one of Peixoto's daughters, recalls the times when he was a student of the researcher and his first wife, Marília Chaves. “The three of us quickly developed a very strong friendship, with a lot of personal contact, that lasted a lifetime. Maurício was a very intelligent, upright, and correct man. Therefore, everything he touched worked very well, both as a researcher and as an administrator of Brazilian science in the institutions he presided over,” he recounts.

Minister of Science and Technology between 1992 and 1999, chemist José Israel Vargas, from the Federal University of Minas Gerais (UFMG), highlights that, during his presidency of CNPq, the founder of IMPA strived to elevate national chemistry to the same prestige that mathematics and physics already enjoyed at the time. “There was a program in England called the Royal Society Professorship, which offered research grants to the best English scientists at universities around the world. He planned to bring five of these professors to Brazilian universities and create a high-quality center in chemistry.”

Vargas fondly remembers his friend, with whom he forged close ties during his years at CNPq. “I greatly admired Maurício's intelligence and modesty. I was curious, interested in learning the meaning of the mathematics he was doing, and he would joke with me, saying, 'you know everything, and I know the rest.' We eagerly hoped to celebrate his 100th birthday, but unfortunately it didn't happen,” he laments.