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Elon Lages Lima and Welington de Melo passed away in May 2017 and December 2016, respectively. Both were towering figures in Brazilian Mathematics. Although very different, their trajectories are intertwined. Elon was a pioneer, and Wellington built on the efforts of pioneers to move our research forward. This article briefly summarizes their lives and main contributions to Mathematics.

Elon Lages Lima was an excellent story-teller. In that which is probably one of his best stories, he used to say that Pelé, the soccer king, had been his second substitute. Such claim was allegedly “proven” by transitivity. As a young soccer player in an amateur team in Alagoas, his home state, Elon had Dida as a substitute. Dida would later become a famous Flamengo and national team player and would be a 1958 World Cup champion. In Sweden, at age 17, Pelé was Dida’s replacement. Therefore, by transitivity, Pelé was Elon’s second substitute!

Lima was born in Maceió, in the state of Alagoas, Brazil. As a young child, he was mostly interested in soccer, but an influential middle school teacher first awakened his interest in Mathematics, and he remained deeply connected to the subject for the rest of his life.

After a brief stint as a college student and school teacher in the city of Fortaleza, Lima moved to Rio de Janeiro to complete his undergraduate studies. He arrived in time to witness the creation of the Institute of Pure and Applied Mathematics (IMPA) in 1952, and to be an early junior fellow of the institute. Although mathematical research in Rio was still incipient, at IMPA, Lima had the chance to closely interact with Maurício Peixoto and Leopoldo Nachbin, Brazil’s first two ICM speakers.

Lima eventually went to the University of Chicago for his graduate studies. He obtained a PhD in 1958, under Edwin Spanier, and his thesis remains influential. Lima spent other productive research periods in the United States in the 1960s. However, he only held permanent positions in Brazil. After a short period at the University of Brasília, which he quit a year after the 1964 military coup, and not considering visiting positions, he spent the rest of his career at IMPA.

Lima was best known as a teacher and textbook writer. He was an elegant and enthusiastic lecturer who combined rigor with geometric intuition. The same qualities shone through his writing: with 41 books, he is the single most influential mathematical author in the Portuguese language. Lima was also a mentor to bright young students, including Carlos Gustavo Moreira (plenary speaker at ICM 2018) and Artur Avila (Fields Medal winner in 2014).

Lima was also involved with many other activities. He organized early editions of the Brazilian Mathematical Colloquium and presided the Brazilian Mathematical Society for one term. He was IMPA’s director on three occasions, helped shape the institute’s library – now one of the best in the world – and created two book series. He also masterminded the PAPMEM program for high school teachers.

Perhaps the best-known aspect of Welington de Melo’s personal life was his love of sailing. In 1987, he sailed for three months accompanied by two famous mathematicians: Fields medalist Stephen Smale and Berkeley professor Charles Pugh.. The trio set off on a sailing ship from California and reached the Marquisas Islands, in the French Polynesia. He would also spend most of his spare time in a beach house of Angra dos Reis, where he kept his boat. He once quipped to a journalist that, when sailing on the Angra Bay, he would always make sure his trajectory was “topologically non-trivial”, in the sense of having nonzero winding number around one the Bay’s many islands.

Welington de Melo was born in Guapé, in the Brazilian state of Minas Gerais. He graduated from the Engineering school at his home state’s federal university. De Melo considered pursuing a career in Physics, but found his true calling in an edition of the Brazilian Mathematical Colloquium. There he took a class from Elon Lages Lima, who was director of IMPA at the time and invited him to pursue graduate studies in Rio de Janeiro.

De Melo arrived at IMPA in 1970. Its mathematical environment was already quite different from what Lima had first found twenty years before. Jacob Palis, who (through Lima’s influence) had studied in Berkeley under Smale, took De Melo as his research student. He graduated in 1972 and went on to do postdoctoral work with Smale. A notable fact is that, during his time at IMPA, De Melo would often travel back to Minas Gerais to teach and help build a graduate program in his home state.

De Melo eventually focused on one-dimensional Dynamical Systems, an area where he became a world leader. He produced seminal papers with Edson de Faria, Alberto Pinto, Sebastian van Strien and others. For these achievements, he was an invited speaker in ICM 1998 in Berlin and received many other honors. He also coauthored a textbook with Palis and advanced monographs with van Strien and de Faria that have been quite influential.

De Melo is remembered by his students and colleagues as a demanding but fascinating teacher and collaborator, who always aimed for the highest possible mathematical standards. Oftentimes this would lead him to devote large amounts of time to understanding, and even fixing, the work of other mathematicians. As befits such a scholar, his list of PhD students is not long, but is extremely strong. Artur Avila, Fields Medalist in 2014, is the best known of his former advisees.

De Melo died shortly after a conference in honor of his 70th birthday. We finish this article with an anecdote from his 60th birthday festschrift (*). Several former students observed there that, while teaching, he would often dismiss certain proof details “trivial”. In a cocktail, he asked his former advisee Daniel Smania whether he really said “trivial” that often. When the former student agreed, Welington argued: “But you must understand that ‘trivial’ does not mean ‘easy’, but rather ‘unimportant’!”

(*) We learned this anecdote from Daniel Smania, one of Welington’s former PhD students. We thank him for his authorization to use it here.