28/11/2019

For Luiz Henrique, 'mathematics is an inexhaustible universe'.

Cecilia Manzoni

Nothing escapes the eyes of mathematician Luiz Henrique de Figueiredo. From the seemingly banal movement of zooming in and out on computer screen text, for example, it's possible to extract intriguing mathematical operations. While for laypeople the image of the characters enlarges with the magic touch of a click, for the IMPA researcher this is a phenomenon that has more science than magic. "For the letter to appear enlarged, the computer has to recalculate its design, using formulas that describe each of its curves," he explains enthusiastically.

A researcher at the institute since 2001 and the first doctoral student at Visgraf (IMPA's Computer Graphics Laboratory), Luiz Henrique works in the area of computer graphics and computational mathematics, focusing on rigorous numerical methods. He is one of the creators of the Lua programming language, used internationally by complex software.

More precisely, his research focuses on robust and adaptive methods for solving problems in computer graphics and geometric modeling using computers to prove properties of curves and surfaces. This is generally done by solving equations in multiple variables, and the main tools used are interval computational methods, employing interval arithmetic and affine arithmetic.

My interest in mathematics began early, in algebra and geometric drawing classes taught by Gilson Puppin, Jacques Chambriard, and Edmar Mattos at Colégio Santo Inácio in Botafogo, Rio de Janeiro. “When I started to unravel this universe, nothing else interested me. I would go to used bookstores in the city center and buy university textbooks. I only wanted to know about mathematics.”

Because he was unfamiliar with the profession, Luiz Henrique opted for an engineering degree. After a few weeks attending PUC-Rio (Pontifical Catholic University of Rio de Janeiro), he was captivated by Professor Geovan Tavares' calculus classes and transferred to the university's mathematics department.

After spending long nights tinkering with an IBM 370 computer available at the university, he enrolled in computer science classes. In the early 1980s, the field of study was still in its infancy in the Brazilian mathematical community. “I mainly used the computer to create drawings and do calculations. I printed little letters one on top of the other to create shades of gray. We didn't even have monitors yet, we used cards,” recalls the researcher.

It was also at university, in 1979, that Luiz Henrique made his debut at the Brazilian Mathematics Colloquium. He noticed the posters announcing the 12th edition of the event on the university campus and, filled with curiosity and interest, set off for Poços de Caldas without knowing anyone. “There, I met Elon (Lages Lima) and took some courses in algebraic equations and topology. It was impressive; I couldn't imagine that there were so many mathematicians in Brazil,” he points out.

The experience motivated him to participate in two summer courses at IMPA, still located in the century-old mansion on Rua Luiz de Camões, in downtown Rio: Algebra, with Yves Lequain, in 1980, and Analysis, with Elon Lima, in 1981. “I was impressed that in the middle of summer in Rio, groups of 200 people would gather to study mathematics,” jokes the Rio native. For his master's degree at PUC-Rio, the mathematician chose to delve into number theory, an area of algebra that studies the properties of numbers in general, and integers in particular.

His interest in computing gained momentum during his doctoral studies at the University of Cambridge (England) in the late 1980s. "Since there were many computers there, I started trying to develop research that intersected algebra and computing. But it didn't go very far," says the researcher.

Returning to Brazil brought new horizons and projects. He enrolled in a doctoral program at IMPA, and soon after, in 1989, Visgraf was inaugurated. Determined to deepen his studies in computing, he shifted the focus of his research to this area, becoming the laboratory's first doctoral student. He was mentored by Jonas Gomes, founder of Visgraf and currently a member of IMPA's Board of Directors.

“The atmosphere was great. We were all together building Visgraf, learning the mathematics relevant to computer graphics, trying to find research topics. The internet was just starting in Brazil, and we helped install it here. I was able to study geometry, which is what I wanted to study before, using computers,” recalls the mathematician.

Moon

Together with Roberto Ierusalimschy and Waldemar Celes, from Tecgraf/PUC-Rio, he created the Lua programming language in 1993, a free and open-source software. Used in games like "Angry Birds" and "World of Warcraft," as well as programs like Adobe Photoshop Lightroom and the Wikipedia website, Lua is the only impactful programming language developed outside the developed world, says Luiz Henrique.

Lua's first client was Petrobras, and it began to gain prominence in the United States starting in 1997. "One of the developers of the game Grim Fandango announced, during a conference, that he was using our language, and from there we gained traction in this niche," said Luiz. According to him, one of the great advantages of the language is that it can be programmed even by people who are not professionals in the field, in addition to being easily coupled with existing programs.

In the open environment of IMPA, Luiz Henrique states that he can do what he loves: mathematics, computing, and "beautiful images." Together with his master's and doctoral students, he seeks answers to unsolved questions in these areas.

“Mathematics is multifaceted; there are many approaches to it. It is an inexhaustible universe, accessible at all levels. You don't need a doctorate in mathematics to enjoy it. It's possible to find pleasure in it at all levels: in school, at university, even without being a professional mathematician. If you know a little mathematics, many things in life become more interesting,” he concludes.