Seminar presents possibilities of AI in mathematical research
Guilherme Silveira highlights the role of the researcher in validating results
The possibilities opened up by artificial intelligence (AI) in mathematical research were discussed on Tuesday (7) at IMPA Tech’s academic seminar with programmer Guilherme Silveira, co-founder of Alura, Brazil’s largest tech education platform. The cycle of meetings, organized by Professor Uéverton Souza, promotes interdisciplinary presentations for students of the Bachelor’s Degree in Mathematics of Technology and Innovation.
A medalist in the ICPC (International Collegiate Programming Contest), the world’s most popular university programming competition, Silveira has used computing in magic, poetry, art and education. In recent years, he has been focusing on how to connect his more recent knowledge of AI and computing to his undergraduate degree in applied mathematics at the Institute of Mathematics and Statistics at the University of São Paulo (IME-USP).
In his talk with the students, the speaker highlighted the centrality of programming in contemporary academic training. “Knowing how to program is a skill. There is a world of calculations and optimizations that we can do. To use the computer as a mathematical research tool, you need to know how to program,” he said.
Silveira also drew attention to the limits and responsibilities of using AI-based tools. According to him, even with the advancement of models capable of writing code, conducting experiments and even helping to write articles in LaTeX, the critical capacity of the researcher remains indispensable. “What hasn’t changed is the judgment barrier. Today, we can produce more results, in less time and on more fronts – but you have to know how to evaluate all this rigorously,” he explained.
Throughout the meeting, examples of mathematical results obtained with computational support were presented, as well as the systems used to achieve them. The speaker also detailed the creative processes involved in developing these solutions, highlighting how AI can broaden scientific research paths.
For student Mateus Bandeira, the lecture provided an innovative perspective on the formulation and exploration of mathematical conjectures. “In a scenario so stuck in a procedural pattern, he had a very innovative idea that in the future will probably be the standard. Through the computational power of LLMs, it is possible to attack several problems simultaneously, making the whole process of observations and tests more efficient,” he said.
The presence of artificial intelligence in everyday academic life was also highlighted by the students, who advocate a strategic and responsible use of the tools. “AI can help develop programs and help with studies, but we must be careful not to stop learning and make real gains. They are highly efficient tools, but there must always be checks on their work,” added Bandeira.
