Do Triângulo Retângulo ao enigma mais famoso da Matemática: o Último Teorema de Fermat

Abstract

This research examines the history of Fermat's Last Theorem, considered the most famous enigma in mathematics, whose formulation arose from the generalization of the Pythagorean Theorem based on a study of right-angled triangles. The objective of this research was to understand how the Pythagorean Theorem, especially through right-angled triangles, influenced the emergence of Fermat's Last Theorem, identifying the main mathematical advances that were fundamental to the solution of the problem obtained by the English mathematician Andrew Wiles. The research is primarily bibliographic in nature, with data collection carried out through electronic searches using Google Scholar and the Scientific Electronic Library Online (SCIELO); books, articles, monographs, dissertations, theses, and journals were considered for data collection. Throughout the research and studies related to Fermat's Last Theorem in this review article, it became evident that the object of study has been the subject of scientific discussion and investigation under different theoretical aspects, mainly due to the complex studies that converged towards finding a proof for the problem at different moments in history. It is important to clarify that the demonstration carried out by Wiles served to legitimize the statement of Fermat's Last Theorem; however, this was not evidenced by the research that Wiles found the proof that Fermat claimed to possess, since Wiles appropriated more sophisticated techniques (discoveries made by other mathematicians) to demonstrate the legitimacy of the Theorem. The results of this research allow us to conclude that the Pythagorean Theorem represents not only a milestone in Euclidean Geometry, but also the starting point for an intellectual trajectory that culminated in Fermat's Last Theorem. The evolution of this problem spurred the development of important concepts in Number Theory, Algebra, and Algebraic Geometry, demonstrating the proof achieved by Andrew Wiles in 1995.