In details

Fermat's Last Theorem

Alamir Rodrigues Rangel Junior
William Paulino, Fellipe Barros de Souza
Jean Carlos Viana de Sousa


This paper aims to make a historical overview of Fermat's Last Theorem, explaining its origin and related events throughout history until it reaches the present day, focusing on its importance for the development of mathematics in the last three centuries, since This is one of the most exciting problems in the history of mathematics and one that has led mathematicians of all ages to try to solve it.

In development, the present paper will attempt to explain why such an interest in a seemingly simple problem. We will see that it is not so simple and that its solution is more relevant than one might suppose at first, leading even to the creation of a millionaire prize for the one who could solve it, and countless achievements during the three centuries of attempts of solution.

1.1 Who was Fermat?

Pierre Fermat lived in 18th century France and was a civil servant in the French city of Toulouse, mathematics for him was a hobby, devoting his free time to it. One of Fermat's distinguishing characteristics was his custom of presenting other mathematicians with challenging problems that often left his contemporaries hopelessly mired in an attempt to solve them. It was with this challenging feature and by researching ancient Greek authors that Fermat created a proposition very similar to Pythagorean theorem, but unlike this one, it had no solution, this proposition crossed the ages and became known as Fermat's last theorem.

An important detail about Fermat is that he was considered an amateur mathematician, although the quality of his production was excellent, so there was no concern on his part to document his work, since his interest in mathematics was not professional, This certainly made it difficult to study his work, of excellent quality, but done in an amateur way. This feature of Fermat's personality helped to create the mystery surrounding his last theorem that cannot be solved immediately as the others were.

1.2 Fermat's observations

The merit of the discovery of this proposition is due to his eldest son, who noticed several notes of Fermat in a book of Arithmetic that belonged to him, because he had the habit of making notes in books. Upon discovery by his son, these notes were published in Diofanto's Arithmetica book Containing Observations by P. de Fermat in 1670, the book presented 48 observations without, however, resolving the demonstrations, which were proven over time, minus one. which, precisely because it was the last, became known as Fermat's last theorem.

Fig 1 .: Special Edition Cover
with Fermat's notes