Title: From Congruent Numbers to Modular Forms Abstract: A positive integer is called a congruent number if it is the area of a right triangle with rational sides. The problem of giving a criterion for deciding if a number is congruent has been open for hundreds of years. The best answer known was given by Tunnell in 1983, using many deep results from modern Number Theory. His work will give a completely satisfactory answer, once the Birch and Swinnerton-Dyer conjecture gets proved. In this talk we will introduce, in a way as friendly as possible, the main ingredients needed to understand Tunnell’s […]