Graduate & Undergraduate Student Seminar (GAUSS)
In this talk, I will give a short introduction to the congruent number problem and its relationship with elliptic curves.
A positive rational number n is called a congruent number if there is a right-angled triangle with rational sides and area equal to n. Characterizing congruent numbers forms one of the oldest unsolved problems in mathematics. One of the major advances in the twentieth century was to place this problem in the context of the arithmetic theory of elliptic curves. The latest solution by Tunnell (1983), in a way, makes it equivalent to proving the famous Birch & Swinnerton-Dyer Conjecture.