Fermat's last theorem and elliptic curves

Abstract: Around 1637, Pierre de Fermat wrote the following statement in the margin of his copy of Arithmetica: “A cube can't be a sum of two cubes, a fourth power to be a sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers." This statement is well known as Fermat's Last Theorem, but it remained open as a conjecture until 1994. 

The proof of Fermat's Last Theorem involves some powerful techniques that opened up entirely new approaches to numerous other problems. In this talk, we will discuss some of the mathematical objects (such as elliptic curves) and ideas that go into proving Fermat's Last Theorem along with a concrete example. We will not go into any details but give a naive overview.