This week’s SUMS talk is by Honours student David Lee. Abstract: Transcendental numbers are real or complex numbers that are not algebraic, that is not a root of a non zero polynomial with rational coefficients. The existence of Transcendental numbers is not immediately obvious. In fact the first proof that a particular number has this property was discovered in the mid-19th century. For this talk we are going to establish the connection between transcendental numbers and approximation by rational numbers. Whilst this connection may seem unusual at first, it is a key approach in proving certain numbers are transcendental.