Gentle Beukers's Proofs that Zeta(2,3) are Irrational

Although Beukers's proof that Zeta(2) and Zeta(3) are irrational are at the level of advanced calculus, they are condensed. This article slows down the development and adds examples of the techniques used. In so doing it is hoped that more people might enjoy these mathematical results. We focus on the easier of the two Zeta(2).