The Gross-Koblitz formula describes Gauss sums on finite fieldsof characteristic $p$ in terms of the $p$-adic Gamma function. Thisformula is a $p$-adic lifting of Stickelberger's congruence on Gauss sums.There have been several proofs of the formula (Gross-Koblitz,Dwork-Boyarsky, Katz, Coleman), which all involve some cohomologicalcalculations. Recently, a proof has been found by A. Robert which isconceptual but truly elementary, at the level of "freshman $p$-adicanalysis." We will discuss Robert's proof and describe possibleextensions