The fact that that skein modules of closed 3-manifolds are finite dimensional is a surprising result, first conjectured by Witten and later proven by Gunningham, Jordan, Safranov. Their proof, which works for any skein module, relies on heavy machinery in category theory and algebraic geometry. In this talk I will present a proof (joint with R. Detcherry) of finiteness for the Kauffman bracket skein module ”by hand”, i.e. in an algorithmic and constructive way, that relies only on basic properties of the KBSM. One of the advantages of this proof is that it allows, without any modification, to also prove a version of finiteness for manifolds with boundary. As an application of this latter result, we are able to prove that the peripheral ideal of any manifold is non-trivial, thus proving that the Reshetikhin-Turaev invariants are q-holonomic.