A classical result in approximation theory due to Korovkin asserts that a sequence of positive unital maps on C([0,1]) converges pointwise to the identity if they merely converge to the identity on the functions 1,x,x^2. This result was later generalized by Saskin, who showed that convergence to the identity on a generating function system implies convergence to the identity everywhere if and only if the system has full Choquet boundary. Arveson's last open conjecture in his seminal work on non-commutative boundary theory predicts that a non-commutative analogue of Saskin's result holds. We refute Arveson's conjecture with an elementary counterexample. All notions will be explained during the talk. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0