  We show that Reed-Muller codes achieve capacity under maximum a posteriori
bit decoding for transmission over the binary erasure channel for all rates $0
< R < 1$. The proof is generic and applies to other codes with sufficient
amount of symmetry as well. The main idea is to combine the following
observations: (i) monotone functions experience a sharp threshold behavior,
(ii) the extrinsic information transfer (EXIT) functions are monotone, (iii)
Reed--Muller codes are 2-transitive and thus the EXIT functions associated with
their codeword bits are all equal, and (iv) therefore the Area Theorem for the
average EXIT functions implies that RM codes' threshold is at channel capacity.
