I personally find recurrent highway networks (RHNs) as described in [1] to be easier to understand and remember the formulas for than the original LSTM. Because as they are generalizations of LSTM, if one understands RHNs, one can understand LSTMs as just a particular case of RHN.
Instead of handwaving about "forgetting", it is IMO better to understand the problem of vanishing gradients and how can forget gates actually help with them.
And Jürgen Schmidhuber, the inventor of LSTM, is a co-author of the RHN paper.