Dynamic time warping
Sakoe and Chiba described how to compare two recordings of the same word spoken at different speeds, by stretching time non-linearly.
Why it matters
The most obvious obstacle to recognition was solved: the same phrase is never spoken twice with the same duration.
The algorithm finds an optimal mapping of one time axis onto another with constraints on slope, so that nonsensical stretches are ruled out. Until hidden Markov models arrived it was the main method in commercial isolated-word systems. It outlived its field: today it is used to compare any time series, from gestures to market prices.