The "new-fangled" AI, as the article calls it, is often useful when the stakes are low, and you can accept mistakes in outcomes. Examples of such applications are: trying to determine which of your friends occur in a photo, which movies a subscriber may be interested in, or which action could lead to victory in a computer game. Getting a rough translation of a newspaper entry, as mentioned in the article, is also a good example.

As soon as you need reliable outcomes, such as certainty whether an erroneous state can arise in a program, whether a proof for a mathematical conjecture exists, or whether a counterexample exists, exhaustive search is often necessary.

The question then soon becomes: How can we best delegate this search to a computer, in such a way that we can focus on a clear description of the relations that hold between the concepts we are reasoning about? Which symbolic languages let us best describe the situation so that we can reliably reason about it? How can we be certain that the computed result is itself correct?

The article states: "The heart of GOFAI is searching – of trees and, more generally, graphs." I think one could with the same conviction state: "The heart of GOFAI is reasoning – about relations and, more generally, programs."