Can neural networks be used to devise algorithms?
According to this blog By Reza Zadeh, training a neural network to produce correct output even for just two-thirds of the training examples is computationally hard:

Indeed, in 1988 J. Stephen Judd shows the following problem to be NP-hard:
Given a general neural network and a set of training examples, does there exist a set of edge weights for the network so that the network produces the correct output for all the training examples?
Judd also shows that the problem remains NP-hard even if it only requires a network to produce the correct output for just two-thirds of the training examples, which implies that even approximately training a neural network is intrinsically difficult in the worst case. In 1993, Blum and Rivest make the news worse: even a simple network with just two layers and three nodes is NP-hard to train!