In 1969 Marvin Minsky and Seymour Papert published a very important book where they demonstrated that a simple neural network (inputs connected directly to the output layer) would not be able to learn even something as simple and critical as the XOR function! Later in the book they show that with additional layers (single layer is sufficient) a neural network would be able to overcome these limitations (a message that was missed). And so the AI winter began.
The history of neural networks goes way back!
