Surely the roots, if we skip over the early preceptron work', are in backpropagation and Hinton, and the work going on at Edinburgh and elsewhere in the 80s.
Indeed I remember buying a set of three conference-papers-as-books around that time, titled Artificial Neural Networks .. proceedings of the whatever the conference was.
No doubt Schmidhuber made important contributions, but I see him pop up claiming to be the 'root' of it all every couple of years.
That's what bugs me about him. So much work has gone into today's models that calling his contributions "the root" isn't really warranted. He's always complaining that Hinton, LeCun, and Bengio get more credit than they deserve, and now he's over-claiming himself.
Surely the roots go back to Turing, Gödel, Hilbert, Frege, Leibniz, Aristoteles.
Hinton did not invent backpropagation.
related paragraph from Wikipedia:
Modern backpropagation was first published by Seppo Linnainmaa as "reverse mode of automatic differentiation" (1970)[26] for discrete connected networks of nested differentiable functions.[27][28][29]
In 1982, Paul Werbos applied backpropagation to MLPs in the way that has become standard.