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The Intuitive Connectionist Resource
The insights that human mathematicians have had is a combination of the intuitive kind of connectionist-like knowledge. I came across this quotation from Henri Poincare while I was walking in the woods with my wife in Northern California late last summer. And what it said on the bench was it is by logic that we prove but by intuition that we discover. It then ultimately becomes a part of the intuition that the next generation of mathematical thinkers have to ground their own thinking on so that they can extend the ideas even further.