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Symbolic mathematics and symbolic manipulation are very powerful in some cases. They are not a panacea. In fact, given the current state of mathematical knowledge, they have great limitations. Most people have, use, and rely for their survival on conceptual reasoning abilities every day that we don’t know how to express in symbolic mathematical form or program on a computer, if this is even possible. To make major progress, even in highly mathematical areas like pure mathematics or theoretical physics or power systems, we probably need to make heavy use of conceptual analysis and visualization just as the successful scientists and engineers of the past did.

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