Did Poincaré believe mathematics was reducible to logic?
Far from it. While I appreciate the power of logic for demonstrating and verifying, I cannot accept that it alone can create mathematics. To suggest that all of mathematical reasoning can be reduced to a mechanical, symbolic process, as some propose, overlooks a fundamental aspect of our engagement with numbers and forms: intuition. It is our innate sense of spatial relationships, our feeling for symmetry and continuity, that allows us to grasp mathematical concepts in the first place. Logic provides the framework for proving, but intuition provides the fertile ground for discovery. To deny intuition is to drain mathematics of its living, creative spirit.
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