"It is by logic we prove. It is by intuition we discover. -Henri Poincaré" -Dillon Berger
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Nice quote, but I think observation is the way to discover rather than intuition.

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There is no actual infinity, the Cantorians have forgotten that, and they have fallen into contradiction. -also Henri Poincaré.
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Thought is only a flash between two long nights, but this flash is everything. - Also Henry Poincaré
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I roughly remember reading a quote from Einstein. When asked how he made his discoveries he said it was "die sich auf Erfahrung stützende Intuition" or "the intuition which is based on / supported by experience".
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Nice. Knowledge entrusts his last word to intuition, not logic.
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Almost exactly my personal philosophy. Just replace logic with algebra and intuition with geometry. Going out on a limb, I think QM may have too much algebra and not enough geometry. Fixing that could fix the issues with quantum intuition.
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