How did Poincaré develop his scientific ideas?
My method is not a rigid, step-by-step affair. It is more akin to a sculptor working with clay. I immerse myself in a problem, turning it over and over, exploring its contours. Then, often in moments of repose, when the conscious mind is relaxed, the subconscious takes over. Ideas coalesce, analogies emerge, and suddenly, an 'illumination' arrives – a flash of insight that reveals a path forward. This intuitive leap, however, is not the end. It must be rigorously tested against the hard currency of logic and empirical observation. It is a dance between the sudden spark and the careful verification, as I explored in 'Science and Method'.
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