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Jared Peterson's avatar

Is rationality perhaps antithetical to revolution and discovery? Rationality seems to imply a playing within the rules and bounds of a system, whereas revolution is often a rethinking of the very ontology of the world. Mathematics seems like it should be the exception because discoveries require using the rules and bounds to their logical conclusion. But even mathematics is heavily intuitive, and the formalisms are often used to prove and codify the intuitions rather than the other way around.

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Arturo Macias's avatar

There are clearly two kind of geniuses: the ultra intelligent type: Euler, Gauss, David Hilbert, von Neumann. They allways produce a massive amount of important work, often by extending the current paradigm.

Then, the imaginative type: Cantor, Einstein, Godel. They often produce a very limited number of seminal papers that create new fields of Research.

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