Insight is essential even if it is fallible
Just because insight is sometimes unreliable, we should not conclude that it plays no essential role in mathematics.
  • Doubts about consistency in mathematics only arise when mathematicians use systems that go beyond ordinary mathematics
  • When we do become assured of the consistency of the mathematical system, it is always because of insight.
Roger Penrose (1990).
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Artificial Intelligence Â»Artificial Intelligence
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No: computers are limited by Gödel's theorems Â»No: computers are limited by Gödel's theorems
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Mathematical insight is non-algorithmic Â»Mathematical insight is non-algorithmic
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The absurdity of algorithmic insight Â»The absurdity of algorithmic insight
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Gödel’s theorem is not decisive Â»Gödel’s theorem is not decisive
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Insight is essential even if it is fallible
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Roger Penrose Â»Roger Penrose
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