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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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Insight is essential even if it is fallible
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Roger Penrose
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