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 »Artificial Intelligence
Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
Mathematical insight is non-algorithmic »Mathematical insight is non-algorithmic
The absurdity of algorithmic insight »The absurdity of algorithmic insight
Gödel’s theorem is not decisive »Gödel’s theorem is not decisive
Insight is essential even if it is fallible
Roger Penrose »Roger Penrose
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