Machines may eventually have mathematical intuition
The incompleteness theorems only show that a machine can't be proven to possess mathematical intuition—not that machines can't in fact possess mathematical intuition.
To the extent that machines are limited by Gödel’s theorems, humans are too. Neither humans nor machines can formulate all of their mathematical intuitions.

It's in the nature of mathematics to be incompletable.

Kurt Gödel (1951).

Note: Also see, the "Does Gödel’s theorem show that a mathematical insight is not algorithmic?" arguments is on this map.
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Artificial Intelligence »Artificial Intelligence
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
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No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
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Theorems show limitations of machine thought »Theorems show limitations of machine thought
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Machines may eventually have mathematical intuition
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