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1. Applying a result incorrectly. 2. Choosing the wrong path. [1] only done by humans, not machines. [2] is done both by humans and machines Choosing the right path needs experience or heuristics |
Penrose fails to distinguish between two types of mathematical mistakes. The first type is where one applies a result incorrectly, for example in simplifying an arithmetic expression. The second type is where one pursues the wrong path in solving a problem, for example in applying integration by parts the wrong way. The first type of mistake is only done by humans, and very rarely by machines. The second type of mistake is done both by humans and machines. Choosing the right path in solving a problem can rarely be done purely logically, and frequently needs to use experience or heuristics. |
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