The claim that mathematical insight is algorithmic can be reduced to absurdity:
**Assume**:
There is a knowable algorithm (AI procedure) that generates mathematical insight.
**It follows that:**
1) If we were aware of this algorithm, or how to generate it, then we would have to believe in the soundness of this procedure. 2) Gödel shows how to construct, for any algorithm for mathematical insight, a sentence whose truth follows from the soundness of the algorithm, yet which is inaccessible to that same algorithm.
3) We can understand and believe in the Gödel procedure.
**Therefore**:
There is *not *a knowable algorithm that generates mathematical insight.
Roger Penrose (1990). |