Re:How close are computers to automating mathematical reason...
by roywiggins on Saturday August 29, 2020 @01:07PM
(#24317577)
> we cannot just ask a computer to find a proof or refutation of Goldbach's Conjecture or other "Goldbach-type" statement and have it do any better than a person
We don't know exactly how good people are at this. Perhaps there's some tier of intelligence that is better than people but worse than the all-powerful algorithm that Gödel proved can't exist.
For instance, a machine that is merely faster would be better than we are. A machine that could instantly simulate an entire civilization from the beginning of time, generate entire generations of mathematicians, and simulate their thinking for thousands of subjective years and then hand you back the results of their thinking would be better at it than we are, even if it wouldn't be better in the sense of being able to deterministically decide whether there's an answer or not.
We don't know exactly how good people are at this. Perhaps there's some tier of intelligence that is better than people but worse than the all-powerful algorithm that Gödel proved can't exist.
For instance, a machine that is merely faster would be better than we are. A machine that could instantly simulate an entire civilization from the beginning of time, generate entire generations of mathematicians, and simulate their thinking for thousands of subjective years and then hand you back the results of their thinking would be better at it than we are, even if it wouldn't be better in the sense of being able to deterministically decide whether there's an answer or not.