Mathematicians insist that in many cases the route toward solving a problem is more valuable than solving the problem itself. This may have been true, and may still be true for now, but this seems to implicitly assume that future generations of AI cannot be creative in similar ways that human mathematicians have been. It assumes that the absence of human comprehension during problem exploration loses a valuable aspect of mathematics that cannot be recovered by aiming future AI at solved problems in a naive environment.
If we get to a future where all frontier mathematics contributions are by AI. A future where AI displays creativity in ways that expand mathematic exploration similarly to the ways humans have in the past. A future where AI explains frontier mathematics to curious humans. What will have been lost? Perhaps just "The pleasure of finding things out".
>this seems to implicitly assume that future generations of AI cannot be creative in similar ways that human mathematicians have been
It's because they can't.
It's a mathematical theorem that no algorithm that "solves mathematics" can exist.
>In mathematics and computer science, the Entscheidungsproblem is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an input statement and answers "yes" or "no" according to whether it is universally valid, i.e., valid in every structure. Such an algorithm was proven to be impossible by Alonzo Church and Alan Turing in 1936.
The halting problem constrains human and machine alike, right? Or are you suggesting there is something unqiue about the human mind that allows us to do things machines cannot do in principle? Most people in the field believe in substrate-independence.
Spacecosmonaut · · focus · HN ↗
If we get to a future where all frontier mathematics contributions are by AI. A future where AI displays creativity in ways that expand mathematic exploration similarly to the ways humans have in the past. A future where AI explains frontier mathematics to curious humans. What will have been lost? Perhaps just "The pleasure of finding things out".
lp4v4n · · focus · HN ↗
It's because they can't.
It's a mathematical theorem that no algorithm that "solves mathematics" can exist.
>In mathematics and computer science, the Entscheidungsproblem is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an input statement and answers "yes" or "no" according to whether it is universally valid, i.e., valid in every structure. Such an algorithm was proven to be impossible by Alonzo Church and Alan Turing in 1936.
<a href="https://en.wikipedia.org/wiki/Entscheidungsproblem" rel="nofollow">https://en.wikipedia.org/wiki/Entscheidungsproblem
Spacecosmonaut · · focus · HN ↗
<a href="https://www.edge.org/response-detail/27126" rel="nofollow">https://www.edge.org/response-detail/27126