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".
> What will have been lost? Perhaps just "The pleasure of finding things out".
I'll kindly disagree on this front, because when I'm walking a path toward solving a solution, I mark a lot of steps for possible diversions to other paths hence solving adjacent or different problems with the method I have at hand.
Currently, AI takes us from A to B, and is improving on that front. However, the paths in science are not lines, but a trees. Methods are cross-pollinated from each other.
Human intuition enables this cross-pollination. AI works with a laser focus. Human intuition and resulting wide perspective sow the seeds for solutions in many areas at once.
I recognize that if a document were to be published tomorrow containing solutions to all formulated open problems in mathematics we will have gained very little in mathematical understanding.
But surely, if we know that the dead ends of exploring a problem are valuable, we should be able to explore them even if a solution is already known. It just requires that the mathematics community reshapes itself. And it must. Two years from now people might be able to run the computation that solved NS on their Iphone.
I'm sure that whatever has been discarded during the NS exploration as a dead end you would be able to rediscover using purpose built tooling in the near future. The purpose of human mathematicians in the medium term might be to explore dead ends, and to provide human insights as context to attack other problems. But whether this type of work will remain necessary in the long term im not sure.
> But whether this type of work will remain necessary in the long term im not sure.
Any and every capability AI can demonstrate today is the result of us, humans doing it in the first place for a very long time. The transfer method of these abilities is a subject of another comment, but as Microsoft and NVIDIA puts it, it's a theft of unprecedented scale [0].
AI labs dream of recursive self improvement as an escape from that, but until we arrive there, humans have to do something so AI can do it as well.
And, as of fully autonomous self driving which should have arrived 5 years ago, RSI and AGI is just around the corner, a corner with a radius so large that it never ends.
We dream of building utopias with these tools, but it's a path to dystopia paved with stones made from utopic dreams.
I dont disagree. Clearly AI leans on the cumulative cognitive labor of humanity without porpper attribution. This is in part due to the design of these sytems. Information is compressed into the weightspace in ways we dont understand, and a concept becomes unlinked from its origin.
I hope you're right about AGI. What we need is time, and we may not have it. <a href="https://www.dwarkesh.com/p/noam-brown" rel="nofollow">https://www.dwarkesh.com/p/noam-brown
>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".
bayindirh · · focus · HN ↗
I'll kindly disagree on this front, because when I'm walking a path toward solving a solution, I mark a lot of steps for possible diversions to other paths hence solving adjacent or different problems with the method I have at hand.
Currently, AI takes us from A to B, and is improving on that front. However, the paths in science are not lines, but a trees. Methods are cross-pollinated from each other.
Human intuition enables this cross-pollination. AI works with a laser focus. Human intuition and resulting wide perspective sow the seeds for solutions in many areas at once.
Spacecosmonaut · · focus · HN ↗
But surely, if we know that the dead ends of exploring a problem are valuable, we should be able to explore them even if a solution is already known. It just requires that the mathematics community reshapes itself. And it must. Two years from now people might be able to run the computation that solved NS on their Iphone.
I'm sure that whatever has been discarded during the NS exploration as a dead end you would be able to rediscover using purpose built tooling in the near future. The purpose of human mathematicians in the medium term might be to explore dead ends, and to provide human insights as context to attack other problems. But whether this type of work will remain necessary in the long term im not sure.
bayindirh · · focus · HN ↗
Any and every capability AI can demonstrate today is the result of us, humans doing it in the first place for a very long time. The transfer method of these abilities is a subject of another comment, but as Microsoft and NVIDIA puts it, it's a theft of unprecedented scale [0].
AI labs dream of recursive self improvement as an escape from that, but until we arrive there, humans have to do something so AI can do it as well.
And, as of fully autonomous self driving which should have arrived 5 years ago, RSI and AGI is just around the corner, a corner with a radius so large that it never ends.
We dream of building utopias with these tools, but it's a path to dystopia paved with stones made from utopic dreams.
[0]: <a href="https://news.ycombinator.com/item?id=49752056">https://news.ycombinator.com/item?id=49752056
Spacecosmonaut · · focus · HN ↗
I hope you're right about AGI. What we need is time, and we may not have it. <a href="https://www.dwarkesh.com/p/noam-brown" rel="nofollow">https://www.dwarkesh.com/p/noam-brown
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