Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.
So, I've seen this mindset a lot lately... The answer is that we simply need to decouple the "right to exist" from "worth." You should have the right to exist and explore the world simply because you're human, not because you can use your skills to provide some sort of transactional value to someone else. Deprogramming so many people is going to be hard...
Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.
So, I've seen this mindset a lot lately... The answer is that we simply need to decouple the "right to exist" from "worth." You should have the right to exist and explore the world simply because you're human, not because you can use your skills to provide some sort of transactional value to someone else. Deprogramming so many people is going to be hard...
All sane and noble in theory, but in practice, how do you see that happening?
Let's start with the first practical step: how do you dethrone the psychopaths in charge of the world who own about everything on Earth and have all the world's lethal force in their pockets?
Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.
Does it terrify you to look at children? Not so many years from now, some of them will surpass you. A few years after that all (that survive to that point) will surpass you. Does that terrify you just as much?
The seeming sincerity of your question in the conext of comparing children to AI is what really terrifies human beings.
I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)
As a mathematician, new, conceptual math is when I'll become interested in reading LLM output. I appreciate very much the work done so far, but this sort of asymptotic/quantitative result didn't interest me much even when it was done by humans. (This is not snobbery, just a personal preference.)
I have no idea about research in mathematics: How will mathematicians judge what constitutes new conceptual math that is actually useful, vs a hallucination that might be novel but doesn't introduce anything actual meaningful?
> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…
I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…
This is pretty much what underlies AI doomer argument of people like EY. Humans will gradually hand over civilization to black box AI they can't understand. As AI becomes more complex and powerful it will be harder and harder to control.
I am cautious about AI "discoveries" after Mythos paper. What was the process of a writing a paper? Was the question asked by a mathematician? Was the paper right from a get-go or was there someone who pointed out mistakes? How much attempts were made before solution was found? I will eat my words if an AI oneshotted that one without any external help, but for know I am left wandering whether it's a new way to attrib…
I'm also wondering about the process. What was the prompt, what they fed into the model, what it was trained on, etc. The article reads like a marketing post.
Nevertheless new maths is exciting and might lead to what I find slightly more interesting - new physics.
Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…
Can you describe what the reaction to these results has been like in your department? Obviously many people are excited, but what else? How do grad students feel about this? Are any professors getting worried about becoming obsolete?
> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…
I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…
I've been thinking about this and I believe the best place to be is a scientist who keeps looking at an AI's output, prods it in the right directions, verifies the proofs, fixes and fills gaps, takes the proof to production with safety, risks etc mitigated and then distribution with a company wrapped around the discovery. I think it wouldn't be black-boxed as much and will require a lot more understanding and reviewing to trust and productize it.
I think one interesting thing to point out is that the proof (disproof) was done by finding a counterexample of Erdős' original conjecture. I agree with one of the mathematician's responses in the linked PDF that this is somewhat less interesting than proving the actual conjecture was true. In my eyes proving the conjecture true requires a bit more theory crafting. You have to explain why the conjecture is correct by…
Searching for a proof and disproof are sometimes not so different. In most cases, you nibble the borders to simplify the problem. For example, to prove something is impossible let's say you first prove that there are only 5 families, and 4 of them are impossible. So now 80% of the problem is solved! :) If you are looking for counterexamples, the search is reduced 80% too. In both cases it may be useful In counterexam…