That's how they are finding these solutions though, unless we are just going to label intuition as something only humans can do. Like a submarine being unable to swim or whatever that example is.
The two places were seeing lots of movement are:
* Updates to lower/upper bounds. In many cases, these kinds of problems are the deep-math equivalent of calculating more digits of pi. Yes, if you throw time at it you'll break the record, but it may not be terribly worthwhile.
* Finding counter examples which disprove conjectures. This is really useful, and helps offset some positivity bias on the human side, often bringing together known tools from distant silos.
If you read the list of ten results, almost all fall into one of these buckets.
I disagree. I routinely let LLMs speculate or generate hypotheses along the way of helping with technical research. Sometimes they can prove the correctness of a concrete math idea but other times even an unproven conjecture helps with the numerical algorithm implementation and the result is then simply supported by additional data. I guess that any autoresearch-adjacent application has LLMs intuiting and coming up with hypotheses/conjectures—as do the steps/lemmas along a complex proof. In my opinion the modern LLMs are powerful intuitive thinkers that generate lots of conjectures of varying quality or importance.
Of course computers can grind in a way that humans can't. But now we have systems that convert the human-comprehensible ideas into a computer's plan of attack, in a way that greatly expands the frontier of ideas thus treatable.
People keep saying this. Why?
Surely the AI can complete the prompt “Generate new research questions based on these observations”?
When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.
They can't exit the hull until the "intuition" starts spawning points outside the convex hull.
The extent to which they are able to do this is the more interesting question!
Humans can “intuit” based on a much larger, if not unlimited, context. Also I just want to say that human cognition is something so insanely complex and deep that we will not understand it at all in my lifetime. To attribute all, or really any, aspects of human cognition to a machine at this point is silly to me.
Most humans are dumber than a box of rocks. Here in Seattle we had one of many light rail-related fuckups where they had to replace part of the line with buses. People piled into the front of one when it was full. When people got out they never moved back. As the driver struggled to close the door and people struggled to get in the wad of people never moved back to fill the ample space.
Chatgpt was smarter than the average person a while ago
This does not demonstrate a lack of intelligence. It demonstrates laziness and a lack of interest in spreading apart. Or just lack of consideration (or even malice) on the part of those at the back of the wad.
> Chatgpt was smarter than the average person a while ago
This is an absurd claim that fundamentally misunderstands what it means to be "smart". Reasoning that would get you to this conclusion would equally well apply to Google's search engine over a decade ago.
There are processes at work there that we don’t even have the language to describe.
(86 billion is the number ChatGPT, ironically enough, has given me a couple of times. I remember hearing for a long time that it was estimated to be somewhere in the ballpark of 100 billion. This is not my field of study.)
For the same reason that you can't draw a 15 of Diamonds from a regular card deck.
"Excuse me, We demand rigidly defined areas of doubt and uncertainty!"
DT: Might I make an observation at this point?
MT: You keep out of this metal nose.
VF: We demand that that machine not be allowed to think about this problem!
DT: If I might make an observation…
MT: We’ll go on strike!
VF: That’s right. You’ll have a national philosopher’s strike on your hands.
DT: Who will that inconvenience?
MT: Never you mind who it’ll inconvenience you box of black legging binary bits! It’ll hurt, buster! It’ll hurt!
DT: [Booming] If I might make an observation … All I wanted to say is that my circuits are now irrevocably committed to computing the answer to Life, the Universe, and Everything.
VF: That’s a -
MT: Ahhh! With -
DT: But, but the program will take me seven-and-a-half million years to run.
“All I wanted to say,” bellowed the computer, “is that my circuits are now irrevocably committed to calculating the answer to the Ultimate Question of Life, the Universe, and Everything.” He paused and satisfied himself that he now had everyone’s attention, before continuing more quietly. “But the program will take me a little while to run.”
Fook glanced impatiently at his watch.
“How long?” he said.
“Seven and a half million years,” said Deep Thought.
Lunkwill and Fook blinked at each other.
“Seven and a half million years!” they cried in chorus.
“Yes,” declaimed Deep Thought, “I said I’d have to think about it, didn’t I? And it occurs to me that running a program like this is bound to create an enormous amount of popular publicity for the whole are of philosophy in general. Everyone’s going to have their own theories about what answer I’m eventually going to come up with, and who better, to capitalize on that media market than you yourselves? So long as you can keep disagreeing with each other violently enough and maligning each other in the popular press, and so long as you have clever agents, you can keep yourselves on the gravy train for life. How does that sound?”
The two philosophers gaped at him.
“Bloody hell,” said Majikthise, “now that is what I call thinking. Here, Vroomfondel, why do we never think of things like that?”
“Dunno,” said Vroomfondel in an awed whisper; “think our brains must be too highly trained, Majikthise.”
So saying, they turned on their heels and walked out of the door and into a life-style beyond their wildest dreams.”