alt Hacker NewsReplace philosophers for mathematicians and Douglas Adams was spot on again.
Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this.
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"Yes we are," insisted Majikthise. "We are quite definitely here as representatives of the Amalgamated Union of Philosophers, Sages, Luminaries and Other Thinking Persons, and we want this machine off, and we want it off now!"
"What's the problem?" said Lunkwill.
"I'll tell you what the problem is mate," said Majikthise, "demarcation, that's the problem!"
"We demand," yelled Vroomfondel, "that demarcation may or may not be the problem!"
"You just let the machines get on with the adding up," warned Majikthise, "and we'll take care of the eternal verities thank you very much. You want to check your legal position you do mate. Under law the Quest for Ultimate Truth is quite clearly the inalienable prerogative of your working thinkers. Any bloody machine goes and actually finds it and we're straight out of a job aren't we? I mean what's the use of our sitting up half the night arguing that there may or may not be a God if this machine only goes and gives us his bleeding phone number the next morning?"
Replies
>Whilst current models can't 'intuit
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.
> Whilst current models can't 'intuit' and come up with conjectures
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.
> they can certainly disprove some of them very quickly through the kind of grind that humans can't do
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.
> Whilst current models can't 'intuit' and come up with conjectures
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.
Ahh, but you missed the continuation, where they get to the heart of the matter: money.
"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.”
From a mathematician who was intimately familiar with some of these problems [0]
>I don’t understand it yet. Maybe it’ll take me an afternoon to check all the calculations, but what would still be missing is why this was an approach that would’ve made sense in the first place. Is there some broader context or theory within which this would’ve been the obvious thing to do? What other results can be proven using these techniques? What is it telling us about quantum information or operator theory? I have no idea. I spent about an hour this morning asking ChatGPT these questions, but it’s somewhat frustrating because it speaks with a mishmash of physicist, operator algebraist, quantum information theorist-lingo, plus the usual LLM breezy lilt that annoys everybody.
They certainly seem to have "intuited", in a way that is not immediately obvious to experts in the field, the way to solve at least some of these problems. This was not just simply grinding away at a method that humans already knew would work and just hadn't gotten to yet.
[0] https://nitter.poast.org/henryquantum/status/208362369543662...