411–420 of 430 posts
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yep. because I find the bias overly negative. Let me state the negative things about LLMs: they hallucinate. They are not as reliable as humans. They can lie. They can be deceptive. But despite all of this people are so negative about it even when 50% of deveopers now don't write code by hand because of AI. The trend from 0 AI to code being written by AI in a couple years cannot be denied and it also spells out a fut…
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The erdosproblems website shows 851 was proved in 1934. https://www.erdosproblems.com/851 I guess 1051 qualifies - from the paper: "Semi-autonomous mathematical discovery with gemini" https://arxiv.org/pdf/2601.22401 "We tentatively believe Aletheia’s solution to Erdős-1051 represents an early example of an AI system autonomously resolving a slightly non-trivial open Erdős problem of somewhat broader (mild) mathemati…
"The erdosproblems website shows 851 was proved in 1934." I disagree with this characterization of the Erdos problem. The statement proven in 1934 was weaker. As evidence for this, you can see that Erdos posed this problem after 1934.
But evidence that it was posed after 1934 is not really evidence it was not solved, because one of the things we learned from LLMs was that many of these problems were already solved in the literature, or are relatively straightforward applications of known, yet obscure, results. Particularly in the world of Erdos problems, the majority of which can be described as "off the beaten path" and are basically musings in papers that Erdos was asking -- many of these are in fact solved in more obscure articles and no one made the connection until LLMs allowed us to do systematic literature searches. This was the primary source of "solutions" of these problems by LLMs in the cited paper.
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"The erdosproblems website shows 851 was proved in 1934." I disagree with this characterization of the Erdos problem. The statement proven in 1934 was weaker. As evidence for this, you can see that Erdos posed this problem after 1934.
You recommended I look at the erdosproblems website. But evidence that it was posed after 1934 is not really evidence it was not solved, because one of the things we learned from LLMs was that many of these problems were already solved in the literature, or are relatively straightforward applications of known, yet obscure, results. Particularly in the world of Erdos problems, the majority of which can be described as…
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Surely higher level math is just linear combinations of the syntax and implications of lower level math. LLMs are taught syntax of basically all existing math notation, I assume. Much of math is, after all, just linguistic manipulation and detection of contradiction in said language with a more formal, a priori language.
LLMs can write theorems, but can they come up with meaningful definitions?
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Can you? Read minds, I mean. If the answer is "yes"? Then, yeah, AI is not coming for you. We can make LLMs multimodal, teach them to listen to audio or view images, but we have no idea how to give them ESP modalities like mind reading. If the answer is "no"? Then what makes you think that your inability to read minds beats that of an LLM?
This is kind of the root of the issue. Humans are mystical beings with invisible sensibilities. Many of our thoughts come from a spiritual plane, not from our own brains, and we are all connected in ways most of us don't fully understand. In short, yes I can read minds, and so can everybody else. Today's LLMs are fundamentally the same as any other machine we've built and there is no reason to think it has mystical s…
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AI cough LLMs don't discover things they simply surface information that already existed.
You're assuming there aren't "new things" latent inside currently existing information. That's definitely false, particulary for math/physics. But it's worth thinking more about this. What gives humans the ability to discover "new things"? I would say it's due to our interaction with the universe via our senses, and not due to some special powers intrinsic to our brains that LLMs lack. And the thing is, we can feed n…
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I am constantly seeing this thing do most of my work (which is good actually, I don't enjoy typing code), but requiring my constant supervision and frequent intervention and always trying to sneak in subtle bugs or weird architectural decisions that, I feel with every bone in my body, would bite me in the ass later. I see JS developers with little experience and zero CS or SWE education rave about how LLMs are so muc…
Have you ever thought about the fact that 2 years ago AI wasn't even good enough to write code. Now it's good enough. Right now you state the current problem is: "requiring my constant supervision and frequent intervention and always trying to sneak in subtle bugs or weird architectural decisions" But in 2 years that could be gone too, given the objective and literal trendline. So I actually don't see how you can hol…
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LLMs can write theorems, but can they come up with meaningful definitions?
I intended to imply this with "detection of contradiction". Coherence seems to me to be the only a priori meaning. Most of the meaning of "meaning" seems to me to be a posteriori. After all, what is the point of an a priori floating signifier?
The search space is much too rich to be explored anything but greedily in timid steps off the trodden path, and the frameworks (arbitrary) set both the highways and the vehicles by which we move along and out of them.
Now, the argument can be made that the "meta-mathematical" (but outright mathematical, really) setting of frameworks follows the same structure, and LLMs could also explore that space.
Even assuming that, a major roadblock remains: mathematics should remain understandable by humans, and yield fast progress in desirable (by whom? until now, by humans) directions, so the constraints on admissible frameworks are not as simple as "yields to coherent results".
Also, to take a step back, I wonder what the pertinence of using numerical math is to derive analytical math when we can already solve a great deal of problems through numerical methods. For instance, is it worth spending however many MWh on LLMs to derive an analytical solution to an optimization problem, which might itself be very expensive to compute (human-derived expressions tend to be particularly cheap to evaluate precisely because we are so limited; machines (formal calculus for instance) will happily give you multi-page formulae with thousands of operations to evaluate), when there's a vast array of algorithms at the ready to provide arbitrarily precise solutions?
What remains is the kind of math that, arguably, is much more precious to understand than to derive.
It's interesting to me that whenever a new breakthrough in AI use comes up, there's always a flood of people who come in to handwave away why this isn't actually a win for LLMs. Like with the novel solutions GPT 5.2 has been able to find for erdos problems - many users here (even in this very thread!) think they know more about this than Fields medalist Terence Tao, who maintains this list showing that, yes, LLMs hav…
Wait, so this is now a contest (or maybe war) that LLMs are supposed to win?
Wild.
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I am constantly seeing this thing do most of my work (which is good actually, I don't enjoy typing code), but requiring my constant supervision and frequent intervention and always trying to sneak in subtle bugs or weird architectural decisions that, I feel with every bone in my body, would bite me in the ass later. I see JS developers with little experience and zero CS or SWE education rave about how LLMs are so muc…
I agree with you on all of it. But _what if_ they work out all of that in the next 2 years and it stops needing constant supervision and intervention? Then what?