For the uninitiated, Paul Erdős was a pretty famous but very eccentric mathematician who lived for most of the 1900s. He had a habit of seeking out and documenting mathematical problems people were working on. The problems range in difficulty from "easy homework for a current undergrad in math" to "you're getting a Fields Medal if you can figure this out". There's nothing that really connects the problems other than…
The article is about solving a previously unsolved one. This is a harder set of course.
I don't have any opinion about "real intelligence" or not. I'm not a P(doom)er, I don't think we're on the bring of ascending as a species. But I'm also allergic to arguments like "they're just statistical text generators", because that truly does not capture what these things do or what their capabilities are.
Just to clarify because I’m not sure I understand: So you agree that LLMs are in fact statistical text generators but you don’t like people use that fact in arguments about the capabilities of the things?
Not parent but I think you're being rather dense. They are _obviously_ statistical text generators. There's plenty of source code out there, anyone can go and inspect it and see for themselves so disputing that is akin to disputing the details of basic arithmetic.
But it is no longer useful to bring that fact up when conversing about their capabilities. Saying "well it's a statistical text generator so ..." is approximately as useful as saying "well it's made of atoms so ...". There are probably some very niche circumstances under which statements of each of those forms is useful but by and large they are not and you can safely ignore anyone who utters them.
Yes, but don't we expect GPT 5.5 Pro will eventually be a free tier? Maybe I'm missing something because I only use the free tier. But the free tier has gotten way better over the last few years. I'm pretty sure, based on descriptions on this site from paid subscribers, that the free tier now is better than the paid tier of say 2 years ago. That's the lag I'm wondering about.
Free ChatGPT is like a fast car with a barely responsive steering wheel. Guardrails on that thing are insane. Even for math. It wont let you think. It will try to fix mistakes you havent even made yet based on intent that was ascribed to you for no reason. It veers off in some crazy directions thinking that's what you meant and trying to address even a little bit of that creates almost a combinatorial explosion of ev…
So this doesn't happen in the paid plans of ChatGPT? But why?
Question for those who believe LLMs aren't intelligent and are merely statistical word predictors: how do you reconcile such achievements with that point of view? (To be clear: I'm not agreeing or disagreeing. I sometimes feel the same too. I'm just curious how others reconcile these.)
Those things aren't mutually exclusive. They are demonstrably statistical token predictors (go examine an open source implementation) and they clearly exhibit intelligence.
Worth mentioning, though, that people have already tried running all of them through LLMs at this point. So this is proof of the models actually getting stronger (previous generations of LLMs were unable to solve this one).
Not definitively. LLMs are stochastic with respect to input, temperature and the exact prompt. It's possible that the model was already capable of it but never received the exact right conditions to produce this output.
Every model is able to solve each problem, given the right prompt. (Worst case, the prompt contains the solution.)
It seems like alot of scientific advancements occurred by someone applying technique X from one field to problem Y in another. I feel like LLMs are much better at making these types of connections than humans because they 1) know about many more theories/approaches than a single human can 2) don't need to worry about looking silly in front of their peers.
As a civilization we went the left-brained/sequential/language based way of thinking (with computers and AI being the crown achievement of it). Personally i for example remember like around 3rd grade i switched from the whole-page-at-once reading mode into the word by word line by line mode and that mode stuck with me since then (at some point while at the University i had for some period of time, probably it was the peak of my abilities, some more deep/wide/non-linear perception into at least my area of math specialization, though not sure whether it was a mastery by the left brain or the right brain got plugged in too) LLMs will definitely beat us in that sequential way of thinking. That makes me wonder whether we will have to push into our whatever is still left there right-brainness, and whether AI will get there faster too. May be we'll abandon the left-brain completely leaving it to AI.