In this link from two weeks ago, somebody pointed Claude Fable 5 (Max) at a Bongard problem and it made up an answer that has an obvious counterexample.

I don't have access to any paid models, but this is my experience with the free models as well -- either they one-shot the problem or they make up a wrong or incoherent solution. I can't solve every Bongard problem either (and in fact I couldn't solve the one Fable got wrong, and the "correct answer" looks unsatisfying to me), but I don't make up wrong answers.

Would be curious to see how GPT-6 does.

I have no idea what you're hoping the contribution would be. The AdS/CFT correspondence is 29 years old by now and it doesn't seem to apply to our spacetime, where the cosmological constant seems to be positive rather than negative. There are some puzzling consequences of the holographic principle in that scenario as well (https://arxiv.org/pdf/hep-th/0208013), but the linked articles don't talk about them?

Quanta articles are written for people with no background whatsoever, which makes them impenetrable if you have a bit of background and are trying to figure out what they're about. I don't know how good Claude is compared to that -- whenever I try asking any LLM about something I don't understand, it produces a wall of text, I have no idea whether it's correct or relevant, and I look for a textbook or review paper instead.

Comments URL: https://news.ycombinator.com/item?id=49341765

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Edited to add: Found a conversation between actual mathematicians that probably could be used to track this down, but at the moment I'd rather go to sleep than pursue it further. https://xcancel.com/ElliotGlazer/status/2086950873523986440

Math is very hit-or-miss; the complexity of a question does not give much of an indication about how complex the answer will be. Look up the formula for solving a degree-4 polynomial equation to get a purely visual idea how this can look (and then degree-5 suddenly forces you to use complicated new functions). And there are problems (like the Collatz conjecture or P vs. NP) that there doesn't seem to be any promising angle of attack for over at least decades.

I would wager that this is a fundamental part of the structure of math that has been a constant from ancient Greece till LLMs. There are even some formal results, similar to Gödel's theorems, that say that the maximum necessary length of a proof grows arbitrarily fast (e.g. more than exponentially, double-exponentially, or any function with a formula) with the length of the statement being proven.

Point is, math will most likely never suffer from this particular problem.

Maybe there's some sense of "remix" that covers all of that, but then that meaning is not the standard one, or maybe you would concede that this happened in the past, but isn't happening now, but then where's the cutoff, or maybe something else...?

In your analogy, I would love to see some elaboration on the "reflective and spans outside of itself" part -- geometry doesn't work that way, do you have a more intuitive metaphor, or ideally a mechanism, or even better, some examples?

For now, caring about a topic (or having somebody you trust care for you) still gets you better information than asking an LLM.

It seems that there was a perfectly legitimate simulation based on the connectome that got published in 2024, and a very bullshit-y startup that briefly went viral later when it claimed to upload a fly to a computer. Not sure which one you saw.

Comments URL: https://news.ycombinator.com/item?id=48985770

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With the Erdős proof, OpenAI added perspectives from working mathematicians that gave some context -- hope something like that appears for this one eventually.

It's also all charmingly tiny. I was surprised at the quality of the LaTeX generated from a network trained on a single book -- it looks like a proof, has sequential lemmas, closes all brackets...

Also interesting to read the original discussion with a decade of hindsight: https://news.ycombinator.com/item?id=9584325

Comments URL: https://news.ycombinator.com/item?id=48834169

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Comments URL: https://news.ycombinator.com/item?id=48757993

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A few things that confused me while trying to read the paper:

- There's two different methods of cell division mentioned -- mechanical extrusion and the autonomous, protein-driven division. Most of the results (e.g. the five generations) focus on the mechanically driven one, while the autonomous one is more "lifelike". Does the autonomous division have a higher failure rate, or can you get the same results with it as well?

- It's mentioned that the bottleneck for survival of many generations is ribozomes degrading, but also that ribozomes are supplied from the outside. Do the degraded ribozomes actively harm the cell? Or is there some other reason why they cannot be replenished?

- You say that after 5 generations, only 30% of the cells have the correct genome, and it's presented like a problem -- but 30% of 2^5 is more than 10, so this sounds like more than enough for continued survival. Is there something missing in this train of thought? Perhaps other failures that can kill the cell?

And some questions about the implications:

- Do you think that the genome you use is already close to minimal? AFAIK a lot of the minimal organisms found in the wild are parasites of some sort, getting most of their complex molecules from the outside, which is a similar spirit to this (a rich medium and the cell "just" self-duplicating). If the multiple plasmids are causing trouble (per the previous point), would it make sense to try and get rid of some of them?

- Are those minimal genes somehow interpretable -- as in "you need functions X, Y, and Z and cannot avoid them by using a better medium"?

- Do you think this is a plausible stage of very early life?

Now, there's a lot of other reasons to be skeptical (e.g. there's no information on what all of this imaging could actually resolve), but please don't shoot the message.