Some of them...

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.

It is unfair to dismiss contributions to decades old open problems as equivalent to calculating more digits of pi. It missed the mark by a lot—as does the two bucket simplifaction.

How does calculating more digits of pi help us?

Five (maybe six?) of the results are improvements on bounds. These kinds of problems tend to have some initial advances, and then stall out as the complexity of the bound skyrockets... until some grad student is bored enough to push the boundary. The big-O complexity of matrix multiplication is a good example of how this works: yeah, it's a useful problem, but the solutions are galactic algorithms, and increasingly convoluted.

As someone with a PhD in combinatorics, I believe that I'm qualified to say that, yes, there are problems as useless as calculating more digits of pi.

Your inverted logic does not hold. The fact that such useless problems for bounds exist does not mean that improving bounds is useless. 9 fields medals in the last twenty years, including the one to Terrence Tao, were for improvements on bounds. 3 of the 4 medals in 2022 were for bounds; 2 of these medals were in combinatorics.

I stated that boring bounds improvement problems exist, not that all bounds problems are boring... Sigh.

I agree boring problems exist; bounds may have a fare share of them. None of the bounds problems in this set are even close to this category; many of them are closer to the type of contributions that in the past got recognized by special awards. Your initial replies were misleading.

As someone with a PhD in combinatorics, you're aware that it takes only one counterexample to invalidate a conjecture.

There's nowhere else to move the goalposts. You've already stashed them in the far corner of the parking garage down the street from the stadium. If you go any farther you'll leave the school grounds entirely.

"It's just brute-forcing the search space."

It can move to any place within the search space but it can't move outside of it and it can't move in between the 'pixels'. Human thought can, as human thought has created the search space.

it could also be that they try every possible approach that has been proposed by humans. it seems that was the case for the non sofic group example. humans are not able to do the same at that scale. it's unfortunate that we don't know what's happening behind the hood with these models, and that's a huge danger also for the rest of us without access to them.

> "matrices"

That's like saying human cognition is "neurons." Matrices are an implementation detail. The important part of a language model is the function that maps tokens to contextual embeddings.

It isn't an implementation for neurons, unless you believe in a designing god.

Matrices are an implementation detail in reconstructing the surface of human knowledge. It's a complex surface, but it's a regurgitation.

What's the argument here? It's not about the implementation method, it is about the behavior that emerges from it. You could calculate the next token by hand on paper if you had enough time.

It's incredible how the “Chinese Room” argument, as well as its counterarguments, is still incredibly pertinent despite being now more than 40 years old. Scientific American published many articles on this topic in the Eighties; they seem as fresh as ever.

Yep, it's a facsimile of a filtered subset of all human behaviour.