[konne88]

I didn't expect such a misleading intro from Knuth. It reads like Claude solved Knuth's math problem. In reality, Claude generated various example solution, and Knuth then manually generalized that to a formal proof. What Claude did is certainly useful, but it would have been nice to be clear about the scope of the contribution in the intro.

[buffalobuffalo]

While not on the same level as these guys, I've done some similar stuff using Claude. This is a classic synergy example, where the output of human + LLM is far greater than just the human or just the LLM working on a problem. My experience has been that the LLM lacks fine grained judgement when it comes to allocating resources, or choosing a direction to work in. But once a direction is pointed out, it can do a deep exploration of that possibility space. Left alone, it would probably just go off on a tangent. But with someone holding the leash and pointing out areas to explore, it is a very useful partner.

[igravious]

> But with someone holding the leash

i've been thinking about why we call them agent harnesses

i know all analogies suck in different ways but here goes:

coding agents are like horses. without a harness and bridle they'll the horse will do as it pleases -- a human can't travel very far and fast by foot but put a bridle and a harness on a horse, give it a bit of coaxing with carrot and stick, add in a bit a pointing the thing in the right direction and bingo you're off to the races!

[whattheheckheck]

Does feel like a mecha suit

[aoeusnth1]

I don't think he's misleading, I think he is valuing Claude's contributions as essentially having cracked the problem open while the humans cleaned it up into something presentable.

[bachmeier]

My interpretation is that Claude did what Knuth considers to be the "solution". Doing the remaining work and polishing up the proof are not necessary to have a solution from this perspective.

[OneManyNone]

Claude did not find a proof, though. It found an algorithm which Knuth then proved was correct.

[iterance]

The insight is the point of research. Proof isn't the desired product of research, it's simply an apparatus that exists for the purpose of verifying and demonstrating correctness of insight.

[CobrastanJorji]

Yes, and his point is that finding that algorithm was, to Knuth, the interesting part. Getting from that to a proof was the boring bit.

[NewsaHackO]

Yeah, and I'm not sure what the other guy's argument is. It's Knuth, the primary researcher, who is giving the praise here. I don't see a possible motivation he would have to falsely give accolades to a AI for a problem he presented, then cleaned up to solve.

[OneManyNone]

That’s fair. Clearly Knuth himself thought it was impressive, that’s a strong signal.

[versteegen]

AFAICT, Claude was not asked to prove its algorithm works for all odd n, but was instead told to move on to even n.

[fooker]

It’s not misleading. This is how research works.

LLMs are really good at the ‘re’ in research.

[rishabhaiover]

That's true but the capability to go back to an older iteration, reflect and find the correct solution (for odd numbers) is, in my book, a sign of undeniable intelligence.

[jdub]

Or, the ability to construct additional sentences influenced by prior ones.

[rishabhaiover]

Those additional sentences are fairly non-trivial to construct, would you agree?

[famouswaffles]

Claude solved it, Knuth developed the proof for the solution.