TechTakes

Even in Knuth's account it sounds like the LLM contribution was less in solving the problem and more in throwing out random BS that looked vaguely like different techniques were being applied until it spat out something that Knuth and his collaborator were able to recognize as a promising avenue for actual work.

His bud Filip Stappers rolled in to help solve an open digraph problem Knuth was working on. Stappers fed the decomposition problem to Claude Opus 4.6 cold. Claude ran 31 explorations over about an hour: brute force (too slow), serpentine patterns, fiber decompositions, simulated annealing. At exploration 25 it told itself “SA can find solutions but cannot give a general construction. Need pure math.” At exploration 30 it noticed a structural pattern in an earlier solution. Exploration 31 produced a working construction.

I am not a mathematician or computer scientist and so will not claim to know exactly what this is describing and how it compares to the normal process for investigating this kind of problem. However, the fact that it produced 4 approaches over 31 attempts seems more consistent with randomly throwing out something that looks like a solution rather than actually thinking through the process of each one. In a creative exploration like this where you expect most approaches to be dead ends rather than produce a working structure maybe the LLM is providing something valuable by generating vaguely work-shaped outputs that can inspire an actual mind to create the actual answer.

Filip had to restart the session after random errors, had to keep reminding Claude to document its progress. The solution only covers one type of solution, when Claude tried to continue another way, it “seemed to get stuck” and eventually couldn’t run its own programs correctly.

The idea that it's ultimately spitting out random answer-shaped nonsense also follows from the amount of babysitting that was required from Filip to keep it actually producing anything useful. I don't doubt that it's more efficient than I would be at producing random sequences of work-shaped slop and redirecting or retrying in response to a new "please actually do this" prompt, but of the two of us only one is demonstrating actual intelligence and moving towards being able to work independently. Compared to an undergrad or myself I don't doubt that Claude has a faster iteration time for each of those attempts, but that's not even in the same zip code as actually thinking through the problem, and if anything serves as a strong counterexample to the doomer critihype about the expanding capabilities of these systems. This kind of high-level academic work may be a case where this kind of random slop is actually useful, but that's an incredibly niche area and does not do nearly as much as Knuth seems to think it does in terms of justifying the incredible cost of these systems. If anything the narrative that "AI solved the problem" is giving Anthropic credit for the work that Knuth and Stapprrs were putting into actually sifting through the stream of slop identifying anything useful. Maybe babysitting the slop sluice is more satisfying or faster than going down every blind alley on your own, but you're still the one sitting in the river with a pan, and pretending the river is somehow pulling the gold out of itself is just damn foolish.