Somehow, I find these results fascinating, but also quite sad, because we used a machine to solve it at all. I feel like some half drunk motivated graduate level humans could have figured it out too.

Then again, once you know the answer, perhaps you have an obligation to share it, keeping it to yourself might be unfair to everyone else.

Honestly I’m not entirely sure how I feel about all this. I would gladly welcome any groundbreaking work Claude might do to solve hard problems and move the world forward by decades or even centuries.

But these sorts of fun problems feel like things we should avoid pointing LLMs at. They remind me of those weird programming puzzles that are difficult to solve but incredibly fun to work through.

My concern is that if Claude ends up solving all the fun problems, will humans be left with nothing but the hard, headache-inducing ones? Tao had raised a similar concern, problems that graduate students would have been expected to solve and learn the process, are now things you can simply point an LLM at.

I’m still not sure how I will ever reconcile with this feeling, about any of this. I just find it genuinely sad that we might be automating away not only the difficult work, but also the joy of figuring things out for ourselves.

Especially finding the solution that is based on using a random number generator.

It's like people seeing proof that the future was written in Harry Potter books by reading the first letter of the top of the page of a weird set of pages.

>provided by the NSA with no explanation or justification.

Really? Nobody is concerned about the NSA just cheerfully dictating that? Smells very rainbow-table-y

This is not very exciting

Uh… did you talk to any cryptographers? This is EXACTLY what a weak curve would look like. Imagine that 1 in a thousand, or one in a million keys, selected at random, are vulnerable to some withheld attack. This approach lets you vary the timestamp or number of iterations until a weak key is found, then have plausible deniability afterward. This is why modern systems choose constants in a way with no free choice of parameters (e.g. sqrt of 2 for first constant, cube root for second constant, etc.).

They even note later in the article that viable curves in the generator sequence seem to have been skipped.