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Comments (129)

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  jdnier
  > I think Claude Shannon’s spirit is probably proud to know that his name is now being associated with such advances. Hats off to Claude!I didn't realize Claude was named after Claude Shannon!https://en.wikipedia.org/wiki/Claude_Shannon
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  mccoyb
  It's fascinating to think about the space of problems which are amenable to RL scaling of these probability distributions.Before, we didn't have a fast (we had to rely on human cognition) way to try problems - even if the techniques and workflows were known by someone. Now, we've baked these patterns into probability distributions - anyone can access them with the correct "summoning spell". Experts will naturally use these systems more productively, because they know how to coerce models into the correct conditional distributions which light up the right techniques.One question this raises to me is how these models are going to keep up with the expanding boundary of science. If RL is required to get expert behavior into the models, what happens when experts start pushing the boundary faster? In 2030, how is Anthropic going to keep Claude "up-to-date" without either (a) continual learning with a fixed model (expanding context windows? seems hard) or (b) continual training (expensive)?Crazy times.
• 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.
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  ecshafer
  I wonder how long we have until we start solving some truly hard problems with AI. How long until we throw AI at "connect general relativity and quantum physics", give the AI 6 months and a few data centers, and have it pop out a solution?
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  faxmeyourcode
  > Filip also told me that he asked Claude to continue on the even case after the odd case had been resolved. “But there after a while it seemed to get stuck. In the end, it was not even able to write and run explore programs correctly anymore, very weird. So I stopped the search.”Interesting snippet towards the end. I wonder if they were using claude.ai or claude code. Sounds like they ran out of context and entered the "dumb zone."
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  beej71
  From my naive standpoint, LLMs like this seem to have some big strengths. One: possession of a superhuman expanse of knowledge. Two: making connections. Three: tireless trial and error.If you put those three things together, you end up with some cool stuff from time to time. Perhaps the proof of P!=NP is tied to an obscure connection that humans don't easily see due to individual lack of knowledge or predisposition of bias.
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  ainiriand
  Are not LLMs supposed to just find the most probable word that follows next like many people here have touted? How this can be explained under that pretense? Is this way of problem solving 'thinking'?
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  ontouchstart
  Fascinating report by DEK himself.Time to sit down, read, digest and understand it without the help of LLM.
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  iandanforth
  TLDR (story, not math) - Knuth poses a problem, his friend uses Claude to conduct 30 some explorations, with careful human guidance, and Claude eventually writes a Python program that can find a solution for all odd values. Knuth then writes a proof of the approach and is very pleased by Claude's contribution. Even values remain an open question (Claude couldn't make much progress on them)
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  Pat44113
  I asked Claude to solve the pentominoes puzzle made famous by Arthur C. Clarke. It struggled mightily until I told it how I'd solved the problem using 64 bit unsigned integers to represent the board and pieces. Then, it created a C# program that solved the problem very quickly. However, in the 20x3 case it found four solutions when there are only two. Turns out it had incorrectly mapped one of the pentominoes. Sort of a silly mistake; the sort a human might make.
• nphardon
  Must be a fun time to work on open problems. I published my graduate research close to a decade ago, often find myself fantasizing about tackling open problems with Claude.
• taylorius
  I thought Claude Monet - Impressionist techniques applied to coding.
• fazkan
  time to use claude code to understand DEKs paper, in plain English. As someone who did a bit of formal verification in grad school. I feel like, there are a long tail of problems that can be solved by human-model collab like this one. The problems may not mean much but hopefully it can stack up understanding of intelligence.
• dfilppi
  [dead]
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  miroljub
  Solves? It's a part of the training set. Nothing more, nothing less.