Henning Dieterichs

@bnielson01 There is also a mathematical proof that says no algorithm can decide in general if a given formal mathematical statement is true. Not even humans in the loop. Every cleverness on one class of problems can be used against it! And still, humans can do math and prove things.

There's a mathematical proof that says no algorithm — no matter how clever, how sophisticated, or how well-designed — can outperform random guessing when averaged across all possible problems. Not A*, not neural networks, not even humans in the loop. Every advantage on one class of problems is paid for, dollar for dollar, somewhere else. It sounds like it should be false. It isn't. Please review the article: the theorem is sound. So you can't just dismiss it. Welcome to the "No Free Lunch Theorem". This raises an interesting question: how can humans be universal learners if this theorem says universal learns are impossible? Make your best arguments here. I hint at one possible resolution to this problem. mindfiretechnology.com/blog/archive/t…

@littmath It is also now trivial to write tools with AI that show you the paragraph of the cited paper, so you (or AI) can easily check that the citation exists and is relevant. (it took me less than an hour to vibe-code the tools needed to get what is shown in the screenshot)

Re: arxiv LLM policies, it is now trivial to catch hallucinated citations, obvious LLM “if you’d like I can etc.” text, and so on, *by using current-gen LLMs*. What we really want is for output to be proof-of-thought, for which the mere existence of a paper no longer suffices.

@NonEuclideanDr1 This pattern reminds me of Rule 30! en.wikipedia.org/wiki/Rule_30

A node with sources of different colors gets the "younger" color. Meanwhile I'm still trying to document all cases of the simplest version. 2/2

Challenged my kid to find a recursive Graph that terminates after gaining some complexity. He solved it by adding complexity to the rule: A node that has exactly one diagonal source changes to the next color, each color has its own recursive rule. 1/2

@littmath The same seems to happen for cellular automata language theory. LLMs try to argue with common sense, but then fail to pin down any coherent technical argument. To quote Sonnet 4.6: > In short: I confused "the obvious construction doesn't work" with "no construction works".

…when I take the exact same prompts that generated these (IMO impressive) solutions and try them on questions in algebraic geometry that I suspect are of comparable difficulty to Erdős problems, they typically produce nonsense (though they can now be helpful with smaller tasks).

Still underrated how uneven frontier models are within math, IMO. I’ve recently been reading through some of the more interesting solutions to Erdős problems and quite enjoying them—here the models are reliably executing nontrivial ideas, combining known techniques, etc. But…

@kirancodes Has there ever been a bug in lean that made it significantly easier/possible to prove a statement, but that didn't make it significantly easier/possible to prove false?

New 0-day in Lean just dropped. Your secure software just got borked. All your bases are mine. kirancodes.me/posts/log-who-…

@tonylfeng "Worthless" is a strong word. That formalization may not advance mathematics directly, as the proof might be "obviously" true/correct to mathematicians. But now it's much more obviously true to non-mathematicians as well. And that is a big win.

Gauss' work was an impressive demonstration of autoformalization, but is there any backing to the claim that it "contributed to mathematicians' understanding of the tools in Dr Viazovska's proofs"? Jeremy Avigad, a mathematician close to the project, writes at arxiv.org/pdf/2603.03684 that "The formalization, on its own, is close to worthless" mathematically.

Very helpful was the Brave MCP server and the Google Scholar API, which AI turned into an MCP server on its own in one prompt. The PDF quotes come from an http server that maps a given range in the extracted text back to the visual bounding boxes.

I've become a fulltime AI addict since January, not being able to stop creating, researching and planning. And I'm still in shock by just how powerful AI is. Any AGI will immediately be an ASI. Here Opus did a literature research for me, it also created all the tools it needed.

I used VS Code Copilot and the debug value editor extension (github.com/microsoft/vsco…) to let AI run/debug a node repl, which it used to go through the papers, extract their text, create embeddings, and look up their metadata.

@Corca_math I love this! Would be interesting to explore what this could do for Lean (which uses unicode math symbols)

Text is a string. Math isn’t. It grows in every direction into multi-line structures. That’s why people still do math on paper. We’re bringing that experience to computers. Corca is WYSIWYG math editor, and it's fast!

Together with ChatGPT, I discovered a fun puzzle I thought was worth sharing: "Finding the Survivor in the Middle" gist.github.com/hediet/a0e9b88… (…or why one-dimensional two-way cellular automata operating in linear time are likely more powerful than their real-time counterparts)

I'm confident that the code is correct because composition has a nice definition of correctness: Applying "e1 composed e2" on a string "s" should equal applying e1 on s, and then e2. A fuzzer verified this for millions and millions of different edits.

Today is a day that I will remember for quite a while - Gemini 3 correctly implemented an algorithm in minutes that I didn't manage to implement in days: Composition of Line/Column-based text edits. I don't even understand the code (but heavily tested it). #diff-5b9bba976759af3b43dcb26d2556dc5349b3ae420684b8f96f43697b81e3d63cR216" target="_blank" rel="nofollow noopener">github.com/microsoft/vsco…

Deleted code in diff editor is now selectable

You asked for more AI analytics in @code - we’re on it. Here’s a peek at some early designs. What would you use these numbers for? What’s missing that would make them genuinely useful?

@VictorTaelin @getjonwithit It's a little bit more complicated than that - for example in "if x >= 0 then x^2 else (-x)^2" - the result of the entire expression doesn't depend on which branch was taken. You would have to employ the time hierarchy theorems/diagonalization!

@getjonwithit this is correct and way less deeper than it sounds. specifically, when a computation depends on a bit of information (via a branching operator, like if/then/else), then, the branches are causally dependent on that bit's result, and they can't run in parallel without wasting work

All parallel operations can be performed sequentially, but not all sequential operations can be performed in parallel. This failure to parallelize is what we call "causality". (Holds true for general relativity, quantum information, Petri nets, monoidal category theory, etc.)

Copilot going open source 🚀🚀🚀 youtube.com/watch?v=GMmaYU… code.visualstudio.com/blogs/2025/05/…

If OpenAIs 4o makes basic math mistakes like this, I don't think it is a good idea to use it for teaching (yet). Me: Can i^(4x) be simplified? 4o: [...] So, the expression simplifies to 1 for any integer or real number x. o1 got the right answer though. chatgpt.com/share/67cc273f…

Introducing the next evolution of completions in GitHub Copilot: Next Edit Suggestions (preview). Most coding activity involves editing existing code as much as it does writing new lines. It's a natural next step for completions to work on existing code as well. Available today in VS Code. Learn more: code.visualstudio.com/blogs/2025/02/…

Finally shipping day 🚀