@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.
@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)
@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".
@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?
@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.
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 (https://t.co/GWCK31319Q) 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.
Together with ChatGPT, I discovered a fun puzzle I thought was worth sharing: "Finding the Survivor in the Middle"
https://t.co/v0rZwvtC2f
(…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).
https://t.co/7N8nhDSZGY
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!
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.
https://t.co/N4tZAJA77O
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: https://t.co/BjtRy03lVP
Copilot Next Edit Suggestions (NES), an evolution of code completions, is now available in preview.
Based on the edits you're making, NES both predicts the location of the next edit you'll want to make and what that edit should be.