any website with a State/Country dropdown post @typesafeai 's Jev that you can't type into and that you have to scroll needs to be drop kicked into the curb.
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David Petrou retweeted
NFL Player Turned Mathematician (@JohnCUrschel) Solves Problem that Eluded Scholars for Decades
On the growth factor for Gaussian elimination – great interview with Christiane @amanpour
youtu.be/W1uiG8rk2Eg?is… via @YouTube
On the growth factor for Gaussian elimination – great interview with Christiane @amanpour
youtu.be/W1uiG8rk2Eg?is… via @YouTube
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David Petrou retweeted
Over the past year, the Discovery team at @GoogleDeepMind, in a project led by student researcher @dsantosmarco, has made new discoveries in one of the most beautiful open problems at the edge of computation: Finding the 6th Busy Beaver (BB) number.
While most AI math systems roblems, like theorems, this work tackles a different aspect of mathematical creativity: Discovering hidden problems.
For years, the BB Community has pursued one of theoretical computer science’s most captivating collaborative quests: finding the simplest programs that run the longest before halting. Because determining whether these programs ever stop is uncomputable, no universal algorithm can solve it, meaning new mathematical techniques need to be found and invented to make progress.
In this way, the BB challenge serves as an open ended domain for mathematical creativity and, in particular, a generator of hard math problems called Cryptids. These are tiny programs whose halting behavior is governed by and equivalent to deep, unsolved math problems in number theory, similar to the Collatz or Goldbach conjectures. Historically, the BB community had recognized ~20 Cryptids in BB(6), and the best problems were selected for the Busy Math Olympiad (BMO).
Building on their work, Marco built a pipeline powered by Gemini 4 Argon that:
1️⃣ Simulates raw Turing machine traces to compress recurring patterns.
2️⃣ Conjectures mathematical transition rules & runs synthetic experiments to test edge cases.
3️⃣ Proves the equivalence formally in Lean 4. Using this pipeline, Marco and the team discovered 20 new potential Cryptids and verified 33 more machines previously studied in the BB community. All the proofs were open sourced and shared in the community discord channel and we hope that they will help the community to make progress towards resolving BB(6). We also contributed related halting/non-halting proofs directly to the community GitHub repository.
Finding these Cryptids shows hidden links between simple programs and number theory, and helps mathematicians map the limits of computation. I'm also excited about Gemini 4 Argon's ability to help researchers both solve hard problems and accelerate scientific discoveries, of which Busy Beaver is just one example.
Work led by our student researcher @dsantosmarco with paper contributions from @vivek_veeriah, @Dahoas1 , Andrew Bolt, @zuza777 , Satinder Singh, and myself with additional contributions from Hussain Masoom, @maxencefaldor , @MoritzFirsching and Petar Sirkovic.
Read more about it in our paper: arxiv.org/abs/2610.22603
While most AI math systems roblems, like theorems, this work tackles a different aspect of mathematical creativity: Discovering hidden problems.
For years, the BB Community has pursued one of theoretical computer science’s most captivating collaborative quests: finding the simplest programs that run the longest before halting. Because determining whether these programs ever stop is uncomputable, no universal algorithm can solve it, meaning new mathematical techniques need to be found and invented to make progress.
In this way, the BB challenge serves as an open ended domain for mathematical creativity and, in particular, a generator of hard math problems called Cryptids. These are tiny programs whose halting behavior is governed by and equivalent to deep, unsolved math problems in number theory, similar to the Collatz or Goldbach conjectures. Historically, the BB community had recognized ~20 Cryptids in BB(6), and the best problems were selected for the Busy Math Olympiad (BMO).
Building on their work, Marco built a pipeline powered by Gemini 4 Argon that:
1️⃣ Simulates raw Turing machine traces to compress recurring patterns.
2️⃣ Conjectures mathematical transition rules & runs synthetic experiments to test edge cases.
3️⃣ Proves the equivalence formally in Lean 4. Using this pipeline, Marco and the team discovered 20 new potential Cryptids and verified 33 more machines previously studied in the BB community. All the proofs were open sourced and shared in the community discord channel and we hope that they will help the community to make progress towards resolving BB(6). We also contributed related halting/non-halting proofs directly to the community GitHub repository.
Finding these Cryptids shows hidden links between simple programs and number theory, and helps mathematicians map the limits of computation. I'm also excited about Gemini 4 Argon's ability to help researchers both solve hard problems and accelerate scientific discoveries, of which Busy Beaver is just one example.
Work led by our student researcher @dsantosmarco with paper contributions from @vivek_veeriah, @Dahoas1 , Andrew Bolt, @zuza777 , Satinder Singh, and myself with additional contributions from Hussain Masoom, @maxencefaldor , @MoritzFirsching and Petar Sirkovic.
Read more about it in our paper: arxiv.org/abs/2610.22603
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cool new @GoogleDeepMind Minecraft paper (@maxencefaldor, Satinder Singh, @robertarail) (arXiv:2610.22319). afaict, their agents act via a bot API (Mineflayer) which takes in coordinates and issues pathfinder calls.
at Continua Research, we're strictly pixels in, keys out.
at Continua Research, we're strictly pixels in, keys out.
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it places the outer two crystals before the middle one, blocking the square it needs to stand on to push the final crystal into the center. pretty sure most humans hit R and restart the room here.
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looking at full traces, the agent's insight: a placed crystal isn't permanent. instead of resetting, it temporarily nudges the right crystal off its switch to free up the pushing square for the center crystal, then loops over the top to push the right crystal back into place.
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i fucking love Argon. Says stuff like this: "I'm already pondering the power of running both an NVIDIA A100 and a TPU Pod in tandem."
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Gemini 4 Argon impressions: it's still early, but there's a really important aspect that might make it now my workhorse model (above Astra): it's coherence across 1M input tokens, such that the chunks of work assigned are both ambitious /and/ don't require compactions.
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in software engineering, everyone is now a Tech Lead. perhaps soon, in math, everyone is a PhD advisor? problem is obviously around education: took me time to learn how to be a TL -- how does that happen anymore?
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David Petrou retweeted
We discovered a new geometric approach to self-attention!
1) We represents weights as functions in GPU memory, rather than materializing weights. This allows the first model that can sample new layers at inference from a curve(8 for a phone, 24 for a server).
The function is matrices that allows us to sample layers on the curve dynamically, even based on the curvature where there's most information.
2) Hierarchical state beats transformers(NanoGPT) KV cache with 14,000x less state and 50% better CE at 2K context.
3) We use forward pass perturbations between pre-training steps to optimize the model further without tokens.
4) We cache experts using a “bundling” trick based on use-case to further compress what we need to run on GPU.
The goal is to accelerate everyone, including all the auto-researchers, and run frontier models on laptops.
I've been working with a Google researcher and my former professor on this the past few months. The week Fable dropped, our progress exploded with auto-research, but we were still working on publishing a paper.
With the clear explosion of decentralized auto-research on Github, I’m open sourcing our work soon :)
It’s very similar to Integer Mult bounds, as we explore new geometries to compress data, so if you’re interested in helping let me know!
I'm testing auto-research.md rails now and plan to publish the Github by the end of the week!
1) We represents weights as functions in GPU memory, rather than materializing weights. This allows the first model that can sample new layers at inference from a curve(8 for a phone, 24 for a server).
The function is matrices that allows us to sample layers on the curve dynamically, even based on the curvature where there's most information.
2) Hierarchical state beats transformers(NanoGPT) KV cache with 14,000x less state and 50% better CE at 2K context.
3) We use forward pass perturbations between pre-training steps to optimize the model further without tokens.
4) We cache experts using a “bundling” trick based on use-case to further compress what we need to run on GPU.
The goal is to accelerate everyone, including all the auto-researchers, and run frontier models on laptops.
I've been working with a Google researcher and my former professor on this the past few months. The week Fable dropped, our progress exploded with auto-research, but we were still working on publishing a paper.
With the clear explosion of decentralized auto-research on Github, I’m open sourcing our work soon :)
It’s very similar to Integer Mult bounds, as we explore new geometries to compress data, so if you’re interested in helping let me know!
I'm testing auto-research.md rails now and plan to publish the Github by the end of the week!
Cool we just got cited in this paper for the new record for Integer Mult bounds :)
PR49 was the previous record, but we're much further than that now(unverified).
Generating the full Lean proof could still take months, but it's clear Github is accelerating faster than we can he progress in the past few days would normally have taken years.
Thanks to everyone contributing! 🫡
@0xdoug @ryaneshea @dysmemic @mrowdays @cfky_
@dom_scholz @a1kindus @aliromman @Rastats_ @a1kindus and more
arxiv.org/pdf/2610.14263
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gemini 4 argon, nice job!
…udio-523198292110.us-central1.run.app
…udio-523198292110.us-central1.run.app
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maybe a generalization of Metcalfe's Law.
Most of what we call human intelligence lives at the level of society, not the individual. None of us knows how to build a toaster from scratch on our own, yet together we can get to the moon.
The most capable AI today operates the same way: as societies of models.
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