Canadian mathematician Jacob Tsimerman, a fresh Fields Medal recipient, has announced the founding of the Mathematical A.I. Safety Institute (MAISI). The article The Mathematical AI Safety Institute wants to prove AI is safe the way cryptographers prove codes are unbreakable appeared first on The Decoder .

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The Decoder / 1:45 PM

GPT-6 Astra gives mathematicians a breather, and OpenAI says that's by design

OpenAI's GPT-6 Astra tops the ErdosBench for open math problems, even though chief scientist Jakub Pachocki says math was deliberately not a priority. Instead, OpenAI is pouring resources into recursive self-improvement and alignment research. That supports the theory of an increasingly "spiky" AI development path, with extreme strength in select domains rather than broad progress, at least as long as AI can't improve itself and still needs targeted optimization with human-generated data. The article GPT-6 Astra gives mathematicians a breather, and OpenAI says that's by design appeared first on The Decoder .

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The Verge AI / 11:00 AM

Mathematicians want proof OpenAI didn’t use their work

Another researcher is challenging OpenAI about the data driving its increasingly impressive array of mathematical discoveries. Just days after a bitter row erupted over whether the company's models benefited from unpublished work, a second mathematician has come forward accusing the AI giant of unethical and "dishonest" behavior and a lack of transparency about the origins […]

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Simon Willison LLMs / 11:55 PM

Some thoughts on the Navier–Stokes Millennium Prize Problem

On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem , one of the seven Millennium Prize Problems that have been subject to a $1,000,000 prize since May 24th, 2000. The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster, an NYU mathematics professor who was collaborating on related problems with Levent Alpöge, an accomplished mathematician who currently works for Anthropic. Tristan's complaint accompanied a hastily published version of their own results. Here's the PDF describing what happened . The very short version is that Tristan and Levent worked on the problem for almost a year, making extensive use of Claude and Codex (mainly GPT-5.6 Sol), then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear and Tristan and Levent heard that OpenAI had heard that Anthropic had resolved "a major open problem", so they reached out and learned that OpenAI had a team working on a related problem, with a similar approach. Quoting Tristan: I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer. It gets more complicated from there. The OpenAI team offered to wait for Tristan to publish, or to have him author a paper about their result, but were clear that Levent would not be invited as a co-author due to OpenAI's competitive relationship with his employer. Here's how OpenAI described their work: On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems. [...] The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra. Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. In the process of resolving the Navier–Stokes problem, the agents sent 2.7 million messages and used approximately 130 billion output tokens. (We don't know the cost structure of the internal model they used, but 300 billion output tokens at public API prices for GPT-6 Astra would cost $15,000,000 .) Here's where they provide their perspective on Tristan and Levent's work (emphasis mine): Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. [...] We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced). My interpretation of what happened here is that OpenAI heard that some Millennium Prize problems had been solved using LLMs and saw this as an opportunity to demonstrate the power of their latest model, without thinking too hard about the optics of scooping a team who had been using OpenAI's own models to work on this problem for the best part of a year. This situation appears to mirror what's happening in the world of computer security right now. Anil Madhavapeddy recently pointed out that Just a rumour of a bug is enough to find a security exploit these days , because if someone knows that some software has an unpatched vulnerability, they can set their agents the task of finding it. Is the same now true of mathematics? Just knowing that there is an unpublished solution to a problem might trigger millions of dollars in LLM spending to get there first. This also highlights one of my ongoing frustrations about how all of this works. When an AI lab says that my data is "used to improve model performance", what does that actually mean ? My two favourite hypothetical questions regarding this used to be: If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe how.) If I brainstorm with ChatGPT about potential new directions for my company, what's the chance that information might be exposed to a competitor in six months' time who asks "what might company X plan to do next"? My new preferred hypothetical for this is: If I use ChatGPT to help me partially solve a Millennium Prize problem, what are the chances that my work will influence training such that a later model helps someone else solve it first? Via Hacker News . Tags: mathematics , ai , openai , generative-ai , llms , training-data , ai-ethics

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Import AI / 12:26 PM

Import AI 472: DeepMind's cheating math agents; populist AI policies; and Forethought theorizes a nightwatchman

Plus, a machine hermeneutics story

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Latent Space / 3:15 PM

🔬“We have foundation models for language, not for physics” — Anima Anandkumar, Bren Professor of Computing

Anima Anandkumar has spent two decades in AI, from classical math to deep learning and back. Now she's using it to model the physical world, from weather to fusion reactors.

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Import AI / 1:12 PM

Import AI 470: No rights for machines; automating environment generation with SPADE; and building better GPU kernels with Hawkeye

Differential acceleration of cyber, math, and AI

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Bloomberg AI / 2:37 PM

Bonta Says Meta Put Profit Over Children’s Safety

California Attorney General Rob Bonta joins Bloomberg This Weekend and calls the landmark youth safety case against Meta a “tobacco moment,” alleging the company knowingly designed Facebook and Instagram features that harmed children and put profit ahead of their safety. Bonta tells hosts Joe Mathieu and Carol Massar the states are seeking financial penalties as well as changes to Meta’s products, while the company denies the allegations and says it has worked to make its platforms safer for young people. (Source: Bloomberg)

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Bloomberg AI / 12:21 PM

Meta Faces Landmark Trial Over Youth Harm Claims

Meta faces a landmark federal trial brought by 29 states over allegations that Facebook and Instagram were deliberately designed to addict young users and that the company improperly collected children’s data. Bloomberg News Tech Reporter Alexandra Levine joins Joe Mathieu and Carol Massar on Bloomberg This Weekend to explain that the case could expose Meta to substantial penalties and potentially more consequential court-ordered changes to how its platforms operate. (Source: Bloomberg)

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AWS Machine Learning Blog / 4:21 PM

Determining playoff clinching scenarios in the NHL using constraint programming

The AWS Generative AI Innovation Center built an automated system that uses constraint programming and custom tree search to determine, with mathematical certainty, when and how an NHL team clinches a playoff spot. The approach was validated against four full NHL seasons of officially published results.

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BAIR Blog / 9:00 AM

From CUDA to MLX: How K-Search Brings Decades of Kernel Expertise to Apple Silicon

Figure 1: CUDA-to-MLX optimization translation map. CUDA optimization knowledge can be translated into architecture-native MLX strategies rather than copied instruction-for-instruction. We face a new epoch in computing. Hardware is changing rapidly — not just faster GPUs, but a growing range of chips from different vendors, each with its own architecture and often tailored to specific AI workloads. Software is changing just as fast, and AI coding tools now generate in minutes what took months of effort a few years ago. With so much of computing now centered on AI, GPU kernels are a crucial component of its success. These are the low-level programs that run inside the GPU, and writing efficient ones is far from obvious — it takes years of expertise to get right. Transferring a kernel from one vendor’s hardware to another is harder still, and often means rediscovering the same optimizations from scratch. The CUDA ecosystem, for example, has accumulated decades of hard-won kernel expertise: hand-tuned implementations of attention, state space models, and other critical operations representing thousands of engineering hours. Newer hardware ecosystems (Apple Silicon, custom AI accelerators, and others) are growing fast but lack this depth. In this work we ask whether that expertise can be transferred automatically. We built on K-Search , an evolutionary kernel search framework introduced by Cao et al. at Berkeley Sky Lab that uses AI to optimize GPU kernels, and extended it with a backend for MLX — Apple’s machine-learning framework for its own Apple Silicon chips. We developed a novel structured CUDA-to-MLX translation layer that lets K-Search take existing CUDA kernels as a knowledge base and adapt them into high-quality GPU kernels for Apple Silicon, rather than rebuilding from scratch. We show that our approach reaches near-expert level performance on Apple Silicon with 0.97x speedup compared to the native MLX Attention kernel, and up to a 20x prefill speedup over the community mlx-lm implementation on the Mamba SSM kernel; we report the numbers, and how much of the gain comes from the translation layer, in the sections below. Although we focus on MLX kernels for Apple Silicon, the method is not specific to MLX and applies to any ecosystem where CUDA expertise is transferable. Why MLX? Apple’s MLX framework has seen remarkable adoption since late 2023. With Apple Silicon in hundreds of millions of MacBooks and Mac Studios, MLX enables local AI inference without cloud costs. The unified memory architecture makes it especially attractive for mid-sized models (7B–70B parameters on M series chips). Yet beneath this momentum lies a significant gap: many performance-critical kernels that the NVIDIA ecosystem takes for granted: paged attention, optimized SSM scan kernels, fused MoE routing are either absent or naive without hardware-specific tuning. MLX runs models correctly but often leaves significant performance on the table. This gap is what motivates the rest of this post. What is K-Search? K-Search is an evolutionary kernel optimization framework originally developed by our first author Shiyi Cao at UC Berkeley Sky Lab. Given a naive kernel and a hardware specification, it runs an iterative optimization loop: an LLM reasons about which optimizations to try next, a code-writing model generates candidate kernels, and those candidates are compiled and benchmarked on real hardware. Measurements feed back into the search, which keeps refining, pursuing promising directions and dropping dead ends until performance converges. Algorithm 1: K-Search via co-evolving world models. The search alternates between selecting the most promising action, instantiating and evaluating code until improvement stagnates, and evolving the world model through insert, update, and prune operations. Adapted from Cao et al. (2026) . Search is grounded by a Spec: a domain-specific document encoding hardware rules, optimization patterns, and mathematical constraints which keeps generated code from hallucinating invalid primitives and ensures candidates will actually compile and run efficiently. In our runs, a single model (Gemini 3.5 Pro Preview) plays both roles: it maintains the reasoning state and writes the kernels. The reasoning half is prompted as a “GPU kernel performance engineer” and asked to work through a fixed analysis before proposing anything: classify the kernel (reduction, scan, attention/softmax, …), rewrite the reference computation in canonical form, map out data layout and access patterns, and hypothesize the likely bottleneck (bandwidth, latency, compute, or synchronization) in each runtime regime. Only then does it emit candidate optimizations, each as a single change implementable in one iteration. We call the persistent reasoning state a world model . Rather than a flat list of things to try, it is a decision (prefix) tree: each root→leaf path composes a full optimization plan, and sibling branches are competing alternatives. Every node is scored — an overall_rating in [0, 10], a confidence in [0, 1], and per-node impacts on memory bandwidth, register pressure, and compute/hardware fit — so the search can rank partial plans and expand the most promising ones. The tree persists and grows across rounds: refining an idea adds a child node rather than overwriting its parent, and if the best score fails to improve for a few rounds (a stagnation window) the search backs off to explore an alternative branch. A single node, as it appears mid-run on the attention kernel, looks like this: { "action" : "Replace the threadgroup-memory softmax reduction with a register-only reduction: each SIMD group owns 8 query rows and reduces across lanes with simd_shuffle_xor, removing a threadgroup_barrier." , "difficulty_1_to_5" : 4 , "impacts" : { "memory_bandwidth" : 8 , "register_pressure" : 4 , // risk: spill if Br > 8 "compute_hw_fit" : 9 // SIMD width 32 ; keep tile 8 x 8 }, "overall_rating_0_to_10" : 8 , "confidence_0_to_1" : 0.7 } Listing 1: Example K-Search world-model node. Each candidate optimization records a concrete action, estimated hardware impacts, an overall priority rating, and the model's confidence. Figure 2: Overview of K-Search. The framework operates on a Search State $S_t$ structured as a search tree. The tree consists of Closed nodes (blue, visited states with attached program like $x_{12}$) and a Frontier of Open nodes (orange, pending hypotheses like $u_{13}$). The workflow iterates through three phases: (1) Action Selection , where the most promising action node is retrieved from the frontier based on world model estimated priority score $V$; (2) Local Refinement , where a stochastic policy $\pi_{\mathrm{code}}$ samples concrete implementations until stagnation; and (3) World Model Update , where the LLM reasons over the trajectory to update the search tree via Insert (adding new actions), Update (adjusting $V$, e.g., $u_{11}$ dropping from 0.9 to 0.6), and Prune (removing less promising nodes like $u_{10}$). The original K-Search paper evaluated this search strategy on CUDA kernels from FlashInfer. Across GQA decode, MLA decode, MLA prefill, and MoE, K-Search improved more consistently than OpenEvolve and ShinkaEvolve over the same 120-iteration budget. These results establish the search framework we build on here; the remainder of this post asks whether its optimization knowledge can transfer beyond CUDA. Figure 3: Main results from the original K-Search paper. Across three runs, K-Search achieves stronger best-so-far search scores, per-workload kernel performance, and speedup distributions than OpenEvolve and ShinkaEvolve on four FlashInfer CUDA kernels. Reproduced exactly from Cao et al. (2026) . Building an MLX backend To bring K-Search to Apple Silicon, we first built a native MLX backend. We implemented a full MLX-specific task adapter for K-Search, including: An MLX task backend in k_search/tasks/ handling kernel compilation and execution on Apple Silicon via MLX’s Metal/C++ APIs. Updated kernel generator prompts for writing and modifying Metal/MLX kernels. MLX-specific benchmarking integration using mlx.core measurement utilities. Translating CUDA expertise to MLX However, the more interesting challenge was not simply running K-Search on MLX. The key insight is that expert CUDA kernels encode decades of optimization knowledge that is transferable to Apple GPU if you can bridge the conceptual gap. Simply handing an LLM a CUDA kernel and asking it to port it is not enough: without deep hardware context, it produces code that is syntactically valid but architecturally wrong (wrong tile sizes, invalid primitives, mismatched memory assumptions). Our translation layer consists of: Concept mapping tables: A structured glossary of CUDA primitives and their MLX/Metal equivalents with hard constraints. For example: __shared__ maps to Metal threadgroup memory but with a hard 32 KB limit (vs. NVIDIA’s 48 KB) warp_reduce maps to MMA (preferred) __syncthreads() becomes threadgroup_barrier(mem_flags::mem_tg) H100’s ~3.35 TB/s HBM3 maps to M3 Max’s ~400 GB/s unified DRAM a bandwidth difference that reshapes which optimizations are worth pursuing. MLX-specific hints and patterns: Concrete code-level patterns for operations with no direct CUDA equivalent, such as register-based row reductions using simd_shuffle_xor in an 8×8 MMA tile layout, or the “exp2 trick” (replacing $exp(x)$ with $exp_2(x \log_2 e)$) for faster softmax on Apple’s fast $exp_2$ hardware instruction. Reusable assertions: Expert kernel behaviors reframed as properties the evolutionary search must preserve, rather than code to copy. Matching expert kernel performance: the Attention kernel We evaluate three configurations of an MLX attention kernel for Apple Silicon: (1) a naive baseline, (2) pure evolution with no additional provided context, and (3) a full context translation layer, which supplies the optimizer with architecture-specific implementation knowledge extracted from high-performance kernels (e.g., FlashAttention-2), letting the evolutionary search reason about implementation strategies rather than starting from a naive kernel. Together, these three configurations let us isolate the exact impact of the translation layer. Figure 4: Performance scaling of the Attention Kernel through stacked optimizations. The "Full Context" configuration successfully discovers and implements advanced strategies like double buffering and loop unrolling, achieving near-expert performance. The jump from 0.26× to 0.97× the speed of Apple’s state-of-the-art attention kernel — illustrates how much the translation layer matters. With full context, the evolved kernel independently discovers the key optimizations in FlashAttention 2: threadgroup memory tiling, online softmax, K-transposition for memory access, and the exp2 trick. The last of these replaces every softmax exponential with a base-2 exponential, \[e^x = 2^{x \log_2 e},\] which is exact and lets the kernel use Apple’s fast fast::exp2() hardware instruction directly instead of paying for a base conversion at runtime. A 20× faster prefill: the Mamba SSM kernel To evaluate whether K-Search generalizes beyond attention kernels, we applied it to the state-space model (SSM) kernel used by Mamba. Unlike attention, the computational bottleneck is a recurrent state update rather than a softmax, providing a substantially different optimization challenge. We compare the evolved implementation against the community MLX implementation (mlx-lm) and the PyTorch reference implementation (mamba.py) on an M1 Max. Evaluated on mamba-370m f16, M1 Max 64GB: Metric mlx-mamba (ours) mlx-lm (community) mamba.py Decode 152 tok/s 116 tok/s 40 tok/s Prefill L=512 5,751 tok/s 329 tok/s 1,089 tok/s Prefill L=1024 6,010 tok/s 327 tok/s 1,127 tok/s Prefill L=2048 6,612 tok/s 326 tok/s 1,092 tok/s Prefill L=4096 6,743 tok/s 339 tok/s 1,042 tok/s Table 1: Prefill and decode throughput on mamba-370m (f16, M1 Max 64GB). mlx-mamba (ours) reaches ~20× higher prefill throughput than the community mlx-lm baseline, while decode remains comparable. The ~20× prefill speedup over mlx-lm comes down to one difference: mlx-lm does not implement a parallel scan for the SSM. The state recurrence \[h_t = \bar{a}_t h_{t-1} + \bar{b}_t\] looks inherently sequential, but each step can be written as a pair $(\bar{a}_t, \bar{b}_t)$ under the associative combine \[(a_2, b_2) \circ (a_1, b_1) = \left(a_2 a_1,\ a_2 b_1 + b_2\right),\] which reproduces the recurrence exactly. Because the operator is associative, the whole sequence can be evaluated with a parallel (prefix) scan in $O(\log N)$ dependent steps instead of $O(N)$. mlx-lm skips this and processes tokens one at a time, leaving most of Apple Silicon’s compute idle; our evolved Metal kernel applies the scan and makes much fuller use of GPU throughput. The gain shows up in prefill, where the full sequence is available to scan in parallel, and not in single-token decode, where there is only one new token per step and no scan to parallelize — which is why the decode row is roughly flat while prefill is ~20×. mamba.py is slow on both prefill and decode because it is a PyTorch reference implementation that falls back to CPU or MPS on Apple Silicon, forgoing the hardware-specific optimizations that MLX’s Metal backend makes possible. What’s next? On the two kernels we studied, AI-driven evolutionary kernel search grounded in structured cross-platform translation knowledge reached near-expert performance on Apple Silicon without a team of GPU experts starting from scratch. We do not yet know how far this generalizes, but the result is encouraging. For us the main takeaway is that the bottleneck was not the LLM’s ability to write Metal code, but the quality of the context and constraints we gave it. Our CUDA translation layer converts existing NVIDIA kernel expertise into actionable guidance for Apple Silicon, and lets K-Search’s evolutionary search do the rest. We are actively extending this work in several directions: supporting new architectures, with current efforts focused on developing new kernels for the IBM Spyre AIU and broader hardware targets; adding more kernels such as paged attention and fused MoE routing; and improving integration with the K-Search evolution loop to make translation context even more automatic. Acknowledgements This work was carried out by IBM Research and builds on K-Search from the UC Berkeley Sky Lab ( Cao et al., 2026 ). We welcome collaboration and feedback from the MLX and broader AI systems communities. If you are working on kernel optimization for non-CUDA hardware, we would love to hear from you. Citation @article { cao2026k , title = {K-Search: LLM Kernel Generation via Co-Evolving Intrinsic World Model} , author = {Cao, Shiyi and Mao, Ziming and Gonzalez, Joseph E and Stoica, Ion} , journal = {arXiv preprint arXiv:2602.19128} , year = {2026} } Appendix: Try it yourself The MLX backend is built on top of the open-source K-Search repo, so the results here can be reproduced directly. The steps are: 1. Clone and install git clone https://github.com/caoshiyi/K-Search.git cd K-Search uv pip install openai wandb uv pip install git+https://github.com/caoshiyi/flashinfer-bench-ksearch.git 2. Set your credentials Open the relevant script under scripts/ and set three variables at the top: KSEARCH_ROOT = /path/to/K-Search API_KEY = your-llm-api-key 3. Run kernel search # Optimize Flash Attention on Apple Silicon (world-model mode) bash scripts/mac_flash_attention_wm.sh # Or a Mamba SSM kernel, e.g. the selective scan bash scripts/mamba_selective_scan_fwd_wm.sh Full CLI reference and documentation are in the README.

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Hacker News AI / 7:04 PM

Solve@Home: An open version of OpenAI's 10k-agent approach to hard math

HN 2 pts · 0 comments

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Hacker News AI / 5:51 AM

The Math Under Every AI Model: James Wilkinson and Backward Error

HN 1 pts · 1 comments

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The Verge AI / 8:53 PM

Drama swirls around OpenAI’s legendary mathematical milestone

OpenAI says it found a solution to a major math problem that has remained unsolved for around 90 years, as reported earlier by The New York Times and Wired. In a blog post on Tuesday, OpenAI announced that it discovered a solution to the Navier-Stokes problem - which relates to the flow of liquid and […]

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Hacker News AI / 12:08 PM

Show HN: Ramanujan – Multi-Model Agent for Research in Computational Maths

HN 5 pts · 0 comments

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The Decoder / 7:25 PM

GPT-6 Astra is the first model making OpenAI willing to declare the "AGI era"

OpenAI has released GPT-6 Astra, its most capable model yet. President Greg Brockman says it marks the start of the "AGI era." Astra tops benchmarks in math, coding, and cybersecurity and is the first model OpenAI rates as "critical" under its safety framework. During testing, it independently found two previously unknown zero-day vulnerabilities. The article GPT-6 Astra is the first model making OpenAI willing to declare the "AGI era" appeared first on The Decoder .

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Hacker News AI / 7:49 PM

Russian Mathematicians Taught AI How to Talk to Each Other Without Using Words

HN 1 pts · 1 comments

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Hacker News AI / 1:28 PM

UC Berkeley professor admits to using AI to edit op-ed on students' math skills

HN 2 pts · 1 comments

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The Verge AI / 2:00 PM

Welcome to the AI crisis in math

Today on Decoder, I’m talking with Robert Hart, The Verge’s London-based AI reporter, about what AI is doing to the field of mathematics and the existential crisis many lead mathematicians are having about it. OpenAI just published a set of solutions to longstanding problems in math that went off like a bombshell in the field. […]

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Hacker News AI / 9:26 AM

Lea – An agent backbone for mathematician-led formalization

HN 1 pts · 0 comments

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Hacker News AI / 9:17 PM

Asked AI to do a mini math breakthrough. It did a mini breakthrough

HN 4 pts · 1 comments

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The Decoder / 6:07 PM

Ex-OpenAI researcher bets $100 billion will flow into training data because scaling alone won't cut it

Former OpenAI employee Andrew Ho and Cambridge researcher Adam Hunt see a growing problem with large language models. Instead of becoming more versatile, the models are becoming more specialized, excelling at coding and math while stagnating or even regressing in other areas. Ho is leaving OpenAI to start a company focused on specialized training data and predicts that AI labs will need to spend more than $100 billion on targeted data collection. The article Ex-OpenAI researcher bets $100 billion will flow into training data because scaling alone won't cut it appeared first on The Decoder .

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TechCrunch AI / 5:32 PM

OpenAI fought dirty on career-making math problem, says NYU mathematician

There is a $1 million bounty for the first person providing a solution to the Navier-Stokes existence and smoothness problem.

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arXiv AI/ML / 4:59 PM

arXiv paper: A Theoretical Analysis of Generalization Dynamics in Neural Networks under Gradient Descent with Weight Decay

A new arXiv AI paper by Yuqing Wang, Ioannis G. Kevrekidis, and Mikhail Belkin studies A Theoretical Analysis of Generalization Dynamics in Neural Networks under Gradient Descent with Weight Decay.

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arXiv AI/ML / 4:42 PM

arXiv paper: Variational Continuation for Double Pendulum Periodic Orbits

A new arXiv AI paper by Leo Yao, Ziming Liu, and Max Tegmark studies Variational Continuation for Double Pendulum Periodic Orbits.

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Simon Willison LLMs / 7:42 PM

One-shotting a Raccoon Heist game using Claude Fable 5

Back in 2022 I tweeted screenshots of a game concept generated by GPT-3 and some concept "art" created using DALL-E. Today, on the fourth anniversary of that tweet, I decided to see if Claude Fable 5 (running in Claude Code for web ) could build the entire game from the content of that tweet. It did a pretty good job of it! You can play the game here . Here's the GitHub repo , and a short video demo: Your browser does not support HTML5 video. How I built this This is the August 5th, 2022 tweet : My GPT-3 prompt back then was: Write a detailed product description of a computer game where a team of raccoons go on heists. This was in the text completion days, where you asked GPT-3 to complete the rest of the text. It completed: In "Raccoon Heist", you and your team of thieving raccoons are tasked with pulling off a series of daring heists. From robbing banks to stealing priceless art, no job is too big or too small for your furry crew. You'll need to use your wits and your skills to avoid the police and make a clean getaway with the loot. With exciting gameplay and a charming cast of characters, "Raccoon Heist" is the perfect game for anyone looking for a light-hearted caper. My prompt to DALL-E was short: Screenshot from a video game where a team of raccoons go on a heist Today's experiment: can I dump those screenshots into Fable 5 with a prompt telling it to write a game, then leave it to its own devices and get a working game at the end? Setting Claude Code for web up to use GitHub Pages A frustrating thing about Claude Code for web is that it can be hard to test what it's working on while it's still working. I've been using GitHub Pages to work around that limitation, and found it to work really well. Here's my process: Create a new repository for the project at https://github.com/new - this can be public or private, the trick works equally well for both. Start a Claude Code for web session, in the Claude iPhone or Desktop apps or in the browser at https://claude.ai/code Tell Claude what to work on, and encourage it to commit an index.html page as quickly as possible. This will create a branch with a name like claude/3d-raccoon-heist-game-50n293 Navigate to the Settings -> Pages area for the repository ( github.com/simonw/raccoon-heist/settings/pages in my case), select "Deploy from a branch", pick the branch name, and hit Save. That's all it takes! Within about 30 seconds of each push the latest content will be visible at yourname.github.io/your-repo/ . If you do this with a private repo, anyone who can guess the name of the repo will be able to view the published content. I don't worry much about this myself. The Fable 5 prompt Here's the prompt I gave Fable 5 (written in the notes app on my phone - this entire project was conducted on mobile). I accompanied it with the two images from the original tweet. Build this 3D game, for the browser. This repo is configured to serve static files so make sure there is an index.html that loads everything else. Make sure it is mobile-friendly (touch controls, works well on small screens). You have an OpenAI API key and access to their image generation model APIs, use that for textures to use with your 3D models. Docs here: https://developers.openai.com/api/docs/guides/image-generation - use gpt-image-2 Work independently - do not ask me to make any further design decisions. Make sure the game is fun, a little surprising, has good raccoon heist vibes, and is visually pleasing. Commit and push as often as possible so I can preview your work - start with an index.html that presents a title screen, then build from there. Append to a notes.md file as you work, including your changes to that as part of every commit. I didn't make any technology choices. I assumed (correctly) that it would probably use Three.js based on previous experiments. Giving Claude access to an OpenAI key turns out to work really well for filling in gaps in its capabilities - in this case we needed some way to generate images to use as textures. Fable is very good at prompting image generators! I said "Work independently - do not ask me to make any further design decisions" because I wanted to see if it could produce a full, working game without any further input from me. I also said "Commit and push as often as possible so I can preview your work". When you use Claude Code in the Claude iPhone app you give it a GitHub repository and it works in a branch. Telling it to "push as often as possible" means commits start landing in that branch straight away. I like asking for notes.md as a bit of added flavor - here's that finished file , and the entry it made when it added the dog: New escalation: from night 3 the yards get a patrolling guard dog — a low-poly brown hound with a spiked red collar and a wagging tail. It wanders between random spots, and within 12 units it catches your scent and tracks you by smell (line of sight is irrelevant — it's all nose, shown by a 👃 over its head and barking). It gives up if you open a 17-unit gap. Getting caught messages are now source-specific: guard / headlights / hound. Verified wander → track → caught with an automated test. Reviewing the transcript You can access the Claude Code shared session , and I also used my claude-code-transcripts tool to export my own HTML version which you can find here . Fable started with an index page, vendored a copy of Three.js, then wrote its own gen_textures.py script ( copy here ). It generated the textures and spot-checked them to make sure they looked OK. The metal.jpg file it generated for the trash can looks like this, though I don't think it was applied exactly right in the game itself: Then it built out the first basic version of the game, then decided to "smoke-test in the pre-installed Chromium" using Playwright. This meant it could take screenshots of its own work and eyeball them . It did that for both desktop and mobile widths of the page, then noticed that the raccoon was invisible at mobile widths, so it fixed that : The raccoon, dumpster hideout, and both crew raccoons are now perfectly visible on mobile. Committing this critical fix. It decided to generate a title screen, which it did using this gen_title.py script. Here's the gpt-image-2 prompt it used for that: Video game key art, low-poly 3D render style, moody nighttime scene: a cute low-poly raccoon wearing a tiny black burglar mask sneaking on its hind legs carrying a glowing gold coin, next to a tipped-over metal trash can, suburban house with warm glowing windows in the background, deep blue night, full moon, fireflies, cinematic rim lighting, charming heist caper mood. No text, no words, no logos. And the resulting image (which Claude thought was "gorgeous" ) - though I note that when it's shown on desktop it gets cropped to just the top third without the raccoon! Then my favorite change: it added the dog : export function makeDog ( ) { const g = new THREE . Group ( ) ; const BROWN = 0x8a6440 , DARK = 0x5e4128 ; const body = new THREE . Mesh ( new THREE . SphereGeometry ( 0.42 , 10 , 8 ) , M ( BROWN ) ) ; body . scale . set ( 0.9 , 0.8 , 1.5 ) ; body . position . y = 0.55 ; body . castShadow = true ; g . add ( body ) ; const head = new THREE . Mesh ( new THREE . SphereGeometry ( 0.3 , 10 , 8 ) , M ( BROWN ) ) ; head . position . set ( 0 , 0.85 , 0.62 ) ; g . add ( head ) ; const snout = new THREE . Mesh ( new THREE . SphereGeometry ( 0.16 , 8 , 6 ) , M ( DARK ) ) ; snout . scale . set ( 0.9 , 0.7 , 1.3 ) ; snout . position . set ( 0 , 0.76 , 0.9 ) ; g . add ( snout ) ; const nose = new THREE . Mesh ( new THREE . SphereGeometry ( 0.06 , 6 , 6 ) , M ( BLACK ) ) ; nose . position . set ( 0 , 0.78 , 1.08 ) ; g . add ( nose ) ; for ( const s of [ - 1 , 1 ] ) { const ear = new THREE . Mesh ( new THREE . SphereGeometry ( 0.12 , 6 , 6 ) , M ( DARK ) ) ; ear . scale . set ( 0.7 , 1.3 , 0.5 ) ; ear . position . set ( 0.2 * s , 1.08 , 0.55 ) ; g . add ( ear ) ; const eye = new THREE . Mesh ( new THREE . SphereGeometry ( 0.05 , 6 , 6 ) , M ( 0x1a1a1a , { emissive : 0x331111 } ) ) ; eye . position . set ( 0.13 * s , 0.92 , 0.86 ) ; g . add ( eye ) ; } const tail = new THREE . Mesh ( new THREE . CylinderGeometry ( 0.05 , 0.09 , 0.5 , 6 ) , M ( DARK ) ) ; tail . position . set ( 0 , 0.8 , - 0.62 ) ; tail . rotation . x = 0.8 ; g . add ( tail ) ; // spiked collar const collar = new THREE . Mesh ( new THREE . TorusGeometry ( 0.22 , 0.05 , 6 , 12 ) , M ( 0xc0392b ) ) ; collar . position . set ( 0 , 0.78 , 0.5 ) ; collar . rotation . x = Math . PI / 2.4 ; g . add ( collar ) ; const legGeo = new THREE . CylinderGeometry ( 0.07 , 0.09 , 0.34 , 6 ) ; const legs = [ ] ; for ( const [ x , z ] of [ [ - 0.22 , 0.35 ] , [ 0.22 , 0.35 ] , [ - 0.22 , - 0.35 ] , [ 0.22 , - 0.35 ] ] ) { const leg = new THREE . Mesh ( legGeo , M ( DARK ) ) ; leg . position . set ( x , 0.17 , z ) ; g . add ( leg ) ; legs . push ( leg ) ; } let phase = Math . random ( ) * 10 ; return { group : g , animate ( dt , speed ) { phase += dt * ( 3 + speed * 10 ) ; const amp = Math . min ( 0.6 , 0.1 + speed * 0.6 ) ; legs [ 0 ] . rotation . x = Math . sin ( phase ) * amp ; legs [ 3 ] . rotation . x = Math . sin ( phase ) * amp ; legs [ 1 ] . rotation . x = - Math . sin ( phase ) * amp ; legs [ 2 ] . rotation . x = - Math . sin ( phase ) * amp ; tail . rotation . z = Math . sin ( phase * 1.5 ) * 0.4 ; body . position . y = 0.55 + Math . abs ( Math . sin ( phase ) ) * 0.04 * ( 0.3 + speed ) ; } , } ; } And did a round of testing on it using Playwright, including another screenshot . // walk near the dog await page . evaluate ( ( ) => { const d = window . __rh . dog ; window . __rh . teleport ( d . x + 6 , d . z ) ; } ) ; await page . waitForTimeout ( 2000 ) ; info = await page . evaluate ( ( ) => JSON . stringify ( { dog : window . __rh . dog , state : window . __rh . state , player : window . __rh . debug ( ) . player } ) ) ; console . log ( 'after approach:' , info ) ; await page . waitForTimeout ( 3000 ) ; info = await page . evaluate ( ( ) => JSON . stringify ( { dog : window . __rh . dog , state : window . __rh . state } ) ) ; console . log ( 'after chase:' , info ) ; await page . screenshot ( { path : __dirname + '/shot-dog.png' } ) ; It made a few more tweaks, then declared itself done : Raccoon Heist is built, tested, and pushed — 7 commits on claude/3d-raccoon-heist-game-50n293 , all verified with automated Playwright playthroughs on desktop, portrait-phone, and landscape-phone viewports. The game: You're a masked raccoon sneaking out of your crew's dumpster hideout into a moonlit cul-de-sac. Grab coins, gems, rings, donuts, and fish (they visibly stack on your back and slow you down), then waddle home and bank them before dawn. Each night raises the goal and the heat: night 1 has one flashlight-sweeping guard, night 2 has two, night 3 adds a scent-tracking hound that ignores line-of-sight entirely. A police cruiser sweeps the street with headlights, homeowners randomly peek out of windows, a seagull periodically dive-bombs your unclaimed loot, pizza slices trigger a 6-second speed FRENZY, and a rare golden TV is worth 120 points if you can haul its weight home. Win ranks: TRASH PANDA ⭐ → CAT BURGLAR ⭐⭐ → MASTER OF DISGUISE ⭐⭐⭐, with your best run saved to localStorage. How it's built: Vendored Three.js (no CDN), procedural low-poly characters, and a procedural WebAudio soundtrack (sneaky walking-bass jazz plus all sound effects — zero audio files). All seven ground/wall textures and the title-screen hero art were generated with gpt-image-2 and committed as static assets, so the deployed game makes no API calls. Mobile gets a dynamic touch joystick (appears wherever you touch) plus a DASH button; desktop uses WASD/arrows and Space. Testing caught two real bugs worth mentioning: the canvas rendered at 2× size on any real phone (a cssText assignment was wiping Three.js's inline sizing — desktop DPR-1 tests masked it completely), and the win screen's star-rating div inherited the title screen's full-screen .stars CSS and silently swallowed every tap on the "next night" button. Both are fixed and regression-tested, along with pickup, banking, chase/caught, dawn, night progression, and lose/retry flows. notes.md has the full build log. The game is live on the branch — just serve the repo root and open index.html . Is the game any good? It's an impressive starting point, but it's not a good game. You move your raccoon around a yard collecting items - donuts, fish, gold coins, jewels - while avoiding guards with flashlights and, in later levels, a dog. You have a limited carrying capacity, and once that's full you need to drop stuff off at the dumpster. If you pick up a pizza slice you get a temporary speed boost. There are no team mechanics at all - there are two other static raccoons next to the dumpster but they're purely decoration. It gets slightly more challenging as the levels progress - the dog introduced in level 3 is the most interesting new mechanic - but it's very, very easy to beat. It's also pretty boring - each night has a fixed duration and you can collect all of the items and then have nothing else to do while waiting for the dawn. I was impressed by the implementation. It's fully 3D, there are trash cans, the flashlight illumination cones are fun, and it has a reasonably coherent visual style. It works on mobile. The music ("a procedural WebAudio soundtrack (sneaky walking-bass jazz plus all sound effects — zero audio files)" according to Claude) is simple but feels about right. As a finished game project, it's mediocre. As a starting point from a single prompt I think it's very impressive. I've vibe coded up quite a few games now. They've all been deeply disappointing from a gameplay perspective - it turns out designing games that are fun remains a uniquely human trait, and one which requires significantly more skill and experience than either Claude or I can bring to bear. That said, I thoroughly recommend tinkering with game development projects as a way to explore the capabilities of agents. It's a fun, low-risk way to try out new things. If you stick at it long enough you might even produce something that's worth playing! Update 7th August 2026 : I posed the same prompt to OpenAI Codex Desktop running GPT-5.6 Sol Ultra and got a significantly better result - GPT-5.6 Sol picked up on the importance of the squad of raccoons going on a heist, and built a game where you must rescue your two crewmates in a museum and then stack on top of them to steal the Golden Sardine. Tags: game-design , ai , prompt-engineering , generative-ai , llms , anthropic , claude , text-to-image , vibe-coding , coding-agents , claude-mythos-fable

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