Since 1995, the known frontier of “good groups” in 4-manifold topology had remained essentially where Freedman and Teichner left it. Today that frontier moves farther. Slava Krushkal, working with Michael Freedman’s Discovery Team at Logical Intelligence, has proved that certain Sturmian groups are good, expanding the class of fundamental groups for which the machinery of topological 4D surgery theory is known to apply. logicalintelligence.com/blog…

The “Coke vs Pepsi” race to superintelligence, consequences be damned, is frustrating to me as a builder. My concern about LLMs is not that every improvement brings us another step toward an inevitable machine apocalypse. It is that we risk continuing to confuse increasingly impressive capabilities to mimic intelligence with real machine intelligence and giving these models increasingly consequential responsibilities. These are general purpose models that are being smushed to fit every role for every customer. Systems are built around the model to keep them on task and staying within the constraints of a particular problem. But it will never fundamentally understand that it can’t violate a constraint. Constraint is not in its nature. The relevant question, therefore, is not, “how intelligent is this model?” We should be asking “what can this system do, what prevents it from doing something else, and what happens when those protections fail?” That should be the starting point for any proposed deployment in a critical setting. logicalintelligence.com/blog…

OpenAI boss says world 'right to be afraid' but 'should trust' AI firms bbc.in/3VgtcYO

I deleted my previous post. I'm just going to post the entire statement page by page. It's a complicated situation. Statement: cims.nyu.edu/~tristanb/state… cims.nyu.edu/~tristanb/euler… cims.nyu.edu/~tristanb/ipm.p… cims.nyu.edu/~tristanb/bouss… github.com/tristanbuckmaster…

For my first post, I’m sharing a letter @NVIDIA signed on why open models matter. AI will transform every industry, power every company, and be built by every country. Open models strengthen safety and cybersecurity, accelerate innovation and diffusion, and enable sovereignty. The world needs both frontier closed models and frontier open models. images.nvidia.com/pdf/Open-W…

It has been our hypothesis since day one that “AI for math” is not a durable business model. Frontier models will continue to expand into specialized capabilities like mathematics, which means competing by building another specialized model yields increasingly diminished returns

How to keep AI spend flat while token usage grows exponentially: Not with friction and spend alerts. With better defaults, routing, and caching. Better Defaults (not Usage Caps) – Engineers can choose any model they want, but defaults matter. We’re experimenting with defaulting to open weight models like GLM 5.2 and Kimi 2.7 through our LLM gateway, while still encouraging engineers to choose the right model for the task. 91% of our employees were never hitting their usage caps, so instead of lowering caps and driving up alerts, we're moving to cheaper defaults. Note that code reviews use a diversity of models, so they can check each other's work. Better Routing – In our custom harnesses, we preprocess prompts and route to the best model for the job, considering cache hits and model pricing. For instance, you may want a frontier model for planning, but not for execution where they can be overkill. Ultimately, humans shouldn't be choosing models - AI can automate this task. Better Caching – Cache misses are the easiest way to drive your cost up. All of our requests are cache aware, so we’re reusing a warm cache wherever possible. For example, our cache hit rate went from 5% → 60% in LibreChat once properly implemented. Keep Context Lean – Start fresh sessions when switching tasks. Scope file context narrowly. Disconnect unused tools. Don't just compact. The goal isn't fewer tokens used, it's fewer tokens wasted. Better Visibility – Our engineers can use as many tokens as they want, from whatever model they want, but we’ve made usage visible – and the more you spend on AI, the more impact we expect. The goal isn't to suppress usage. It's to build the infrastructure that makes exponential growth sustainable. Putting this into practice has cut our AI spend nearly in half, while our token usage continues to grow.

Palantir CEO Alex Karp on what customers actually want, the real business of frontier labs, and the importance of open source models: “What the technical customers want is control over their compute, their models, their data stack, and their alpha. They want to know they own the means of production, and it's not being transferred to someone else.” "Who owns the data? Are the prompts secure? Is this being transferred to you?" "If it was so valuable, and I can make you a billion dollars, wouldn't I say I'll make you a billion dollars and I want 30%? Why are they charging for tokens if it's so valuable?"

We are awash with buggy LLM-generated code. It costs more to fix than to create. The volume is growing quickly, and methods like testing are insufficient to keep up. Formal verification is one path out. It has been hard for AI. But EBRMs may hold the key logicalintelligence.com/blog…