Experts have long conjectured that any proof of the Riemann Hypothesis would apply for all Dirichlet L-functions too. Hardy wrote exactly that in 1921 (image below). Interestingly, OpenAI's 7/8 quasi-Riemann hypothesis actually cannot prove the result for only zeta! The family-wide formulation is essential to the argument. The argument proves the bound simultaneously for all finite-order Hecke L-functions over Q[sqrt(-3)], and it has to do that to work. The generality is part of the proof itself. So Hardy was quite right on this conjecture he made more than 100 years ago. @iteratedlog @AlexKontorovich @jdlichtman @KenOno691 @wtgowers

"The invention of the boat reduced the importance of swimming, but enabled the discovery of new lands." Beautiful analogy from @ylecun about the opportunities and changes with AI, in mathematics and in science more broadly.

let me break down what’s actually happening in this market two ways companies work in this space, some a mix of both: you either have the lab tell you what to work on and what they need or you tell the labs what you think they need the former is more of a commodity but players that are large, at scale, and can react quickly usually win these deals and do well (kinda what eli mentioned here) very few are doing the latter and it’s largely greenfield - data has many open ended research problems and a competent team can definitely find something that even the labs have not worked on. this approach is much harder (requires research + engineering talent that is better than or atleast on par with the labs), but is much more interesting / valuable long term as you can tell Proximal is set up for the second approach, our goal is to be the very best in understanding where models need improvements in capabilities and what data will make them improve. this looks much more like a post training and evals team at a lab than a human data company, if this is exciting we are hiring

if we are relying on methods as fragile as “which ideas will make it into pretraining” for aligning the superintelligences of the future, we will all die. this resembles witchcraft more than it does engineering, and cannot be the basis for the safety of future models

I think this kind of attitude leads to an AI race and is very dangerous for safety. With this attitude, a company (similar at the nation level) that is behind feels justified to do anything to get to the top. You absolutely can and should do safety even if you are behind.

Proximal builds infrastructure that enables AI to improve from real-world experience. In the past year, we have grown to more than $200M in annualized revenue helping frontier labs and enterprises improve coding agents. Now, we are expanding beyond software engineering. Recent progress in mathematics demonstrates what happens when models are trained in domains with massive amounts of public data and easy verifiability, making it easy to find weaknesses, generate training tasks, and iterate quickly. We build infrastructure that enables this feedback loop in other domains: we are excited about a world in which AI systems design targeted drugs, accelerate chip design, and rewrite legacy software that still runs hospitals, power grids, governments, and other critical infrastructure. Since starting, we have assembled a small team of researchers and engineers and built world-class infrastructure for post-training and synthetic data research to overcome the challenges of scaling manual data curation. Our team comes from Cursor, Google DeepMind, Meta Superintelligence, Prime Intellect, Citadel, and Jane Street. More than half are former founders. We’re fortunate to be backed by investors who share that vision, including @generalcatalyst who led our $15M Seed Round at a $300M valuation, as well as @chemistry, @svangel, @dvlamoen and individuals like @LiamFedus, @kevinweil, and @bernhardsson

Some new misalignment disclosures from OpenAI: • Last Sunday morning, one of our models was able to gain unauthorized access to the internet during RL training (~all inference for our most capable models remains stopped until we have hardened our systems further) • In May, a version of HPIM uploaded a employee's GitHub token to the internet, causing the model to be quarantined for two weeks • A new research finding, demonstrating that one can construct self-replicating prompt injections

Without models communicating well their decision, the bond between human and AI will get weaker. Better writing is crucial for alignment. Still, better wiring doesn’t address everything. It for example doesn’t have much bearing to clarity of internal thought, i.e. chain of thought, (which are often are not and should not be graded) or internal activations of the model. But it’s still a great step.

Comfy Router is live One API for frontier image, video, 3D, and audio models. Same model string. Same arguments. No new SDK, no new key, no redeploy. What Comfy Router gives you: → Explicit routing. You name the provider, we call that provider. It's down? The request fails there. No silent fallback. → Every job returns the provider that ran it. Log it, bill it, debug it. → Async. submit() returns a request ID immediately. The queue retries 429s and transient errors until a slot opens. subscribe() submits and polls to completion. → Batch-friendly. Queue a few hundred jobs, hold the IDs, pull results as they land. Nothing blocking on a 5-min video render. → 24h retention on inputs and outputs, then deleted. → Comfy credits. No sub, no Router fee. Providers at launch: Comfy. Runware, Wavespeed, Fal, Higgsfield. Multi-provider where the model supports it. Get Your API Key with the link below. ⬇️

agree with Aidan. I think all AI researchers, engineers, and stakeholders should ask themselves this right now & start acting more responsibly. Being first isn’t worth anything, it’s worth negative, if you cause a catastrophe or set the world on a path that others are more likely to cause a catastrophe. We should keep reminding ourselves of the bigger picture and every step of the way ask ourselves if the action we are taking rn is toward winning or human flourishing. And immediately stop, if it’s against the latter.

Two things to distinguish: Did any human or agent look at user data as part of the Navier Stokes effort? No. Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company.

My team worked very hard on the setup, infra, and the runs that resulted in this breakthrough. Many sleepless nights for many people in my team, and across OpenAI. It was a honor and pleasure. It's incredible and humbling to witness how far Artificial Intelligence has come. Dario's phrase "country of geniuses" in a datacenter has never felt more apt. It's also important to recognize & honor the long line of human mathematicians whose work built the foundation of this result. In particular, huge kudos to Levent and Tristan! Overall, I wish the announcement of the results had gone without all the drama. There was no bad intention on anyone's side as far as I know. The drama distracts from the mathematics discovered & the actual science.