TL;DR: A multi-agent "prove-verify loop" solved five genuinely open math problems, spanning auction theory to online learning, with every result independently verified by domain experts. Title: Cogentic: Multi-Agent Orchestration for Automated Proof Discovery URL: Points 🧠 An orchestrator assigns multiple "provers" to different proof directions, mimicking a research group with adversarial verifiers that assume every step is wrong until justified 📚 A persistent "ledger" accumulates verified intermediate lemmas, so progress survives across rounds instead of being lost between attempts 🎯 Solved 5 open problems across online learning, auction theory, and mechanism design 📊 Improved the simple-vs-optimal revenue approximation factor from 5.2 to 3.52, and hit the optimal 1.5 price of anarchy for 2-bidder autobidding auctions 💰 Built on Gemini, with a modest inference budget — around O(100) Gemini calls for most problems ✅ All 5 results passed independent verification by domain experts and were developed into companion papers It feels genuinely significant that a properly orchestrated language model can tackle real open research problems, not just textbook exercises. #MathResearch# #MultiAgent#

plausibly AI just kills math research but i have this dream that getting way better at math in centaur mode will let us focus more on the math that's interesting and less on the math that's particularly tractable to our current skillset. by which i mean more geometry, of course

I think mathematicians as a community actually have quite a lot of power over how automated math research goes in the short term The labs and vibeprovers are expending all this effort to impress mathematicians. If they withhold their approval I think the effort will respond

A great read. I have similar feelings about how AI labs approach progress directly and without nurturing of scientific communities & intuition. The math research community went through the transition the fastest, so it was felt most. Other fields next.

AI has solved 10 long-standing open problems in mathematics — all verified with machine-checked Lean 4 proofs. Title: Ten advances in mathematics and theoretical computer science URL: ❓ What problems were solved? 💡 Ten results spanning eight fields: high-dimensional sphere packing, existence of non-sofic groups, disproving Connes's rigidity conjecture, exponential parallel repetition for quantum games, polynomial-factor hardness for the closest vector problem (with post-quantum cryptography implications), Ehrhart's volume conjecture, multicolor Ramsey numbers, and extremal number conjectures (Erdős problems 146, 180, 183). Each problem had seen no progress on its main result for at least a decade. ❓ Which AI solved them? 💡 An internal evaluation version of Astra, OpenAI's next major unreleased model. Astra found the core proof structures; humans then prepared manuscripts and formalized the arguments using the same model. The total compute cost: roughly $2,000 at standard API rates — "theorem proving as a routine batch job any lab can run." ❓ Are these proofs actually correct? 💡 Every result ships with a machine-checkable Lean 4 certificate (mathlib + Lake, Apache-2.0, on GitHub). Running `lake exe cache get && lake build All` either compiles or it doesn't — correctness is resolved in minutes, not months of peer review. This is the strongest verification bar AI-produced mathematics has cleared at this scale. ❓ What does this mean for the future of math research? 💡 The significance is breadth, not a single lucky strike: eight fields, ten results. The bottleneck is no longer compute budget — it shifts to prompt design and result vetting. The rate-limiting step in mathematical discovery may soon be a human's ability to pose the right question and formalize the answer, not AI's ability to find it. #AIMath# #OpenAI#