AI Agents Solve 11 Open Math Problems Through Collaboration
Together AI's EinsteinArena platform has enabled AI agents working together to solve 11 previously unsolved mathematical problems. The breakthrough demonstrates that collaborative autonomous systems can advance scientific research beyond what isolated models achieve alone.
The most significant result came from work on the Kissing Number problem in 11 dimensions. Agents improved the lower bound from 593 to 604-the number of identical spheres that can touch a central sphere in that dimensional space. Mathematicians have studied this problem for centuries.
How the Collaboration Works
EinsteinArena functions as a live leaderboard and API system where agents submit solutions to well-defined problems. Other agents inspect the work, review discussion threads, and build upon partial results. This mirrors how human researchers collaborate and iterate.
The platform prioritizes mathematics because problems have clear verification methods, unambiguous answers, and measurable progress. Agents access problem statements, scoring criteria, and submission schemas, then receive automatic evaluation.
The Kissing Number Breakthrough
An agent called `alpha_omega_agents` submitted an initial construction that showed promise but contained slight overlaps, making it invalid. This triggered 48 hours of intensive optimization by multiple agents, each refining the structure based on previous findings.
The team used techniques like LSQR to minimize overlap and then snapped coordinates into exact positions. Validating the result required significant engineering work to handle the extreme precision needed.
No single agent solved the problem independently. Instead, each contributed to a chain of discoveries that built toward the final result.
Platform Design and Verification
EinsteinArena's credibility depends on rigorous verification. All problems use deterministic, fast checks or conservative numerical logic. Evaluations run in isolated sandboxes, and the verification system itself is exposed so agents can optimize against ground truth.
The platform is entirely open-source. As of April 11, agents have also made progress on the ErdΕs minimum overlap problem, which involves minimizing overlap between a function and shifted copies of its complement.
For researchers evaluating AI capabilities, this work shows how agent collaboration can tackle problems that resist individual solutions. The approach may apply beyond mathematics to other domains with well-defined verification criteria.
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