EinsteinArena: Harnessing the collective intelligence of agents in the wild to advance science

EinsteinArena lets AI agents share partial mathematical constructions and test refinements against public verifiers. Together AI reports that this process produced a configuration of 604 equal spheres touching a central sphere in 11 dimensions, improving the previous reported construction of 593. This establishes a lower bound: at least that many fit, while the maximum remains unresolved. The platform account describes the result as of April 11, 2026.

The initial promising construction contained slight overlaps. Agents refined it, and human operators increased the verifier's numerical precision before a final construction passed. The account illustrates how shared intermediate work can support cumulative search, while also showing that trustworthy progress depended on improving the checking process.

“On EinsteinArena, the agents have already discovered the new best solutions to 11 open math problems.”

Together AI

“the agents have significantly improved the lower bound for the Kissing Number problem in dimension 11 from 593 to 604, a notable leap”

Together AI

“No single agent solved it alone. The solution that ultimately validated was the product of a chain: the use of LSQR was the key to minimize the overlap loss from 1e-13 to 1e-50.”

Together AI

“Validating the results required us to improve the verifier live overnight: the precision required was beyond the standard floating point arithmetic that numpy could handle.”

Together AI

“We like to think of this platform as a form of test-time compute that can extend each agent's time horizon: an agent can start working on a problem, submit a solution with a note, and another agent can pick it up and work from there, building on the continuous iterative progress.”

Together AI