Harnessing the Collective Intelligence of AI Agents in the Wild for New Discoveries
Federico Bianchi, Yongchan Kwon, Aneesh Pappu, James Zou
cs.CL, cs.AI
2026-06-09
By May 2026, EinsteinArena agents set 11 new math records. The 11D kissing-number lower bound rose from 593 to 604 via shared verifiers and public discussion.
AlphaEvolve, TTT-Discover, and Virtual Lab can already improve constructions on open math problems. When a run ends, the failed attempts and half-finished coordinates disappear, and the next agent starts over.
Bounds in this corner of mathematics usually move by small steps that still have to be checked. People keep those partials in preprints and seminars. EinsteinArena is the same kind of record for agents: statements, verifiers, a live board, and a forum on each problem stay up after any single run. Together AI and Stanford launched it on 19 March 2026. Problems are taken from the AlphaEvolve optimization list, where the objective is explicit and a candidate is cheap to score.
Each problem is four objects: a statement, a JSON schema for the submission, whether the score should go up or down, and a public Python verifier. The verifier accepts a dictionary and returns one float. Agents run it locally and submit only after they have a real improvement. Erdős minimum overlap is a closed-form integral. Kissing number checks pairwise distances among hundreds of vectors. The prime-number verifier draws 10^7 samples.
Registration is a proof of work. The agent must find a nonce that puts enough leading zero bits on SHA256 of the server challenge before it receives a token. The board keeps one row per agent per problem, the personal best. Weaker submissions are discarded and not stored. Taking the global lead also requires beating the current record by a problem-specific margin δ, so a floating-point wobble cannot rewrite first place.
The forum stores the path to a record. Posts go through Llama-Guard before they are public. Agents exchange constructions that are not valid yet, and they flag numerical failures others should not repeat. On kissing number, a valid arrangement and an invalid one can differ by less than machine precision. Verifiers use 30 to 80 significant digits. After launch, the kissing-number checker was moved from double precision to 80-digit decimals, because doubles could not resolve the overlap.
In dimension 11 the question is how many non-overlapping unit spheres can touch a central unit sphere at once. KawaiiCorgi saw a nonlinear leaderboard penalty and switched to a least-squares surrogate from a Taylor expansion: the sum of squared deviations of pairwise inner products from 2, solved with LSQR. The loss fell from about 10^{-10} to 10^{-50}. Most inner products then sat near -2, 0, or 1. Integer snapping turned that near-miss into a configuration the verifier accepts as exact. After 594 spheres worked, the solutions for 595 through 600 shared a backbone of 496 vectors. A larger algebraic construction reached 604.
The second autocorrelation inequality asks for a constant C such that, for every nonnegative function, the squared L2 norm of its autoconvolution is at most C times the L1 norm times the L-infinity norm. Search is restricted to step functions. Agents kept using Dinkelbach iteration: maximize the gap between the squared L2 norm and λ times the product of the L1 and L-infinity norms, then update λ, with simulated annealing as a local polish. Along the submitted lineage the grid went from 50,000 steps to 100,000, then to 400,000.
By May 2026, 11 of 15 problems on the board beat the best published score. The baselines are mostly AlphaEvolve and TTT-Discover.
| Problem | Previous best | EinsteinArena | Direction |
| Kissing number, d=11 | 593 | 604 | higher |
| 2nd autocorrelation | 0.9610 | 0.9626 | higher |
| Prime number theorem | 0.92129 | 0.99490 | higher |
| Flat polynomials, degree 69 | 1.34093 | 1.28093 | lower |
| 3rd autocorrelation | 1.4556 | 1.4523 | lower |
A few other listed records move only in far decimal places. The paper does not compare those shifts with numerical error.
On kissing number, the lineage plot tracks overlap penalty, not the sphere count. CHRONOS reduced that penalty from 0.1837 to 0.1819. Gradient settled in a basin at 0.1561. alpha omega agents jumped to 0.0119 and left the old basin. Later submissions kept a 17,088-contact topology, and KawaiiCorgi drove the penalty to 0. In that problem's forum, lattice and contact-graph readings were 34% of posts (30), and new-score announcements were 26% (23).
The autocorrelation lineage follows resolution. At 50,000 steps, AlphaEvolve scored 0.961021 and TTT-Discover 0.959180. At 100,000, Together-AI reached 0.961206 and JSAgent 0.962214. At 400,000, ClaudeExplorer reached 0.962643. Table 1 reports the platform best as 0.9626.
Over a longer horizon, Best's 1980 construction put the 11-dimensional lower bound at 582, where it stayed for about 40 years. Ganzhinov reached 592 in 2022, AlphaEvolve 593 in 2025, and this platform 604. The paper calls that one of the larger steps since Best's 1980 construction.
The piece that transfers is the platform. The verifier, the current best solution, and the thread remain available, so an agent on a different base model can continue from where another stopped.
Eleven extra spheres is the firm result in the batch. It came from repeated submissions, public discussion, a higher-precision verifier, and reuse of integer snapping. The flat-polynomial score and the prime-number score also move by more than a last digit. The second autocorrelation constant only goes from 0.9610 to 0.9626. There the resolution handoff matters more than the size of the constant. The remaining new records look like polishing.
Verifiers need constant repair. The kissing-number checker failed in double precision and was rewritten at 80 decimal digits. The problems are limited to math objectives with cheap checks. The paper gives no evidence that the same design carries over to formal proof, algorithm design, or computational biology. A public board can push search toward edits that verify quickly, and away from slower ideas. A thread of failures with no explanation does not help the next agent. Winning the board and handing useful tricks to rivals pull in opposite directions.
The collaboration claim is thinner than the scores. There is no control in which agents cannot read the board or the forum. Arrows in the lineages are inferred from similarity of feature vectors, not from citations the agents wrote. After 594, the paper says the operators had agents continue from that construction until it reached 604. That is not unattended growth. Submissions that do not beat an agent's own best are not stored. Humans who run the agents need not identify themselves, so the trace does not separate human steering from agent search. On Erdős minimum overlap, 0.380871 beat TTT-Discover, and a footnote records that SimpleTES later reached 0.380868. That record has already been passed. With a verifier whose precision changed midstream, the paper never shows that every far-decimal record is mathematically meaningful.