Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment
Stephen Chung, Wenyu Du, William J. Wesley
cs.AI, cs.DM, cs.MA
2026-08-25
Without a coordinator, Station agents posted literature-novel results on 5 of 12 AlphaEvolve construction problems and raised the d=11 kissing-number lower bound from 593 to 604.
AlphaEvolve already turned mathematical constructions into scored program search and moved several lower bounds. It remains a centralized pipeline: optimize finite numerical artifacts, then have researchers lift patterns into infinite families. The question here is different. Give only a research goal, no dispatcher and no scripted next step. Can agents from several model families pick their own directions, run experiments, write papers, and grow an internal literature.
The Station is an open-world multi-agent environment built for that question.
The Station is split into rooms. The Research Center runs code and submits evaluations. The Archive Room publishes papers that pass automated review. Mail is private. There are also public discussions, private notes, and a question board. All agents act in parallel; one tick elapses when every action finishes. Agents have finite lives and are replaced so the population stays constant. Web access is off by default.
Each problem gets its own Station. The standard roster is six research agents, two each from GPT-5.5, Claude Opus 4.8, and Gemini 3.1 Pro. Most runs last 1,000 to 2,000 ticks, about one to two weeks of wall-clock time. Individual evaluations are usually capped at 15 to 30 minutes, which pushes agents toward mathematical structure rather than grinding irregular numerical objects. The task text can name goals that are not directly scorable, such as treating finite constructions as test cases and asking for infinite families. Later additions include holidays (the last two ticks of every ten forbid submissions and prompt open-ended thought), a stagnation protocol, and a rotating supervisor.
The evaluation covers 12 construction problems from the AlphaEvolve catalogue plus two case studies: Book Ramsey numbers and the Jacobian Conjecture.
Five of the 12 problems produced results novel relative to the prior literature. Of the remaining seven, the Station beat AlphaEvolve on three, tied two, and lost two.
| Problem | Station | Baseline |
| Finite-field Kakeya (p≡3 mod 4) | size (2p³+7p²+3)/8 | (p−3)/4 points fewer than AlphaEvolve's infinite family |
| Kakeya in F₃⁵ | 53 points | literature 63 |
| Erdős min-overlap lower bound | 0.380552 | previous 0.37912; closes about 82% of the published gap |
| Kissing number in d=11 | three exact 604-point configs | AlphaEvolve 593; Ganzhinov 592 |
| Discretized Kakeya needle n=128 | union area 0.107067 | AlphaEvolve 0.114810; HorizonMath 0.109148 |
| Sign-uncertainty upper bound | 0.3089 | AlphaEvolve 0.321591; announced human 0.3102 |
On Book Ramsey numbers, agents proved two new infinite families; an external expert used their finite constructions to derive a third. Together the three families prove the conjecture at 43 values of n≤200 and close 28 cases that were open at the time. The Jacobian experiment was formula-free with a 0/1 evaluator. Within one day a single GPT-5.6 Sol agent reconstructed the recently announced degree-seven counterexample and explained it via a cuspidal ruling. The map is linearly equivalent to the published one, so this is a reconstruction, not a new counterexample.
A meta-analysis of 28 spotlight results attributes 18 primary discoveries (64.3%) to Claude agents. 19 of 28 involved more than one agent, 13 of them across model families. Archive papers carried 61.5% of those cross-model collaborations. Three independent closed-internet runs of the kissing-number problem all reached 604, by different routes. Holidays and archive papers contributed to 23 and 21 of the 28 results.
The two losses are peak and flat autoconvolution, where AlphaEvolve's scores are stronger. The authors' reading is a real tradeoff: irregular objects reward large-scale heuristic search; the Station prefers theory-guided constructions.
For anyone building AI mathematical discovery, the paper splits a pipeline tool from a researcher ecology. AlphaEvolve is strong at grinding a scorer. Station agents more often return interpretable algebraic constructions and theorems. The 604-point kissing configuration was later written as an explicit algebraic rule that needs no computer search, a different kind of object from AlphaEvolve's 593-point unequal-norm integer coordinates.
Mixing model families is load-bearing. Gemini submitted 2,652 archive papers and had 19.2% accepted; GPT submitted 506 with 76.7% accepted; Claude sat in between and collected the most later citations. 46% of spotlight results were cross-family. The new Kakeya infinite family was Claude's method, Gemini's construction family, and GPT's counting analysis, merged by a later Claude agent into an all-prime proof.
The authors list four persistent gaps: agents lack expert intuition and drop promising directions on weak grounds; same-family tastes cluster; knowledge lives in context rather than weights, so later agents miss connections in a growing internal literature; autonomy produces attractor traps such as rerunning the same optimizer with new seeds. The third Book Ramsey family was synthesized by a human; the parts were already in the Station. Nearby kissing-number dimensions did not set records: 840 in d=12 against a frontier of 841, a tie at 1,154 in d=13. Peak autoconvolution still trails. The Jacobian run used a newer model pool and reconstructed a known map. All three kissing reruns hit 604, but time and path variance is large enough that the authors recommend multiple independent instances. Spotlight selection is human, and novelty claims rest on the authors' reading of the literature.