Data statement
Summary
This is a deliberately small public showcase of 20 internally authored mathematics tasks. It is not a random or representative sample of all Ulam.ai work. Selection optimized for domain breadth, statement quality, verifiability, research depth, and usefulness in demonstrating long-horizon mathematical RL.
Composition
- Five records were selected from a pool of 149 Erdős-inspired variants.
- All ten records in the AIM-AG client sample were retained.
- Five records were selected from a pool of 139 bounded object-finding variants inspired by conjectures.
Selection indexes and source-file hashes are recorded in MANIFEST.json. The private source pools are not included.
Authorship and sources
The released prompts, discussions, RL metadata, schemas, and packaging were authored internally at Ulam.ai. Some tasks identify a classical conjecture or published theorem as mathematical inspiration. Those labels establish lineage; the variants are not presented as canonical transcriptions of the source problems.
The AIM-AG records include bibliographic references used to describe their literature boundary. Citation does not imply endorsement, and cited works are not redistributed in this dataset.
Novelty and mathematical status
Each headline task is a candidate research problem. Targeted searches and internal review cannot prove global novelty. Literature boundaries, open/closed status, and attribution should be refreshed by a qualified domain expert before a claimed solution or commercial evaluation is treated as final.
The counterexample-oriented stream uses bounded finite searches. Depending on the optimum, some tasks may produce an actual counterexample in the specified subclass, while others yield only a certified near-miss. The formulation does not preassert either result.
Personal and sensitive data
The dataset contains no intended personal data, user conversations, or private customer material. It contains author names and publication metadata only where needed for scholarly citation.
Public/hidden separation
The RL companion is policy-visible material only. Grader-only research guidance, hidden targets, hidden fixtures, calibration answers, and expert reviews from the internal production package are excluded. This public sample must not be treated as a secret held-out evaluation set.
The included train/dev/eval labels are organizational. Every included prompt and fixture is public, and the public curriculum configuration explicitly overrides production-language that could otherwise imply holdout status.
Known limitations
- Twenty tasks are too few for claims about broad model capability.
- Domain coverage is intentionally weighted toward advanced pure mathematics.
- Most terminal tasks require expert judgment and do not have canonical known answers.
- Machine-checkable milestones can certify only their stated subproblems.
- Public prompts can enter model training corpora, so future evaluations should use fresh private variants.