README.md

metadata

license: cc-by-4.0
task_categories:
  - question-answering
language:
  - en
tags:
  - mathematics
  - arxiv
  - open-problems
  - research-level
size_categories:
  - 100K<n<1M
configs:
  - config_name: numerical
    data_files:
      - split: train
        path: data/numerical-*.parquet
  - config_name: yesno
    data_files:
      - split: train
        path: data/yesno-*.parquet
  - config_name: answers
    data_files:
      - split: train
        path: data/answers-*.parquet

ResearchMath-2-6Sol-Rewrite

534,298 research-level mathematics questions reformatted into benchmark-shaped items, derived from amphora/ArXivOpenProblems, plus an answer key of 154 literature-verified answers.

config	rows	contents
numerical	140,248	answer is a single number; math_intent labelled for 35,274 of them
yesno	394,050	answer is Yes or No
answers	270 (154 verified)	literature search results, with link, theorem, derivation and solution sketch

v2 — full coverage (this version)

v1 (tag v1, 97,497 items) was a budget-limited subset: questions were rewritten in order of expected numerical yield — conjectures first, then math.CO and math.NT — so analysis, probability and physics were heavily under-represented.

v2 rewrites every question in amphora/ArXivOpenProblems (534,298 of 534,309 rows) with the same model, prompt and settings as v1 (openai/gpt-6-sol, batch tier, temperature 0.2). v1's items are kept unchanged; source_run records where each row came from.

Category share of the numerical config relative to the source (1.00× = proportional):

category	v1	v2
math.CO	3.29×	1.62×
math.NT	1.60×	1.39×
math.AP	0.47×	1.01×
math.PR	0.34×	0.80×
math.DS	0.27×	0.83×
math.OC	0.34×	0.49×

The selection bias is gone. What remains is a format bias: route B ("smallest counterexample, −1 if none") suits "for all n" statements, so combinatorics converts to a number 42.5% of the time and optimization 12.9%. For a category-balanced numerical benchmark, sample from this set by primary_category.

On 1,872 questions rewritten in both runs, 89% got the same format and 93.6% of numerical pairs the same distinguished_value; format flips were symmetric (101 vs 104), i.e. noise on borderline questions, not drift.

⚠️ Most items have no answer key

Every item derives from a future-work or open-problem statement in an arXiv paper, so for the vast majority the answer is not known. The answers config covers only the small subset where a later paper resolved the question — see below. Do not compute accuracy on numerical/yesno without an answer source.

How a research question becomes a number

route records the construction used for numerical items:

route	construction	share
B	minimal counterexample: "smallest p at which the property fails; −1 if none"	79.0%
E	size of the exceptional set (0 = the original's "yes")	8.8%
A	the question already asked for a quantity	5.8%
C	sharp constant in an inequality	2.1%
D	critical value of a continuous parameter	2.2%
G	count of a finite classification	1.8%
F	minimal/maximal multiplicity or order	0.4%

distinguished_value is the number equal to the original question's "yes" (usually -1). Route B strengthens the problem: "what is the smallest counterexample?" is strictly harder than "is there one?".

math_intent (numerical config)

What each question is about — orthogonal to question_category (its logical shape). Assigned by openai/gpt-6-sol from the source question; labelled for the 35,274 numerical rows of v1 only (null elsewhere); the counts below are for those rows.

math_intent	n	share
structural_characterization	7,423	21.0%
existence_construction	6,802	19.3%
generalization	6,749	19.1%
bound_improvement	6,374	18.1%
hypothesis_weakening	2,545	7.2%
classification	1,590	4.5%
asymptotic_rate	1,535	4.4%
uniqueness	971	2.8%
algorithmic	677	1.9%
other	608	1.7%

math_intent_secondary gives a second label where one clearly applies.

The answers config

270 questions were searched against the literature; 154 have a verified answer (is_verified_answer = true). Each verified row has:

field	meaning
answer	the answer, in the item's own convention
answer_link	the paper containing the answer
resolving_paper / resolving_theorem	authors, title; exact theorem number
theorem_statement	the theorem, quoted verbatim
derivation	how that theorem answers the question as literally phrased; steps not stated in the paper are marked INFERRED
solution_sketch	1–3 paragraphs on how the paper proves it, from the paper's own outline
confidence, provenance, notes	caveats

Unanswered rows keep their status (STILL_OPEN, IMPROVED_BOUNDS, SOLVED_DIFFERENT, …) and, where known, current_bounds.

Answer mix: −1 (83), Yes (34), No (17), exact values (20) — including 7/32, (3-sqrt(5))/2, κ = 2, finite minimal counterexamples such as 6, 3 and 2, and two +infinity.

Filter by provenance

124 answers are "clean": high confidence with none of these tags.

provenance tag	n	meaning
RECENT_PREPRINT_2026	19	resolving paper not yet refereed
AI_ASSISTED_RESOLVER	9	resolving paper declares AI/LLM involvement
COMPUTATIONAL	4	rests on a computer(-assisted) check
NON_FINITE_ANSWER	2	answer is +infinity; handle specially when grading
HAS_INFERRED_STEPS	79	derivation contains an inferred step — usually the routine "proved for all n, hence −1"

How it was built

1. Citation graph. Semantic Scholar citations for all 12,019 pre-2020 source papers.
2. Candidate filter. Citing papers whose title/abstract announces a proof, disproof or resolution.
3. Abstract screen. openai/gpt-6-sol judged each (question, citing-paper) pair as DIRECT, SPECIAL_CASE, SIBLING, BOUNDS_ONLY or UNRELATED — most candidates resolve a different conjecture from the same source paper.
4. Full-text verification. Claude Code subagents read each DIRECT candidate in full, checked the main theorem against the exact question, traced priority to the first proof, and wrote the entry.
5. Citation check. Every resolver arXiv ID was matched against arXiv author metadata.

Verification changed many screen verdicts: disproofs mistaken for proofs, special cases, retracted or corrected proofs replaced by valid later ones, and "proofs" from predatory venues rejected.

Mis-transcriptions in the source data

19 of 270 searched questions (7%) are flagged MISTRANSCRIPTION: the source paper misstated its conjecture — a dropped hypothesis, a typo, a reversed sign, a wrong constant, or a degenerate edge case (e.g. n = 1) — so the literal question is trivially answerable while the real problem is different. These are excluded from the verified answers. They cluster by source paper; a paper with one confirmed mis-transcription should be treated as suspect.

13 further questions are flagged AMBIGUOUS_QUESTION (vacuous, about a proof method, or mixing an empirical and an asymptotic claim) and are also excluded.

Fields (numerical / yesno)

uid, arxiv_id, paper_url, primary_category, signal_type, question_category, format, route, question, answer_convention, distinguished_value, source_question, engine, source_run, and for numerical also math_intent, math_intent_secondary.

Caveats

• No answer key for most items — see the warning above.
• yesno items are unverified claims, not labelled true/false.
• Route B items are harder than their sources.
• numerical still leans toward combinatorics — a property of the conversion, not of selection (see v2 above).
• 636 fields had LaTeX swallowed as a JSON escape (e.g. \\theta read as a tab) and were restored deterministically.
• A small number of arxiv_id values are wrong, inherited from the source dataset.
• signal_type is an extraction label, not a verified claim that a problem is still open.

Licensing

Questions, labels and answer-key fields: CC-BY-4.0. source_question is inherited from amphora/ArXivOpenProblems; theorem_statement quotes short excerpts from the resolving papers, with attribution via resolving_paper and answer_link.

Citation

@article{son2026researchmath,
  title={ResearchMath-14K: Scaling Research-Level Mathematics via Agents},
  author={Son, Guijin and Yi, Seungyeop and Gwak, Minju and Ko, Hyunwoo and Jang, Wongi and Yu, Youngjae},
  journal={arXiv preprint arXiv:2605.28003},
  year={2026}
}

Collaborations

I'm interested in creating larger datasets to train open models for research-level math. If you are interested let me know. (guijin.son@snu.ac.kr)