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Inventory of the AlphaEvolve problem set

• Domain: mathematics
• Role: denominator frame
• Metric: per problem, whether it has a live numeric record and how many dated prior works the paper cites
• Coverage: the 65 problems the paper numbers 6.1 to 6.65; cited works span 1852–2025; built 2026-07-26
• Data: alphaevolve-inventory.csv
• Upstream: https://arxiv.org/abs/2511.02864 and https://github.com/google-deepmind/alphaevolve_repository_of_problems
• Verdict: baseline — 65 problems inventoried, 31 with a live numeric record; built 2026-07-26

The 65 problems, by literature depth and recency

Each point is one problem from the AlphaEvolve paper's section 6.

Definition

The AlphaEvolve mathematics paper reports improved bounds across a set of 67 mathematical problems; its problem section numbers them 6.1 to 6.65 [@georgiev2025mathexploration]. This folder is an inventory over those 65 numbered problems, not a discovery series: per problem it records what the quantity is, which prior work the paper cites, what year each cited work dates from, and how the companion repository classifies the outcome. The record series drawn from this frame are the record sequences.

The paper states its own scope on problem history:

"For reasons of space, we do not attempt to exhaustively survey the history of each of the problems listed here, and refer the reader to the references provided for each problem for a more in-depth discussion of known results." — Georgiev, Gómez-Serrano, Tao and Wagner, arXiv 2511.02864, 2025 [@georgiev2025mathexploration]

An entry in this inventory is one numbered problem. A problem counts as having a live numeric record when the repository's classification places it in the world_record, worse_than_record or former_record groups: the matched-optimal group's history has terminated at a proven optimum, and the unclassified group is mostly conjectures and non-record tasks.

Facts

• status composition: 19 where AlphaEvolve holds the record, 11 where it matched a known optimum, 8 where it came in below the record, 4 where its result has since been surpassed, and 23 unclassified
• live records: 31 of the 65 problems have a live numeric record (the first, third and fourth groups above)
• funnel: 65 numbered in the paper · 31 with a live numeric record · 12 drawn as the pre-committed sample · 6 that yielded a dated scalar record sequence · 2 carrying both AI and human steps
• citation depth: of the 65 problems, 64 cite at least one dated reference, 52 cite at least two, and 31 cite at least four
• cited-year spans: among problems citing two or more dated works the median span between earliest and latest cited year is 42 years

This folder has no cumulative view on the collection-wide cumulative index: the inventory is a one-date snapshot of a problem set, not a time series. The dated record sequences it feeds are the records folder's, which has one.

Method

The CSV is built by fetch.py, which reads a local pdftotext extraction of the paper plus a checkout of the companion repository. It locates each problem's definition inside the paper's problem section, then records the title, the topic group, the bracketed references cited within that span, the publication year of each of those references from the parsed bibliography, any inline bound string, and the repository's status classification. Neither input is vendored here and the paper's text is not redistributed; only derived counts and short quoted bound strings go into the CSV. The parsed bibliography yields 302 entries, of which 298 carry a year.

n_citations is the full number of parsed references. To keep the inventory compact, cited_refs lists at most the first twelve reference IDs; three rows have thirteen or fourteen parsed references.

Two extraction bugs were found and fixed during construction, and both would have corrupted the output silently: a cross-reference to a problem occurring before its definition made the preceding problem's span swallow its content, and the topic-group headings were only partly matched, so group labels drifted forward. Two rows with independently known histories anchor the extraction: the Sidon autoconvolution problem (6.2) returns 2010 and 2017, matching the Matolcsi–Vinuesa and Cloninger–Steinerberger attributions its own notebook gives, and the classic moving sofa (6.62) returns 1992 and 2024, matching Gerver and Baek. check.py re-asserts both anchors along with the fact lines above.

figure.py counts the status column of alphaevolve-inventory.csv for the left panel and reads the first two funnel rows off the same counts; the last three funnel rows — the sample size, the number of sampled problems that yielded a sequence, and the number of quantities with steps of both kinds — come from the record sequences and are written into the figure rather than computed here.

Limitations

• a cited year is not a record year. It is the year of a cited work: background references, surveys and method papers are mixed in with the papers that moved the bound. Separating them requires reading the cited papers, a manual step this inventory scopes rather than performs; the CSV is not a record sequence.
• the index mapping is an assumption. The paper numbers problems 6.1 to 6.65 while the repository's status.json indexes 1 to 67, so the two enumerations cannot be identical. The identity mapping is assumed and every row carries status_mapping = assumed to say so.
• the 65 are not 65 distinct problems. At least twelve of the repository's 67 experiment directories are the same problem under two names, so the set is closer to 50 distinct problems.
• the status classification is the vendor's. What counts as holding the record, matching an optimum or falling below one is the repository's own judgment, not an independent adjudication.
• bound strings are pattern-extracted from lightly normalised LaTeX and are recorded for orientation only.
• the frame states the selection problem rather than fixing it. Tractability correlates with being well-curated and therefore with progress rate, so a sample drawn from this frame is still a sample of problems an AI system was pointed at.
• on the packing problems the historical baseline is itself machine search. Record improvements there have been machine-generated since the 1990s and many are unpublished, with Packomania reporting improvements arriving daily; an AI-versus-history comparison on those problems is automated against automated unless each prior record's finder type is coded per problem.

AI attribution

No AI system contributed to this inventory, which is a frame rather than a result, and no row of alphaevolve-inventory.csv scores an AI event. The set it inventories is the output of an evolutionary coding agent that mutates programs under an automated evaluator [@novikov2025alphaevolve], published with a companion repository carrying the status classification used here [@deepmind2025problems]. The AI and human steps on these problems are scored in the record sequences.

Sources

• [@georgiev2025mathexploration] — the mathematics paper the problem definitions, citations and bound strings are extracted from; quoted above on its own scope.
• [@novikov2025alphaevolve] — the AlphaEvolve system paper.
• [@deepmind2025problems] — the companion repository whose status.json supplies the status classification.
• [@tao2025exploration] — co-author's account of the run across the problem set.
• [@arxiv2026horizonmath] — HorizonMath, a benchmark of over 100 unsolved problems with automated verification that compares AI output to best-known published results and carries no historical dimension.
• [@deepmind2023funsearch] — FunSearch's cap-set improvement of December 2023, the dated precedent for this line of work.
• [@sherry2021fast] — measured heterogeneity of improvement rates across algorithm families; records arrive in bursts with long gaps.
• Series drawn from this frame: the record sequences and sums and autoconvolution.