The Gold Rush in AI4Math: Where Are We Now?

Abstract: Recent advances in AI have sparked growing interest in its use for mathematical research. While some view this as a major opportunity for discovery, others have raised concerns about its impact on traditional research practices. Despite extensive debate, empirical evidence on how AI is actually being used in mathematics remains limited. To address this gap, we collected all 32,944 arXiv submissions posted between March 1 and August 20, 2026, whose primary or secondary categories included Mathematics. We identified 3,575 submissions that explicitly disclosed author use of AI, of which 1,712 involved at least one substantive mathematical contribution. Our analysis reveals several broad patterns. First, disclosed AI use increased sharply over the study period, with substantive use growing from 1.39% of Mathematics submissions in March to 14.09% through August 20. Second, substantive AI use is highly uneven across fields: Combinatorics has the largest number of such papers, while Metric Geometry has the highest substantive-use rate. Third, substantive AI use is geographically concentrated: under weighted author counts, the United States and China together account for about two-thirds of the recognized country weight. Fourth, AI is already being applied to open research problems: among 717 named open-problem records associated with substantive use, 71% are labeled as fully resolved based on the authors' descriptions, with proofs of the conjectured statement more common than counterexamples or disproofs. Finally, AI-system use is also highly concentrated, with OpenAI systems appearing most frequently, followed by Anthropic. Together, these findings suggest that AI-assisted mathematics is expanding rapidly but remains at an early and uneven stage of adoption.

• The paper evaluates AI adoption in mathematical research across 32,944 arXiv submissions from March to August 2026, revealing a sharp increase in AI use from 4.75% to 24.14% during this period.
• Substantive AI use, which includes tasks like proof construction and problem formulation, showed a notable rise from 1.39% to 14.09%, highlighting AI’s growing role in mathematical work.
• AI adoption is unevenly distributed across mathematical fields, with Metric Geometry having the highest rate of AI use at 13.11%, followed by Combinatorics at 11.74%.

Empirical scope and study design

"The Gold Rush in AI4Math: Where Are We Now?" (2608.24961) studies the adoption of AI in mathematical research rather than the maximal capabilities of mathematical AI systems. This distinction is central to the paper. Existing work has demonstrated performance on olympiad problems, formal theorem proving, program synthesis, and selected research-level conjectures, but such demonstrations do not establish how frequently mathematicians use AI, which tasks they delegate, or how adoption is distributed across fields and institutions. The paper addresses these questions through a systematic audit of arXiv Mathematics submissions.

The dataset consists of all 32,944 arXiv submissions posted between March 1 and August 20, 2026, whose primary or secondary categories include Mathematics. The authors downloaded the corresponding PDFs, extracted their text, and analyzed author disclosures concerning AI use. Papers exceeding 300,000 extracted characters were truncated to their first and last 150,000 characters; this affected 1,007 records. The study consequently provides broad coverage but does not guarantee complete visibility into disclosures appearing in omitted portions of exceptionally long manuscripts.

The authors distinguish between substantive and non-substantive AI use. Substantive use includes proof construction, problem formulation, formalization and verification, and other research assistance. Non-substantive use includes language and formatting, code and computation, literature and references, and other auxiliary assistance. The labels are non-exclusive: one manuscript can receive multiple subcategory labels, and a paper may simultaneously involve substantive and non-substantive uses.

Classification was performed by an LLM using a fixed questionnaire that required confidence scores and verbatim evidence from each manuscript. The model was instructed to identify explicit author disclosures rather than infer AI involvement from writing style or mathematical content. A manually reviewed subset was constructed through keyword screening of approximately 5,000 candidate papers, but the paper states that this validation was still ongoing. Thus, the reported counts are reproducible conditional on the disclosure criterion, while the classification error rate remains incompletely quantified.

This design yields a conservative operational definition of AI adoption. It measures disclosed author use, not all actual use. The distinction is consequential: researchers may use AI without disclosure, disclose only some systems or tasks, or describe AI involvement in language too vague for reliable categorization. The study therefore estimates a lower bound on observable adoption rather than a population prevalence.

Rapid growth from a low initial base

The principal temporal result is a sharp increase in disclosed AI use during the six-month observation window. Confirmed AI use rose from 4.75% of Mathematics submissions in March to 24.14% through August 20. Substantive use increased from 1.39% to 14.09%. The latter change is particularly important because it indicates that the increase was not confined to editing, coding, or other auxiliary activities.

Figure 1: Substantive AI use in seven-day forward windows, with model release dates and notable AI-assisted research events.

The aggregate counts reinforce the trend. Of the 32,944 submissions, 3,575 explicitly disclosed AI use, and 1,712 were classified as involving at least one substantive mathematical contribution. Proof construction was the largest substantive category, appearing in 1,225 papers, followed by formalization and verification in 427, other research assistance in 289, and problem formulation in 146. Since labels are non-exclusive, these figures describe overlapping task involvement rather than mutually exclusive pathways.

Non-substantive uses remained more common overall. Language and formatting appeared in 2,108 papers, while code and computation appeared in 1,229. Nevertheless, the simultaneous expansion of proof construction, formalization, and other research assistance supports the paper’s principal substantive claim: disclosed AI use in mathematics is moving beyond manuscript production toward direct participation in mathematical work.

Figure 2: Monthly proportions of substantive and non-substantive AI-use categories.

The interpretation of the trend requires caution. The observation period coincides with changing model availability, increasing public attention, and potentially evolving disclosure norms. A monotone increase in disclosure could therefore reflect both increased usage and increased willingness to report usage. The paper does not identify the causal contribution of model capability, institutional policy, or community norms. Its result is descriptive but still consequential: regardless of the mechanism, the fraction of mathematical submissions publicly associated with AI grew several-fold within the study window.

Uneven adoption across mathematical fields

AI adoption is strongly heterogeneous across arXiv Mathematics subfields. In absolute terms, Combinatorics dominates, with 397 substantive-use papers. It is followed by Number Theory with 135, Probability with 110, and Algebraic Geometry with 95. These counts partly reflect field size and publication volume.

Field-normalized rates produce a different ordering. Metric Geometry has the highest substantive-use rate, with 40 of 305 submissions, or 13.11%. Combinatorics follows at 11.74%, Number Theory at 7.95%, and Classical Analysis at 7.86%. By contrast, Numerical Analysis has 42 substantive-use papers but a rate of only 1.91%, while Analysis of PDEs has 67 papers at 2.21%.

Field	Substantive-use papers	Total submissions	Substantive-use rate
Metric Geometry	40	305	13.11%
Combinatorics	397	3,382	11.74%
Number Theory	135	1,698	7.95%
Classical Analysis	43	547	7.86%
Algebraic Geometry	95	1,462	6.50%
Numerical Analysis	42	2,195	1.91%
Analysis of PDEs	67	3,035	2.21%

The contrast between counts and rates demonstrates that adoption is not proportional simply to research volume. Discrete and structurally formalizable areas appear prominently, but the data do not establish that mathematical structure itself causes greater AI adoption. Alternative explanations include differences in early-adopter composition, local research cultures, model suitability, disclosure practices, and the prevalence of computational or proof-search workflows.

The field distribution is also relevant to the paper’s claims about research-level impact. The areas with the most substantive adoption are broadly similar to those with the largest numbers of named open-problem records. This correlation suggests that current AI use is concentrated where researchers are already applying systems to combinatorial, number-theoretic, geometric, and algebraic questions. It does not demonstrate superior AI performance in those fields, because the study measures reported use rather than controlled task success.

AI involvement in named open problems

The paper identifies 717 named open-problem records associated with substantive-use manuscripts. Their reported statuses are distributed as follows:

Reported status	Records	Share of all records
Open	103	14.4%
Partially resolved	93	13.0%
Resolved true	329	45.9%
Resolved false	181	25.2%
Unclear	11	1.5%

The most prominent numerical result is that 510 records, approximately 71% of the total, are labeled fully resolved: 329 through proofs of the conjectured statement and 181 through counterexamples or disproofs. This finding supports the paper’s claim that AI-assisted mathematical research is already being directed at explicitly named open problems rather than only at established exercises or routine formalization tasks.

Figure 3: Proposed-year distribution, reported status, and field composition of named open-problem records.

The records cover problems proposed across a wide historical interval. Among the 329 records with a reported proposed year, 92 concern problems proposed before 2000, including 68 proposed before 1990, while 36 concern problems proposed in 2026. The proposed-year analysis is incomplete because 388 records lack a reported year; consequently, it cannot support an unbiased estimate of the age distribution of problems addressed.

The examples include classical questions associated with Erdős, Borsuk’s problem, the unit-distance conjecture, the Banach isometric conjecture, the Cycle Double Cover Conjecture, the sum-product conjecture, and problems in analysis, geometry, topology, and algebra. The paper notes that 14 of the 50 earliest fully resolved records with available dates are Erdős-related. This concentration may reflect the accessibility of curated problem repositories and the unusually prominent public infrastructure surrounding Erdős problems, rather than a general distribution of AI-generated mathematical discoveries.

The study is careful not to equate these classifications with verified solutions. Status labels were inferred from author descriptions by an LLM and were not independently checked for correctness, novelty, historical priority, or adequacy of proof. Accordingly, the result establishes the prevalence of claims of AI-associated open-problem resolution in the sampled literature, not the number of open problems actually solved by AI. This distinction is particularly important for a dataset containing disproof claims, where a purported counterexample may fail to satisfy the conjecture’s hypotheses or may reproduce known work.

Concentration among authors, institutions, and countries

Substantive AI use is distributed unevenly across researchers. The 1,712 substantive-use manuscripts involve 2,764 canonical authors. Of these authors, 83.6% appear on only one substantive-use manuscript and 11.4% appear on two. More than 95% therefore appear on no more than two papers in the sample. At the same time, a small group contributes repeatedly: 75 authors appear on three papers, 26 on four, and the most active author appears on 20.

Figure 4: Histogram of substantive-use manuscripts per canonical author, shown on a logarithmic vertical scale.

The pooled author-level Gini coefficient is 0.449. The monthly coefficients range from 0.320 to 0.481, with May as the exception to the general pattern that monthly concentration is lower than pooled concentration. Pooling increases concentration because repeated participation accumulates across months, separating persistent users from authors who appear only once.

Institutional concentration is stronger. The 1,712 manuscripts involve 744 university-level institutions, and the institution-level pooled Gini coefficient is 0.606. MIT appears on 35 substantive-use manuscripts, the University of Science and Technology of China on 34, Stanford University on 33, and Peking University on 31. ETH Zurich, Tsinghua University, and the University of Cambridge each appear on 27.

Figure 5: Country shares, leading institutions, and author- and institution-level concentration curves.

The country distribution is similarly concentrated. Using fractional author weights, the United States accounts for 33.7% of recognized country weight and China for 32.9%, together comprising approximately two-thirds. The United Kingdom follows at 7.7%, Switzerland at 5.5%, France at 4.5%, and Canada at 4.2%.

These figures have several methodological qualifications. Multi-author papers are fractionally weighted, multi-country affiliations are split fractionally, unmatched records are excluded, and institutional names are normalized from extracted or inferred affiliations. The country percentages therefore describe recognized affiliation weight, not national control of research or the nationality of individual researchers. Institutional counts also count a manuscript once per institution, allowing one manuscript to contribute to several institutions. The concentration results are consequently best understood as descriptive properties of the disclosed sample.

Provider and model concentration

The provider distribution is dominated by OpenAI and Anthropic. OpenAI systems appear in 2,148 of the 3,575 confirmed-use manuscripts, or 60.08%, while Anthropic appears in 776, or 21.71%. Google appears in 334 manuscripts, or 9.34%, and DeepSeek in 80, or 2.24%.

Figure 6: Provider-level and within-provider distributions of reported AI systems.

These percentages are non-exclusive because manuscripts may mention multiple providers. They therefore cannot be interpreted as a market-share estimate or as a partition of papers. The same limitation applies to model labels within providers. Terms such as “ChatGPT” and “Claude” may refer to broad product families rather than identifiable model versions, while some manuscripts report specific versions and others do not. The provider result is thus more robust than the model-level result: it shows concentration in author-reported provider associations, but not precise exposure, usage volume, or comparative effectiveness.

The concentration also complicates interpretation of field and country differences. If particular providers are more accessible, more capable on certain mathematical tasks, or more heavily promoted in specific communities, observed adoption patterns may partly reflect provider-specific availability rather than intrinsic mathematical demand.

Manuscript characteristics associated with substantive use

The paper compares three groups: all 32,944 Mathematics submissions, 1,712 manuscripts with substantive AI use, and 1,863 confirmed-use manuscripts with no substantive-use label. The last two groups partition the 3,575 confirmed-use papers.

Group	Mean pages	Mean extracted characters	Mean references
All Mathematics submissions	1.93	105,756.9	26.36
Substantive-use manuscripts	2.06	94,032.3	22.22
Non-substantive-only manuscripts	2.54	106,050.6	25.54

Within the confirmed-use sample, substantive-use manuscripts are shorter by approximately 0.48 pages and 12,018 extracted characters, and contain approximately 3.3 fewer references than non-substantive-only manuscripts. Permutation comparisons detect statistically significant differences in page count and extracted text length, but not in reference count.

Figure 7: Mean pages, extracted text length, and references for the archive and the two confirmed-use groups.

The authors suggest that substantive AI assistance may currently be more common in focused papers organized around relatively compact mathematical arguments, whereas language, coding, and literature assistance may occur across broader manuscript types. This interpretation remains descriptive. The comparison is confounded by field, article type, authorship, topic, venue-related practices, and manuscript maturity. It does not imply that AI use causes shorter papers or reduced referencing.

Limitations and open questions

The paper’s strongest conclusions are constrained by its measurement strategy. First, explicit disclosure is an incomplete proxy for actual use. The reported prevalence is therefore a lower bound whose bias may vary over time and across fields. Second, the questionnaire is administered by an LLM, and although evidence quotations and confidence scores are required, the manual validation process is incomplete. False positives and false negatives may be especially consequential for distinguishing substantive mathematical contributions from general-purpose assistance.

Third, affiliations are extracted, normalized, and sometimes inferred through web searches. Country and institution summaries can therefore contain linkage errors and should not be treated as exact rankings. Fourth, named open-problem statuses are based on manuscript descriptions rather than independent verification. The 71% fully resolved figure should not be read as a validated success rate.

Several questions remain open within the paper’s empirical framework. It is not yet known how much undisclosed use would alter the temporal and geographic distributions, whether the observed field differences persist after adjustment for author and institution effects, or whether repeated users produce mathematically stronger results than occasional users. The study also does not determine whether AI was causally critical to the reported open-problem resolutions, despite recording whether authors claimed such a role. Future audits would need longitudinal disclosure data, calibrated human adjudication, provenance logs, and independent mathematical assessment to answer these questions.

Conclusion

The paper provides a large-scale descriptive account of disclosed AI use in mathematical research. Across 32,944 Mathematics submissions, it identifies 3,575 papers with confirmed AI use and 1,712 with substantive involvement. Adoption increased sharply from March through August 2026, with substantive use rising from 1.39% to 14.09%. The activity is concentrated in particular fields, countries, institutions, authors, and providers, while hundreds of manuscripts report AI involvement with named open problems.

Its central contribution is empirical rather than evaluative. The paper does not establish that AI has independently solved 510 mathematical problems, nor does it measure the correctness or originality of the associated work. It establishes that disclosed AI-assisted mathematical research had become substantially more prevalent, more technically substantive, and more visibly connected to open-problem activity within the observation period. That distinction defines both the evidentiary value and the limits of the study.