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REVIEW 4 major objections 5 minor 1 cited by

Fraudulent Publishing in the Mathematical Sciences

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read This report argues that the Highly Cited Researchers list is not a marker of mathematical quality, and that the citation data behind it can be gamed.

desk verdict Useful, authoritative position statement on fraudulent publishing in math; the HCR 'useless' claim is overstated but the report's core warning stands. read the letter →

arxiv 2509.07257 v2 pith:MWIV56TP submitted 2025-09-08 math.HO

Ilka Agricola , Lynn Heller , Wil Schilders , Moritz Schubotz , Peter Taylor , Luis Vega This is my paper · ORCID
classification math.HO MSC 01A80
keywords bibliometricsHighlyCitedResearcherscitationcartelspapermillspredatorypublishingself-citationmathematicaluniversityrankings
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This report from a joint working group of two international mathematical unions tries to establish that fraudulent publishing and bibliometric manipulation are now systemic in the mathematical sciences, and that the main commercial indicators used to evaluate mathematicians fail at their job. Its central case study is the annual Highly Cited Researchers (HCR) list: in 2019 the 89 mathematicians on it were almost disjoint from major-prize winners, concentrated in a narrow set of applied subfields, and cited themselves roughly twice as often as prize-winning or top-cited mathematicians. The report argues that the HCR list measures citation optimization rather than mathematical influence, and therefore is 'useless for detecting mathematics of good quality.' It also surveys the broader ecosystem—commercial paper factories, coordinated citation rings, fake journals, sale of authorship, false affiliations—and stresses that the small citation numbers typical of mathematics make the field especially vulnerable to gaming. If the report is right, hiring, funding, and university-ranking decisions that lean on these metrics are being made on contaminated data.

What carries the argument

The argument is carried by a cohort comparison built on two ratios: the self-citing score (SCS), the share of citations to an author's papers that come from the author's own papers, and the self-referencing score (SRS), the share of an author's references that point back to that author. Comparing median SCS and SRS across three cohorts—HCRs, the 1000 most-cited mathematicians, and post-2000 major-prize winners—makes the self-citation inflation of HCRs visible and measurable. The second supporting mechanism is the near-disjointness test: the overlap between the HCR list and the prizewinner list is taken as a check on whether raw citation counts track the kind of influence that prize committee

What would settle it

If a direct check found that mathematicians listed as HCRs in earlier years went on to win major prizes at a rate far above a matched control group, or that a peer-nomination panel of mathematicians endorsed a large fraction of HCRs as genuinely influential, the conclusion that HCR is useless would be refuted. A simpler version: compute the overlap between an HCR list and the winners of a broad set of peer-awarded prizes over the following decade; high overlap would show the list carries signal.

Watch

Extended reading notes

Core claim

The report's central factual claim is that the 2019 Highly Cited Researchers list in mathematics is not a marker of mathematical influence. Of the 89 HCRs, only five had won a major mathematics prize, using professional-society and international prizes including the Fields Medal as the benchmark, and the HCR and prizewinner lists were almost disjoint despite more than six hundred prizewinners over all time. The HCRs' fields were also unrepresentative: none worked primarily in geometry or algebra, and about three-quarters came from partial or ordinary differential equations, statistics, numerical analysis, and operator theory. On self-citation measures, HCRs had median self-citing and self-re

Load-bearing premise

The argument assumes that winning a major mathematics prize is a reliable stand-in for genuine mathematical influence, so that the near-absence of HCRs among prizewinners means the HCR list is contaminated rather than that prizes and citations track different but legitimate kinds of mathematical work.

Editorial extensions

If this is right

  • If HCR status is not a quality signal, then university rankings that count HCRs as an indicator of excellent researchers inherit the distortion and could be improved by deleting that indicator.
  • Evaluation of mathematicians by absolute citation counts should be replaced or supplemented by peer review and by curated, expert-maintained indexes of the mathematical literature.
  • Because mathematics produces small citation numbers, even modest manipulation can shift positions, making cross-field comparisons via these metrics especially unsafe.
  • Retraction rates are rising and paper mills will likely adopt AI, so publishers need automated screening combined with human oversight rather than relying only on stylistic red flags such as machine-generated 'tortured phrases.'
  • Incentives created by publication fees and large journal bundles reward volume over quality, so changing the publishing model is part of fixing the metric problem.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension would be to run the same SCS/SRS cohort comparison in other disciplines: if chemists or medical researchers on the HCR list also self-cite about twice as often as prizewinners, the mechanism identified here is general rather than a mathematics anomaly.
  • The prize-disjointness test could be inverted by checking whether earlier HCR cohorts went on to win major prizes later; if HCR status predicted future recognition, the verdict that the list is useless would be too strong.
  • Because institutions can gain ranking points through HCR affiliations, the finding implies that institutional prestige itself is being repriced; dropping the HCR input from a ranking would measurably reshuffle well-known university names.
  • The report stops short of proposing its second publication's remedies, but a natural direction is an author-level citation-hygiene baseline: flagging SRS values far above the prizewinner cohort's median as a low-cost screening signal for possible manipulation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This IMU/ICIAM working group report surveys fraudulent publishing practices in the mathematical sciences and argues that bibliometric measures—especially Clarivate's Highly Cited Researchers (HCR) list—are vulnerable to manipulation and are unsuitable for evaluating mathematical research. Drawing on Dunne's 2021 analysis of the 2019 HCR list, retraction databases, and numerous documented cases of paper mills, citation cartels, and hijacked journals, the authors contend that the HCR indicator is 'useless for detecting mathematics of good quality' (§3.3). The report also discusses the Clarivate exclusion of mathematics, university rankings, and emerging AI-related risks. It is the first of two publications; a second will offer recommendations.

Significance. If its central claims hold, the report strengthens the case that quantitative rankings and HCR lists should not be used as proxies for mathematical quality. Its main strengths are the synthesis of a large body of recent evidence, the specific and checkable case references, the glossary of fraudulent-publishing phenomena, and the institutional weight of the IMU/ICIAM working group. The paper is also useful as a community-awareness document. However, the statistical argument in §3.3 falls short of supporting the universal conclusion that the HCR list is 'useless': the overlap with prizewinners is not calibrated against any baseline, and the self-citation comparison is confounded by subfield and database differences. These are fixable with additional analysis or more measured wording, but they are load-bearing for one of the report's main claims.

major comments (4)
  1. [§3.3, item 3 and summary] The claim that the HCR list is 'useless for detecting mathematics of good quality' rests on the near-disjointness of 89 HCRs and 636 all-time prizewinners. This is not calibrated against any baseline. Since only 365 post-2000 prizewinners are spread across the entire discipline, a random sample of 89 active mathematicians would also be expected to contain very few prizewinners. To support the inference, the authors should report the overlap for the MRDB top-1000 cohort or a matched control sample, and ideally show that the overlap is significantly lower than expected. Without this, the conclusion should be rephrased as a claim about mismatch with prize-based recognition, not about uselessness.
  2. [§3.3, Table 2] The SCS/SRS comparison is confounded. The cohorts come from different databases (Clarivate/WoS for HCRs versus MRDB for the top-1000 cited cohort), and the HCR group is concentrated in PDE, statistics, numerical analysis, and operator theory, while prizewinners are concentrated in algebraic geometry and number theory. Self-citation norms vary across subfields and career stages, so the observed twofold difference may partly reflect citation culture rather than manipulation. At minimum, the authors should acknowledge this limitation and, if possible, control for subfield and career stage. The sentence 'HCRs cite and reference themselves about twice as often' should be qualified.
  3. [§2.3, paragraph on Scopus/SJR] The 'quick analysis' that about 20% of Q1/Q2 SJR mathematics journals are not in zbMATH Open is the only quantitative contribution attributed to the authors themselves, but no methodology, data, or list is provided. Non-inclusion in zbMATH does not by itself imply poor quality or irrelevance; it may reflect scope or classification decisions. Because this statistic later feeds the argument that commercially produced rankings are unreliable, the authors should either document the analysis and state the criteria, or label it explicitly as a preliminary observation.
  4. [§3.4, 'Retractions'] The statement that seven of the 89 HCRs appear in the Retraction Watch database is presented as evidence of an association between HCR status and retractions, but no baseline rate is given. The Retraction Watch database contains over 1,000 retractions with mathematics as primary field, so the expected number among 89 randomly chosen mathematicians may be nonzero. The authors should compare with a matched cohort and specify the retraction reasons; otherwise the reader cannot assess whether HCR status and retraction records are related beyond chance.
minor comments (5)
  1. [§A Glossary] Typographical and copy-edit issues: 'rigourous' should be 'rigorous'; reference [80] has 'regurlaly'; the German 'Süddeutsche' is typeset incorrectly in the text.
  2. [§3.5] The sentence 'one can assume that this has to do with the exclusion of mathematics' is speculation. Either provide evidence for the causality or remove the conjecture.
  3. [References] References [70] and [71] show placeholder URLs ('http:xxx'). These must be completed before publication.
  4. [Table 1] Specify the source year and the definition of 'primary affiliation' used for the 2019 HCR list, and provide a direct reference for the claim that China Medical University Taiwan has no mathematics program.
  5. [§3.1] The passage on the 2024 HCR list notes that '48% were not associated with any definite research area' and that one listed person died in 2021. It would be helpful to cite the exact Clarivate source and clarify whether these are the authors' own calculations or are taken from the cited literature.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the HCR 'uselessness' claim rests on external Dunne data, not on the report's own fitted inputs or a self-citation chain.

full rationale

The report's central inference—that the Clarivate Highly Cited Researchers list in mathematics is 'useless for detecting mathematics of good quality' (§3.3)—is supported by external empirical work, chiefly Edward Dunne's investigation [24] and Clarivate's own public statements, rather than by a derivation that assumes its conclusion. The HCR/prizewinner overlap and the elevated SCS/SRS values in Table 2 are reported as data from [24], not calculated from definitions in this paper. The one self-citation of note, Adler, Ewing and Taylor [1] (with Peter Taylor as a co-author of both), is used only as background context in §2 and §3.1 ('It has been argued [1] for a long time that the commonly-used bibliometric metrics are inappropriate'); it is not the load-bearing evidence for the §3.3 conclusion. The 'useless' conclusion may be statistically under-supported because it lacks a calibrated baseline for prize overlap and controls for subfield and career stage, but that is an external-validity or correctness concern, not a circularity. No equation or derived measure is equivalent by construction to its input; no fitted parameter is renamed as a prediction; and no uniqueness or ansatz is imported from the authors' prior work. The report is therefore not circular in the sense relevant to this analysis.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The report rests on several domain assumptions about the reliability of the data sources it uses (Retraction Watch, Clarivate HCR lists, zbMATH Open) and about the validity of prize-winning as a quality benchmark. These assumptions are reasonable but not proven in the text.

assumptions (4)
  • domain assumption Major mathematics prizes are a reliable indicator of mathematical influence.
    Used in §3.3 to compare HCRs against prizewinners and infer that HCRs are not top mathematicians. No justification is provided for this benchmark.
  • domain assumption The Retraction Watch database accurately captures retractions in mathematics.
    Used in §3.4 to count retractions and correlate with HCRs. The database is community-curated and may have incomplete coverage.
  • domain assumption Clarivate's HCR list and its disciplinary categorization are accurate enough to identify the listed mathematicians.
    The paper criticizes the list but uses it as a cohort without checking whether the names and categories are correct.
  • domain assumption zbMATH Open's indexing is a reliable standard for determining which journals are relevant to mathematics.
    In §2.3, the SJR comparison uses zbMATH as the ground truth to judge whether journals are legitimate mathematics journals.

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Cite this review

Pith. "Pith review of Fraudulent Publishing in the Mathematical Sciences." pith.science (2026). https://pith.science/paper/MWIV56TP

@misc{pith2026250907257,
  author       = {Pith},
  title        = {Pith review of: Fraudulent Publishing in the Mathematical Sciences},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWIV56TP}},
  note         = {Machine review of arXiv:2509.07257}
}
read the original abstract

This report is the first of two publications of a joint Working Group of the International Mathematical Union (IMU) and the International Council of Industrial and Applied Mathematics (ICIAM). In it, we shall analyze the current state of publishing in the mathematical sciences and explain the resulting problems. Our second publication will offer concrete recommendations, guidelines, and best practices for researchers, policymakers, and evaluators of mathematical research. It will explain how to detect and counteract attempts to game bibliometric measures, empowering the community to reclaim control over research evaluation and drive necessary change.

Figures

Figures reproduced from arXiv: 2509.07257 by the authors.

Figure 1
Figure 1. A simplified depiction of the academic publishing ecosystem [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. How to Fight Fraudulent Publishing in the Mathematical Sciences: Joint Recommendations of the IMU and the ICIAM

    math.HO 2025-09 unverdicted novelty 3.0 of 10

    A joint policy statement recommending expert-led research assessment over bibliometrics to fight fraudulent publishing in mathematics.

Reference graph

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.