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REVIEW 3 major objections 6 minor 6 references

The rise and rise of interdisciplinary research: Understanding the interaction dynamics of three major fields -- Physics, Mathematics & Computer Science

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Citations from Physics and Mathematics to Computer Science have grown sharply since the 1990s, with Mathematics' references to machine learning increasing exponentially.

desk verdict A visually compelling descriptive map of cross-field citation growth, but the arXiv-only title-matched data and an unmodeled 'exponential' claim make the strong version of the result fragile. read the letter →

arxiv 1908.03793 v1 pith:UDZP67ZU submitted 2019-08-10 cs.DL

Rima Hazra , Mayank Singh , Pawan Goyal , Bibhas Adhikari , Animesh Mukherjee This is my paper · ORCID
classification cs.DL
keywords interdisciplinaritycitationanalysisscientometricsPhysicsMathematicsComputerSciencemachinelearningtemporalbucketsignatures
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 paper analyzes citation flows among Physics, Mathematics, and Computer Science using more than 1.2 million papers from a preprint repository. It claims that over the past two decades, citations from the core sciences (Physics and Mathematics) to Computer Science have risen sharply, with Mathematics' citations to the machine-learning subfield growing exponentially in recent years. The authors also show that subfield popularity is unstable: some subfields such as Computation and Language fade while others such as Information Theory and Learning gain ground. This matters because it indicates the intellectual center of gravity among these fields is shifting toward Computer Science, and particularly toward learning-related areas. If the measurement is correct, the interaction between these disciplines is becoming less symmetric over time.

What carries the argument

The analysis is carried by a citation network built from the papers' reference lists, where a reference counts only if its title string matches a paper in the same preprint repository. Two visualization tools carry the argument: Sankey diagrams, which draw citation flow between fields and subfields as link widths proportional to the number of citations, and temporal bucket signatures, stacked histograms showing the relative age of cited papers within fixed five-year time buckets. These tools let the authors separate self-field from non-self-field citations and track both the volume and direction of cross-field exchange over time.

What would settle it

Compute the same citation flows from a complete bibliographic index covering journals and conference proceedings, and test whether the exponential rise in Mathematics-to-machine-learning citations survives once the growth of each field's output in the sample is accounted for.

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Extended reading notes

Core claim

The paper's central empirical discovery is a directional shift in citation patterns between 1995 and 2017. In the earliest five-year bucket, Mathematics and Physics almost exclusively cite each other, with no citation flow to or from Computer Science. By the 2010s, Computer Science had become a net recipient of citations from both Mathematics and Physics, and in the final bucket (2015–2017) the two core fields cite Computer Science papers about equally. At the subfield level, the most striking pattern is Mathematics' growing citation flow to the Computer Science subfield 'Learning,' which the authors describe as exponentially increasing and attribute to the rise of machine learning and deep learning. The paper also documents that Physics and Mathematics tend to cite older work from each other but recent papers from Computer Science, consistent with the view of computer science as a fast-moving field.

Load-bearing premise

The load-bearing assumption is that the citation flows measured from a sample of papers in one preprint repository represent the true citation behavior of the three fields; if the repository's coverage, title-matching, or the five-reference filter distort the sample, the observed rise could be an artifact of changing repository usage rather than real intellectual exchange.

Editorial extensions

If this is right

  • If the trend persists, Mathematics and Physics are likely to keep increasing their citation share to Computer Science, especially to machine-learning subfields.
  • Subfield popularity is volatile across time: a subfield that is highly cited in one period (such as Computation and Language) can decline sharply, while others (Information Theory, Learning) rise.
  • The age profiles imply that Computer Science is a fast-moving field: it cites recent work within its own field, while Mathematics and Physics cite older work from each other.
  • The measured asymmetry suggests that interdisciplinarity among these fields is not a balanced exchange but a growing one-way flow toward Computer Science.

Reading between the lines

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

  • The exponential growth in Mathematics-to-machine-learning citations may reflect mathematicians moving into the foundations of learning algorithms; testing whether the citing mathematics papers cluster in subfields like probability and analysis would sharpen this picture.
  • Applying the same method to other triples such as biology, chemistry, and computer science could show whether the pull toward computer science is general or peculiar to physics and mathematics.
  • The overall rise in cross-field citations might be concentrated in a few computer science subfields; re-analysis measuring how much of the growth comes from Learning and Information Theory would tell whether the headline is 'interdisciplinarity' or 'concentration in a few topics.'
  • Because the dataset ends in 2017, extending the analysis to recent years would test whether the exponential growth continued past the deep-learning boom or flattened out.
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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

3 major / 6 minor

Summary. The paper analyzes citation interactions among Physics, Mathematics, and Computer Science using a corpus of more than 1.2 million arXiv papers from 1990–2017. The authors construct a citation network by parsing .bbl files and matching referenced titles to arXiv, retaining only papers with at least five extracted references. They then use Sankey diagrams, temporal bucket signatures, and subfield-level analyses to show that citations from Physics and Mathematics to Computer Science have 'drastically increased,' and that citations from Mathematics to the machine-learning subfield of Computer Science are 'exponentially increasing.' The paper also reports shifts in the popularity of specific subfields over time.

Significance. If the central descriptive claims are reliable, the paper documents a measurable and policy-relevant shift in the intellectual center of gravity across three major scientific fields, with learning-related subfields of Computer Science gaining attention from Mathematics and Physics. The analysis is transparent about its filtering rules and provides the raw dataset and supplementary material, which are strengths. However, the current evidence is insufficient to establish the headline quantitative claim of exponential growth, and the arXiv-only, title-matched reference extraction raises a real risk that the observed trends are artifacts of coverage change rather than genuine shifts in citation behavior.

major comments (3)
  1. [§2 (Dataset construction) and Table 2] The arXiv-only title-matched reference extraction with the five-reference filter creates a time- and field-dependent selection that directly confounds the central trend. Only 86 Computer Science papers survive the filter in B1 (1995–1999) and 104 in B2, even though Table 1 lists 141,662 CS papers overall. If early CS research was published in venues not deposited on arXiv or cited non-arXiv literature, those papers are systematically missing, making the later increase in PHY→CS and MA→CS citations appear steeper than it really is. The manuscript does not quantify arXiv coverage per field and time period, nor does it validate against a complete citation database (e.g., MAG or Scopus). This is load-bearing because the abstract's claim of a 'drastic' increase rests on these counts.
  2. [Abstract and §3 (subfield analysis, Figure 3)] The claim that citations from Mathematics to the machine-learning subfield of Computer Science are 'exponentially increasing' is not supported by any fitted model, growth-rate estimate, confidence interval, or goodness-of-fit test. A raw citation count can grow exponentially simply because the number of machine-learning papers itself grows rapidly, even if the per-paper citation propensity is constant. The paper should either fit a statistical model (e.g., Poisson or negative-binomial regression on per-paper citation rates) or substantially temper the claim to a descriptive statement about raw counts.
  3. [§3 (Bucket B1 observations)] The statement that during B1 'we do not observe in-/outflow of citations to/from CS' is based on extremely small sample sizes: only 86 CS papers, 726 MA papers, and 7553 PHY papers in the filtered set. Zero observed counts are weak evidence of absence of citation flow. The paper should report uncertainty intervals or model the count data (e.g., Poisson rates) to distinguish genuine absence of interaction from small-sample sampling noise, especially because the B1 zero is presented as the starting point of the temporal narrative.
minor comments (6)
  1. [§2] The threshold of 'at least five extracted references' is introduced without justification; a sensitivity analysis varying this threshold would help assess how much the main trends depend on this arbitrary cutoff.
  2. [Table 1] The number '1,41,662' uses Indian digit grouping; for an international readership, the standard comma grouping '141,662' would be clearer.
  3. [Figure 2 caption] The caption 'Fraction of citation going from one field to another field over the years' should be 'Fraction of citations going from one field to another field over the years' (grammatical agreement).
  4. [References] Reference [2] is incomplete: it lists 'Organisation for economic cooperation and development (oecd). (1998)' without a title or publication details.
  5. [§1 and §3] The field abbreviation is inconsistently rendered as 'PH' in the Conclusion and 'PHY' elsewhere; unify to one abbreviation.
  6. [Supplementary material] The supplementary material is linked via a tinyurl; a permanent DOI or stable repository link would be more appropriate for archival purposes.

Circularity Check

0 steps flagged · score 1.0 of 10

Largely self-contained empirical citation analysis; minor reliance on authors' prior TBS visualization technique but no circular derivation.

full rationale

The paper's central claims are direct empirical observations: counts and proportions of citations among Physics, Mathematics, and Computer Science over temporal buckets, derived from a citation network built from arXiv metadata and .bbl files. No parameter is fitted and then renamed as a prediction; no mathematical derivation reduces to its own inputs. The only self-citation is the use of temporal bucket signatures (TBS), introduced in the authors' own KDD'17 paper and referenced as [4]. TBS is used as a visualization tool to display citation-age distributions, not as a theoretical premise that forces the observed cross-field citation trends. The 'exponentially increasing' statement is a qualitative description of raw citation counts, not the output of a fitted model, so it is not circular in the sense of a prediction that is equivalent to its fitting input. Concerns about arXiv-only title matching and field-dependent coverage are threats to the validity of the measurements, but they do not make the argument circular: the analysis is self-contained against the data it uses, even if that data may be incomplete. Thus the circularity score is low.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new entities or fitted physical parameters. Its central quantitative claims depend on data-construction choices: the arXiv-only corpus, title matching, the minimum reference threshold, and the bucket width. These choices are reasonable but unvalidated, and they influence every reported trend.

free parameters (2)
  • minimum extracted references per paper = 5
    Papers with fewer than five parsed references are discarded. This hand-chosen threshold shapes the dataset and could exclude short, early, or non-standard papers.
  • temporal bucket width = 5 years
    Citation links are grouped into five-year buckets. The authors assert results hold for other sizes but provide no sensitivity analysis.
assumptions (3)
  • domain assumption arXiv citations matched by title string are a valid sample of the three fields' citation behavior.
    Section 2 uses title matching on arXiv to construct the citation network. If arXiv coverage or matching accuracy varies by field or year, the observed trends could be artifacts.
  • domain assumption Self-field citations dominate, so separating self and non-self citations is meaningful.
    Section 3 states this as an empirical observation without statistical testing, yet the analysis and interpretation rely on this separation.
  • domain assumption The five temporal buckets B1 to B5 capture the relevant dynamics.
    Buckets are defined in Section 3 with an arbitrary width of five years and an arbitrary start at 1995, which affects all temporal conclusions.

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Cite this review

Pith. "Pith review of The rise and rise of interdisciplinary research: Understanding the interaction dynamics of three major fields -- Physics, Mathematics & Computer Science." pith.science (2026). https://pith.science/paper/UDZP67ZU

@misc{pith2026190803793,
  author       = {Pith},
  title        = {Pith review of: The rise and rise of interdisciplinary research: Understanding the interaction dynamics of three major fields -- Physics, Mathematics & Computer Science},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UDZP67ZU}},
  note         = {Machine review of arXiv:1908.03793}
}
read the original abstract

The distinction between sciences is becoming increasingly more artificial -- an approach from one area can be easily applied to the other. More exciting research nowadays is happening perhaps at the interfaces of disciplines like Physics, Mathematics and Computer Science. How do these interfaces emerge and interact? For instance, is there a specific pattern in which these fields cite each other? In this article, we investigate a collection of more than 1.2 million papers from three different scientific disciplines -- Physics, Mathematics, and Computer Science. We show how over a timescale the citation patterns from the core science fields (Physics, Mathematics) to the applied and fast-growing field of Computer Science have drastically increased. Further, we observe how certain subfields in these disciplines are shrinking while others are becoming tremendously popular. For instance, an intriguing observation is that citations from Mathematics to the subfield of machine learning in Computer Science in recent times are exponentially increasing.

Figures

Figures reproduced from arXiv: 1908.03793 by the authors.

Figure 1
Figure 1. Citation flow among three fields of science, Computer Science, Physics, and Mathematics over the (a) entire time-period, and (b-f) five temporal buckets. period. In contrast to the previous bucket, the number of citations from P HY to CS has increased. B4 (2010-2014): Interestingly, in this time span, we witness a complete shift in the citation patterns received by the CS papers. In particular, CS seems to have star… view at source ↗
Figure 2
Figure 2. Fraction of citation going from one field to another field over the years [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Citation outflow from fields to other field’s subfields over the year range 1995– 2017. tion Networks, Information Theory, Computer Vision & Pattern Recognition, Computational Complexity and Learning and MA subfields such as Probability and Analysis of PDE. The subfield Information Theory in CS remains popular for both P HY and MA. Similarly, MA’s subfield Probability remains popular for both CS and P HY . The most … view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

6 extracted references · 4 canonical work pages

  1. [1]

    Morillo, F., Bordons, M., G\' o mez, I.: Interdisciplinarity in science: A tentative typology of disciplines and research areas. J. Am. Soc. Inf. Sci. Technol. 54(13), 1237--1249 (Nov 2003)

    work page 2003

  2. [2]

    Organisation for economic cooperation and development (oecd). (1998)

    work page 1998

  3. [3]

    Scientometrics 81(3), 719 (Apr 2009)

    Porter, A.L., Rafols, I.: Is science becoming more interdisciplinary? measuring and mapping six research fields over time. Scientometrics 81(3), 719 (Apr 2009)

    work page 2009

  4. [4]

    In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

    Singh, M., Sarkar, R., Goyal, P., Mukherjee, A., Chakrabarti, S.: Relay-linking models for prominence and obsolescence in evolving networks. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 1077--1086. KDD '17, ACM (2017)

    work page 2017

  5. [5]

    , " * write output.state after.block = add.period write

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