The Effect of Gender in the Publication Patterns in Mathematics

Helena Mihaljević-Brandt1,¶, *, Lucía Santamaría2,¶, *, Marco Tullney3,¶, *

1 Independent Researcher, Berlin, Germany

2 Independent Researcher, Potsdam, Germany

3 German National Library of Science and Technology (TIB), Hannover, Germany

¶These authors contributed equally to this work.

*<EMAIL_ADDRESS>(HMB) http://orcid.org/0000-0003-0782-5382<EMAIL_ADDRESS>(LS) http://orcid.org/0000-0002-5986-0449<EMAIL_ADDRESS>(MT) http://orcid.org/0000-0002-5111-2788

## Abstract

Despite the increasing number of women graduating in mathematics, a systemic
gender imbalance persists and is signified by a pronounced gender gap in the
distribution of active researchers and professors. Especially at the level of
university faculty, women mathematicians continue being drastically
underrepresented, decades after the first affirmative action measures have
been put into place. A solid publication record is of paramount importance for
securing permanent positions. Thus, the question arises whether the
publication patterns of men and women mathematicians differ in a significant
way. Making use of the zbMATH database, one of the most comprehensive metadata
sources on mathematical publications, we analyze the scholarly output of
$\sim\\!150,000$ mathematicians from the past four decades whose gender we
algorithmically inferred. We focus on development over time, collaboration
through coautorships, presumed journal quality and distribution of research
topics—factors known to have a strong impact on job perspectives. We report
significant differences between genders which may put women at a disadvantage
when pursuing an academic career in mathematics.

## Introduction

The overall number of women in Science, Technology, Engineering and
Mathematics (STEM) has undoubtedly been increasing in the past decades [1].
There is a growing presence of women on all academic levels: more female
students, university graduates, PhDs, and professors. However, gender
inequities persist, in particular towards higher academic ranks. Women are
still significantly underrepresented when it comes to permanent academic
positions such as tenure-track and university faculty posts.

Providing comprehensive figures and statistics on women in mathematics is not
trivial, due to scattered data among countries, national differences in
academic careers, and the difficulty to exactly define what “mathematical
research” entails, among others. Among the available surveys, Hobbs and Koomen
[2] is the most complete report on women in mathematical research in Europe
and shows a comparison between data taken in 1993 and 2005. While the
proportion of female mathematicians had increased in the 12-year-long span in
almost all countries, women are still underrepresented, especially in northern
and western Europe. More specifically, the London Mathematical Society’s
report on Women in Mathematics from 2013 surveyed the university mathematics
departments in the UK and states a 29% female representation at the lecturer
and a mere 6% at the professor level [3]. For the faculty positions in the
U.S., the Conference Board of Mathematical Sciences (CBMS) 2015 study [4]
reports an increase in percentages of women among tenured and tenure-eligible
faculty, with a relatively low level of 11% women in tenured faculty of
doctoral university departments. On the other hand, the share of doctorates
granted to women remained almost constant at around 30% between 2000 and 2010
[4]. For a list of more descriptive statistics see [5].

Scholarly publications are (still) the major means of communicating research
results. A solid publication record is a key factor in achieving and
sustaining a successful academic career in every discipline. The relentless
pressure to promptly and steadily publish in the hope of sustaining one’s
career has lead to the coining of the phrase “publish or perish”. The central
role of scholarly productivity when pursuing a professorial post bears the
question whether men and women in mathematics differ regarding their
publication patterns, and whether these differences have changed over time.

Due to the difficulty in obtaining complete records, many studies on gender
effects in academia are restricted to small amounts of data, mostly from
surveys, or limited to a few journals or countries. While small-data studies
might suffer from lack of generality and the danger of “anecdata”, they do
typically deal with cleaner, less ambiguous data sources. In particular,
surveys based on self-reported data have built-in authorship disambiguation
and can acquire gender assignments from the respondents. Large-scale
publication databases instead often suffer from missing information, which
then needs to be inferred. In this article, we analyze publication metadata
from zbMATH, an online bibliographic database comprising more than 3 million
mathematical publications classified by research topics and enhanced with
author profiles. Based on the authors’ first names, we attribute a gender to
$\sim\\!150,000$ mathematicians from the past four decades. To the best of our
knowledge, this is the most comprehensive large-scale study of this kind in
the field of mathematics.

Our analysis addresses four dimensions which are crucial for understanding the
impact of publication patterns on the gender gap in mathematics: (1) research
activity over time, (2) choice of journals and their perceived quality, (3)
collaboration through coauthorship, and (4) distribution across specialisation
fields.

The growing presence of women in mathematics in particular and in STEM
disciplines in general has often led to the belief that achieving a balanced
gender ratio is merely a matter of time. Yet, the increasing number of women
mathematicians entering graduate school will only translate into an overall
increase of women in academia if they move on towards higher scholarly ranks,
which motivates our longitudinal analysis. For active researchers in
mathematics, journal articles are the predominant publication form, and the
perceived quality of a journal is an important criterion when judging the
excellence of a researcher’s publication record. Said quality is often
measured by means of journal rankings, which are highly controversial.
Nevertheless, they are widely in use, often relieving evaluators of the onus
of reading and judging an article by its content. For authors pondering which
journal to submit to, or for university administrators, research funders, or
governmental bodies evaluating publication lists, journal rankings are
presumed to be helpful, thus we employ them in our study. A further career
determinant worth analyzing is the interaction with other researchers: a
prospering network advances the chance of citations by peers, facilites
building collaborations and can help securing a university position. On the
other hand, the share of single-authored publications in mathematics is, in
contrast to many experimental sciences, very high. Such publications act as
proof of one’s individual capabilities, and are thus particularly valuable at
an early career stage. They show that one is not “completely dependent on
senior people for ideas, guidance, techniques, […] Hence, one is ready for a
faculty position” [6]. Last but not least, mathematical topics differ in terms
of general popularity, preferences of journal editors, the overall community,
and particular gatekeepers. Some topics bear higher chances for a scientific
career in mathematics than others, and popular journals reflect a certain bias
for particular mathematical fields [7].

Our analysis shows a higher dropout rate of women as authors of mathematics
papers, despite an upwards trend in the share of women mathematicians over the
last four decades. Women publish less articles than men during their careers
and write less articles alone but establish networks of comparable size. Their
work is significantly less published in journals of high presumed quality,
measured in terms of the Thomson Reuter’s journal impact factor (JIF) as the
most prominent journal ranking schema and the manually compiled Australian ERA
ranking. In three highly regarded journals, Annals of Mathematics, Inventiones
Mathematicae, and Journal of the AMS, a significant underrepresentation of
women persists without notable uptrend over the last four decades. While the
presence of women is shown to strongly fluctuate across mathematical fields,
the choice of research fields is found not to be responsible for the
substantial underrepresentation of women in said three journals.

### Related work

Several studies have looked at publication patterns in the context of gender.
Frietsch et al. [5] studied women’s share among patent applications and
scientific publications. Using two large data sets from the 1990s and 2000s,
the authors estimate the average proportion of women in mathematics
publications of 14 countries in 2005 as 16.5% in total, being lowest in
Germany (11.7%) and highest in Italy (19.6%). Bentley [8] studied data from
two international surveys in 1993 and 2007 involving academic staff in
Australian public universities. While gender differences in publication
productivity decreased significantly within the 14-year time period, in 2007
women published on average only 76% of what men published.

West et al. [1] analyzed JSTOR data, a digital library corpus spanning several
centuries of publications in sciences and humanities. Across all disciplines,
the authors found 21.9% women; for mathematics, the estimated percentage of
female authors is significantly lower at only 10.6% (= 6,134 persons). The
authors showed that authorships by women are not evenly distributed over the
dimensions time, field/subfield, coauthorship, and authorship position, the
latter being particularly relevant for disciplines such as molecular biology
or medicine. A recent, large-scale study based on Thomson Reuters’ Web of
Science (WoS) unveiled the persistence of women’s underrepresentation in
Russian science between 1973 and 2012 across many disciplines, particularly in
mathematics and physics [9]. Using fractional authorships computed by
weighting an authorship as a reciprocal of the total number of (gender-
identified) authors of the respective publication, the authors show
disparities between women and men regarding research output, productivity,
collaboration and scientific impact. Employing similar methods, the analysis
of all articles published between 2008 and 2012 and indexed in WoS by
Larivière et al. [10] confirms the persistence of gender imbalances in
research output worldwide.

Collaboration, e.g. in the form of joint research, publishing or grant
proposals, is considered a strong indicator for productivity and integration
within the research community, and hence has been the subject of various
studies. For various career stages of mathematicians, a positive correlation
between the number of distinct coauthors and the overall number of
publications has been observed [11]. The understanding of the structural
factors that affect men’s and women’s collaboration could lead to the
development of policies to address differences in power and resource dynamics
[12]. A similar argument is made regarding interdisciplinary research and the
possibility to use it to foster career success. Bosquet and Combes [13] use
publication records of a group of French economists to evaluate the impact of
various factors on two measures of article quality defined via journal quality
and Google Scholar citation numbers, respectively. Among others, they show a
high impact of the coauthor network size with respect to both quality
measures. Effects of topical diversity and specialisation are considered as
well, showing disparities between single subfields regarding the number and
average quality of publications, as well as the number of citations.

According to Garg and Kumar [14], female and male Indian researchers in life
sciences differ with respect to team work and choice of journals: women tend
to work in smaller teams with less international collaborative papers, and
their publications are more often published in domestic journals with lower
impact factors. Using a set of high-quality Spanish journals across various
fields of science, Mauleón et al. [15] analyzed the gender distribution over
time of authors and editorial board members as representatives of active and
leading scientists, respectively. While the share of female authors grew over
the years, only a minimal effect was visible in editorial board membership.
Restricting to eight international mathematics journals, Mauleón and Bordons
[16] calculated the share of women in 2004 to be 4% in editorial boards and
10% of all authors. The authors could not discover any relation between gender
and the journals’ impact factors. They showed only slight differences in the
collaborative behaviour and a slight disadvantage for women regarding citation
metrics.

Finally, questions related to productivity, amount of scholarly output, and
merit are the topic of multiple studies. For a discussion on why some faculty
members in political science publish more than others, see Hesli and Lee [17].
The construction of the concept of “academic excellence” is analyzed in Brink
and Benschop [18]. Recently, in a detailed discussion on productivity based on
arXiv publications, Pierson [19] expresses hope that the gender productivity
gap is closing, albeit recognizing that there is still a long way to go until
gender parity is accomplished. Her analysis of almost 1 million arXiv articles
on STEM disciplines supports some of the findings that we present in this
paper.

## Materials and methods

### The zbMATH corpus

zbMATH (formerly Zentralblatt MATH) is an abstracting and reviewing service in
mathematics, produced by FIZ Karlsruhe – Leibniz Institute for Information
Infrastructure and coedited by the European Mathematical Society (EMS) and the
Heidelberg Academy of Sciences and Humanities. Along with MathSciNet, zbMATH
is one of the main services that provide bibliographic information (e.g.
author names, title, source), abstracts and expert reviews as well as
aggregated data (e.g. keywords) on mathematical publications to the scientific
community.

#### Author profiles

The process of attributing authorship of bibliographic records to specific
individual researchers, known as “author name disambiguation”, is essential to
perform analyses on publication data. This is by no means a straightforward
task, due to the fact that personal names are not sufficiently distinct to
unambiguously identify each individual within the large number of researchers
active today and in the past. The problem is exacerbated by the inconsistent
way in which author names appear in publications.

Author name disambiguation, and the more general problem of word sense
disambiguation, is an open issue in computational linguistics and natural
language processing. A taxonomy of automatic author name disambiguation
methods can be found in [20]. zbMATH provides author profiles for its indexed
publications. They are constructed following a multifaceted approach based on
automatic, manual, and collaborative methods. Initially, the assignment of a
publication to an author is performed algorithmically, using mainly the name
string and coauthorship information; some authorship assignments are post-
processed manually by the zbMATH staff, and, recently, users can contribute
corrections through an online form [21].

Name-string-based authorship attribution suffers from various well-known
issues such as confusion of authors with frequent names (John Miller), missing
name parts (middle names), variability through transliteration (Chebyshev vs.
Tschebyscheff), or name changes throughout a researcher’s life (after a change
of civil state). In zbMATH, an ambiguous authorship is initially attributed to
all possible candidates, e.g. an article authored by “P. Smith” will appear in
the profiles of “Paul Smith” and “Patricia Smith”. Hence an author profile in
zbMATH can contain wrongly assigned articles, or publications can be missing.
A combination of both issues is possible as well. Some types of assignment
error are more frequent in relation to certain regions; for instance, authors
with Chinese names are often assigned to ambiguous profiles due to common
surnames and transliteration problems. Due to this latter factor, authors from
the former Soviet countries frequently suffer from profile splitting.

Cases such as “P. Smith” referred above, when the author name string does not
suffice to unequivocally assign an author, are marked as ambiguous and are not
to be trusted. We excluded such authorships from our analyses.

#### Mathematics Subject Classification (MSC)

The Mathematics Subject Classification (MSC) is a universally accepted
classification schema in mathematics jointly produced and maintained by
MathSciNet and zbMATH. It is a tree-like, three-level alphanumerical scheme to
label publications according to their subject matter. For instance, “35”
stands for the area of “Partial Differential Equations”, “35J” refers to
“Elliptic Equations and Systems”, and “35J75” is the classification for
“Singular Elliptic Equations”. The MSC exists since 1970; it is revised every
10 years, with MSC 2010 being the current version [22]. All entries in zbMATH
since 1970, and even some older data, are classified by its editorial board
according to the MSC. The first code of an article is its primary
classification, supposedly reflecting its most important content; subsequent
codes are secondary.

Articles classified with first-level MSC codes between 03 and 65 belong to
mathematics subfields such as Logic, Discrete Mathematics, Algebra, Analysis,
Geometry, Topology, Probability Theory, Statistics, and Numerical Mathematics.
Those with codes between 68 and 94 fall into mathematical applications related
to Computer Science, Physics, or Economics. The areas 00 and 01 refer to
general topics and history of mathematics; 97 is Mathematical Education.

#### Focus on core mathematicians

The zbMATH corpus includes publications in which mathematical concepts are
applied to scientific subjects such as quantum theory or computational
biology. Hence, the zbMATH author records necessarily contain individuals
whose primary research is not in mathematics. Their publications usually
appear in interdisciplinary journals. For our analysis we have decided to only
consider authors as mathematicians if they have published at least one article
in a “core mathematics journal”. To extract such journals, we resort to the
MSC labels applied to a journal’s articles to identify core mathematics
publications, using the following heuristics: a journal belongs in the group
of core mathematics journals if at least 90% of its articles with primary
classification between 03 and 94 fall within the range 03–65. Our corpus
consists of publications drawn from 4064 journals. By including the rather
applied areas of Statistics (62) and Numerical Mathematics (65) we retain a
comparatively large number of 1,050 core mathematics journals, representing
26% of all serials indexed by zbMATH with publications after 1970.

### Guessing an author’s gender

In general, the gender of a person cannot be inferred programmatically from
the name string—hence the use of a database of annotated names for gender
assignment is often unavoidable. Several studies have made use of annotated
data from varied sources: West et al. [1] used a two-gender data set provided
by the US Social Security Administration containing the top 1,000 annual girl
and boy baby names since 1888; Frietsch et al. [5] worked with a first name
database comprising 8,291 names from six European countries. This database was
created as part of a project carried out by the European commission in 2002,
in which first name assignments were collected from various data sources, then
post-processed in order to achieve a high quality level, and finally tested
[23]. Implementations of gender guessing procedures include the Python library
Gender Detector [24] and the R package gender [25]. A benchmark comparison of
gender detection algorithms can be found at [26].

We tried to attribute a gender to all zbMATH author profiles. The zbMATH
corpus contains no supplementary metadata on authors’ genders. We resorted to
the annotated collection of first names described in [27]. The dictionary file
contains a list of more than 42,000 names with gender assignment [28]; at the
time of the last update in November 2008 the list was assumed to cover the
vast majority of names in all European and some non-European countries like
China, India, Japan, USA. According to the author Jörg Michael, for some
countries such as Turkey or Korea all names have been independently classified
by native speakers, indicating a high quality of the data. Yet the zbMATH data
contains no information on the country of origin of the authors, hence we
could not use this additional facet. Every name in the dictionary is labelled
as “unknown”, “female” or “male”, with additional information on the certainty
levels of the assignment.

On top of this algorithmic assignment, we have performed a manual check of the
most prolific profiles. Specifically, we have reviewed the gender assignment
for the top (in number of publications) 300 profiles classified as men and 500
women. These typically correspond to well-known mathematicians, whose gender
we were able to assess. We found no instances of women mathematicians being
incorrectly classified and a $\sim\\!5\%$ error in men that were incorrectly
labelled as women. We manually changed the gender of the latter, resulting on
cleaner and more trustworthy gender data. We observed that these errors were
more frequent for names from India, Pakistan and Japan. We conclude that our
study overrepresents the amount of women by at most $\sim\\!5\%$.

We point out that troughout the text, we speak of men and women as if those
categories were real. Gender binary is a concept that lacks both complexity
and suitability. But categories are constructs and results of societal action.
Almost all databases and publications connecting names with gender operate
within this binary schema. Since we do not have access to detailed author
profiles and data on how authors identify when it comes to gender, we use the
name as an indicator of the perceived gender of each author. Thus, our
categorization of mathematicians into men and women is following societal and
academic action and is due to pragmatic and substantive reasons.

### Data overview

Our data set contains information on all publications by authors we identified
as “core mathematicians” as described in subsection Focus on core
mathematicians. For every such publication we extracted the authors, their
order of appearance, the title, the publication year, all MSC classification
codes, and the journal name together with ISSN and e-ISSN codes, if the
publication appeared in a journal. We additionally tagged authorships with a
value indicating the quality of the authorship assignment (manually curated,
algorithmically unambiguous, and ambiguous). The MSC classification exists
since 1970. We restricted our analyses to authorships published since then to
ensure consistency when addressing our key questions.

The corpus consists of 2,245,205 document entities corresponding to 3,433,553
instances of authorship, yielding 1.53 authors per article. The amount of
ambiguous authorships which could not be assigned by zbMATH to a unique author
amounts to 226,500 ($6.6\%$). We excluded these authorships from the analyses
since we cannot decide which attribution might be correct.

We applied a gender assignment algorithm as described in [29] to 262,146
author identities, the remaining 47,319 ($\sim\\!15\%$) authors were listed
without a first name. We were able to assign a gender to $\sim\\!55\%$ of all
profiles with a real first name; among those, 27,596 ($\sim\\!19\%$) authors
were classified as women and 116,657 as men.

We were able to guess the gender for $61.4\%$ of all (non-ambiguous) instances
of authorship. Fig 1 displays the percentage of all authorships that could be
labelled as women since 1970. It is undeniable that the amount of women that
publish in mathematics has been increasing—their share has tripled over the
past four decades.

Fig 1: Percentage of authorships by women since 1970. The darker green line
shows the share of authors that could be identified as women, marking the
lower limit. The shadowed region delimits the extrapolated values taking into
account that we could only assign a gender to $61.4\%$ of all authorships. We
estimate the proportion of women in the remaining group of authors to be
smaller than their share in the identified group and conclude that the
percentage of women among all authorships lies within the shadowed region.

As shown in Table 1, profiles of women are on average slightly less ambiguous
than those of men; profiles with a high level of ambiguity are significantly
more frequent among those authors we could not classify as women or men. One
explanation for the latter observation is the fact that our gender assignment
algorithm requires the first name (which is missing for $15.3\%$ of authors in
our corpus), and the name string is also the main information used for
authorship assignment by zbMATH.

| Ratio of non-ambiguous publications per profile
---|---
|  100% |  90% |  80% |  70% |  60%
all authors |  49% |  52% |  55% |  58% |  65%
women |  71% |  73% |  75% |  77% |  84%
men |  62% |  67% |  71% |  73% |  81%
Table 1: Distribution of the level of correctness of author profiles with
respect to gender: to 71% of all women and 62% of all men no ambiguous
authorships are assigned.

## Results

### Cohort analysis

A fundamental metric to understand the gender gap among scientists is the
distribution of researchers that successfully sustain a career in academia
over time. We analyse this aspect with a cohort analysis of authors since
1970. A cohort is a group of individuals that share a common characteristic
over a defined period of time. Comparing the development of cohorts allows for
longitudinal studies that unveil patterns over large periods of time. In our
study, we assign authors to a given cohort according to the year of first
recorded publication, which acts as an approximation for the beginning of
their scientific career. We then follow the publication records of all authors
in every cohort and select those individuals that continue publishing at least
5 and 10 years, respectively, after their first paper. We roughly assume
researchers to be at the postdoctoral stage 5 years after their first
publication and to have secured a permanent position at professorial level
another 5 years later.

#### Women mathematicians have tripled their number since 1970

The total number of authors that continue publishing 5 and 10 years after
their first paper appears in the upper panel of Fig 2. Despite a brief
stagnation in the 1980s, the number of mathematicians at our estimate of
professorial level (10 years) has increased from $\sim\\!1500$ in the 1970s to
$\sim\\!1800$ per year in the 1990s. Note that the decreasing number of
authors after the 1990s reflects the fact that data for the most recent
cohorts is partially incomplete: members of the early 2000s cohorts may well
be still active today, eventhough they do not have a publication in the early
2010s. Therefore we regard the figures from the 2000s as non-conclusive.

Fig 2: Cohort analysis since 1970. Data corresponds to mathematicians with a
first publication in the years 1970–2003 and another publication at least 5
and 10 years later, respectively. The upper panel shows the total number of
authors per year and gender with continued careers 5 and 10 years after their
first recorded publication. The lower panel displays the percentage of authors
identified as women per cohort year and with careers lasting at least 5 and 10
years.

Whereas a mere $\sim\\!6\\!-\\!8\%$ of all authors in the early 1970s were
women, their percentage has tripled within the following three decades (Fig
2). Roughly 20% of all authors with careers lasting at least 10 years that
started publishing in the late 1990s are women. However, this is still far
from the percentage of women that pursue mathematics education at the
undergraduate level.

#### Women publish less than men at the beginning of their careers

An important metric that reveals differences between genders is the amount of
publications. A shorter publication record at the time of applying for an
academic position diminishes the chances of success. Our findings confirm the
phenomenom known as productivity gap, agreeing with those of Pierson [19]. We
have analyzed the average amount of publications of men and women during the 5
and 10 years after their first article appeared; we find that men routinely
surpass women. Fig 3 illustrates this fact, showing the excess of publications
by men per cohort year. Despite the visible trend towards a narrower
productivity gap, men are shown to publish on average 9% and 13% more papers
than women within their first 5 and 10 years as authors, respectively.

Fig 3: Excess of publications by men during the 5 and 10 years after their
first article. On average, men publish 9% and 13% more papers than women
within the first 5 and 10 years of their publishing career, respectively.
Notably, the productivity gap has been closing since 1970.

#### Women leave academia at a higher rate than men

In Fig 4 we evaluate the percentage of men and women that stop publishing at
some point between 5 and 10 years after their first paper. This we interpret
as them having discontinued their research careers. The results clearly show
an overall increase in the dropout rate for both genders over the past
decades. This phenomenon reflects the fact that an increasing number of
doctorates and postdoctoral scholars find it impossible to secure a permanent
position in science, thus being forced to leave academia even after a
comparatively large publishing trajectory of at least 5 years.

Fig 4: Dropout rate in authors per cohort year within 5 to 10 years of their
first publication. The figure shows the percentage of men and women that,
having published for at least 5 years, disappear from our records 5 to 10
years after their first article.

On top of that, women end their research career in this period at a higher
rate than men, as can be seen in Fig 4. A larger comparative drop in the years
that roughly correspond to the postdoctoral stage may indicate that women
either lack support to reach the stable professorial ranks, or do not wish or
are not able to continue holding temporary positions in a period of life often
coincident with family-planning decisions. This evidences the existence of a
leaky pipeline, understood as a continuous loss of women in academia as they
climb the career ladder, that prevents the number of women in mathematics from
increasing as fast as the rates of women enrolling at the graduate level would
suggest.

### Perception of quality

We analyze two of the most prominent journal rankings in mathematics, the
Australian ERA list and the journal impact factor. ERA (Excellence in Research
for Australia) is an initiative of the Australian Research Council to measure
the quality of Australian research. ERA compiled a ranked journal list with
ranks reaching from A* (with the expectation that almost every article in
these journals will be of very high quality) over A (most articles of very
high quality) and B (only some articles of very high quality) to C (very high
quality not expected) and “not ranked”. We use the ERA 2010 ranked journal
list which is the most recent list of this kind. It comprises 20,712 journals
of all academic fields. Since 2012 ERA does not rank the journals anymore and
publishes instead an unranked but more complex list of journals.

The journal impact factor (JIF) is calculated based on Thomson Reuter’s
Journal Citation Reports. It is defined as the average number of article
citations in a journal in the last two years. There is widespread criticism of
the impact factor, as there are many means to manipulate it [30]. Based on
different publication and citation practices in various academic fields, it is
difficult to compare the impact factor across disciplines. We refer to the
2015 edition of Journal Citation Reports (which uses publication data from
2013/2014) and investigate impact factors for 7 subject categories:
“Mathematics”, “Mathematics, Applied”, “Mathematics, Interdisciplinary
Applications”, “Computer Science, Theory and Methods”, “Logic”, “Physics,
Mathematical”, “Statistics and Probability”.

We identify the ERA rank and JIF by ISSN, which leads to 1,768 matched
journals in the ERA list and 728 journals with a JIF (663 journals appear in
both indexes). We investigate publications from 2004–2013. Note that we refer
to the most recent impact factor from 2015 which in most cases is not the
impact factor of the journal at the submission or publication date. We further
restrict our sample to publications with conclusive gender attribution and in
journals from the ERA list or with an impact factor. We do not limit the
analysis to core mathematics journals (see subsection Focus on core
mathematicians) after our tests showed no major differences with respect to
the full analysis.

For both rankings we investigate how the percentage of women among the authors
per rank deviates from the average in the complete data set. We use the ranks
A*, A, B, and C as assigned by ERA. Since the impact factor is not discrete,
we calculate percentiles of the journals in our list, the highest (lowest)
containing the 25% journals with the highest (lowest) impact factors. We end
up with four groups of publications for each ranking. In both cases, the
number of articles per group differs. Furthermore, we examine authorships of
single-authored publications versus all authorships (including single- and
multi-authored) and quote separate results.

#### High-ranked mathematics journals publish less articles authored by women

We uncover significant differences between female and male authors in both
these rankings. There are fewer women amongst the authors of top-ranked
journals than could have been expected from the overall distribution of men
and women in our samples. Our analysis of the ERA ranked journal list shows
that only $8.5\%$ women are authors of single-authored publications in A*
journals, a deviation of $-21.3\%$ from the average, while there is a
deviation of $+20.9\%$ in the low-ranked category C. The results for all
single- and multi-authored papers are similar, since the A* journals show
$18.9\%$ less authorships by women while there is an excess of $16.6\%$ with
respect to the average in C journals. The results are displayed in Fig 5.

Fig 5: Deviation of the share of women’s publications from the average ERA
ranking. ERA values rank from A* (excellent) to C (very high quality not
expected). Annotated over or under each bar is the absolute number of single-
authored publications and all authorships by female authors per group.

For the percentiles of the JIF we obtain a significantly smaller share of
female authors in the top 25% journals with $17.4\%$ and $7.8\%$ less women in
the single-authored and all-authorships samples, respectively, when compared
to the corresponding overall shares. Details are shown in Fig 6.

Fig 6: Deviation of the share of women’s publications from the average impact
factor. JIF values are shown as percentile, each containing 25% of the indexed
journals in our sample. 1.0 to 0.75 contains the highest impact factors, 0.25
to 0.0 contains the lowest. Annotated over or under each bar is the absolute
number of respective authorships by female authors per percentile bracket.

#### Women are drastically underrepresented in three top-ranked journals

Female authors publish significantly less in the top journals according to the
two ranking mechanisms we examined. To look further at the peak of what is
perceived as good journal quality, we analyze the gender distribution of
authors in three highly regarded serials: “Annals of Mathematics”,
“Inventiones Mathematicae”, and “Journal of the AMS”. Our aim is to shed light
on the percentage of female authorships and its development over the last
decades. Fig 7 illustrates that the share of female authors is significantly
lower than in the overall sample of mathematical journals, but also lower than
in the top categories of the ERA list and the JIF. Even more remarkable: no
upward trend is discernible: in the Journal of the AMS, for instance, we do
not identify a single female author in the last years (2012: 42 men/23
unknown; 2013: 43 men/16 unknown; 2014: 20 men/9 unknown). Note that these
numbers include all authorships. Limiting the analysis to single-authored
publications results in very low absolute numbers, but following a similar
tendency.

Fig 7: Share of authorships by women in three reference journals since 1970.
Percentage of authorships by women in Inventiones Mathematicae, Annals of
Mathematics, and Journal of the American Mathematical Society. The dark green
line shows our estimation of the share of female authors, the shadowed region
indicates the error margin we consider to be realistic (same proportion of
women in the unknown group).

### Collaboration through coauthorship

Often, the idea of mathematics is associated with the image of a solitary
researcher, whose work requires only pen and paper and hence can be performed
in pure isolation. It is therefore no surprise that more than 95% of all
publications of “core mathematicians” in zbMATH before 1950 were single-
authored; in our corpus they still comprise almost 60% of all records. Despite
the strategical relevance of single-authored publications, a strong shift
towards collaborative authoring is evident. This trend is supported by our
data: among the publications that appeared after 2000, only 39% had been
authored by a single person. On the other hand, almost 25% of the publications
were authored by more than 2 authors compared to e.g. less than 8% in the
period 1970–2000, indicating a growing interest in building networks. We
investigate coauthorship patterns in terms of two metrics: share of single-
authored publications per author and number of distinct coauthors (“network
size”). In contrast to other studies, we do not analyze the positions of
coauthors with respect to gender, since in mathematics, authors are usually
listed in alphabetical order (see, e.g., [1]).

We examine the records of mathematicians that started publishing in 1970 or
later for whom we were able to successfully assign a gender (25,050 women and
77,792 men). Since the odds of collaborating with different coauthors increase
with publication record length, we segment authors according to their number
of publications. We sample the data as to include the same number of female
and male authors per total number of publications. The sample size is thus
determined by the maximum number of authors in the women’s group.

#### Women publish less single-authored papers

On average, men write 38% of their scientific records as single authors, in
contrast to 29% among women. This trend remains unchanged when looking at
groups according to the total number of publications, in segments of at most
5, 10, 20, 50, or more than 100. Fig 8 illustrates this conclusion, showing a
statistically significant gap between men and women in the percentage of
single-authored publications across all segments. A similar tendency has also
been reported in [31] for UK-authored journal articles in Social Sciences, or
in [32] for the field of Information Systems; in the later study, the
percentage of male authors with a single-authored publication was twice as
large as for their female counterparts.

Fig 8: Mean and median of the amount of single-authored publications per
author. Authors are grouped in segments defined by length of publication
record: at most 5, 10, 20, 50, or more than 100 publications. The rightmost
bar refers to the full data set.

Sooner or later, many mathematicians publish an article on their own. In our
data set, this is the case for 52% of the women; in the men’s sample this
holds true for 61%. The single-authored paper is usually not the author’s
first publication, in particular in the case of female mathematicians. Women
write their first publication most often together with coauthors: only 33% of
their first publications are single authored, for men it is 43%.

#### Women’s and men’s coauthor networks are of similar size

Although women mathematicians have significantly less single-authored
publications than their male counterparts, they do not collaborate with a
considerably larger number of peers. On average, women have 3.6 distinct
coauthors, 0.2 more than men. Fig 9 shows the network size for men and women
in more detail, split according to the length of publication record. The dark
and light green bars display the average network sizes of women and men,
respectively, with the enclosed triangles representing the medians. The mean
network size of women is slightly larger in each of the groups; however, the
gap decreases with a growing number of publications from factor 1.15 in the
group of authors with at most 5 publications (i.e. the network size of women
in this group is on average 1.15 times larger than that of men) to 1.02 in the
two groups of authors with more than 50 publications. The median values for
women and men are equal in the first two and the fourth group; for authors
with 11-20 publications in total, women have a median of 6 compared to a
median of 5 for men. In the last two groups, the median value for men is
larger; among authors with more than 100 publications the group of men
exhibits a median of 42 versus 38 for women.

Fig 9: Mean and median of the number of distinct coauthors per author. Authors
are grouped as in Fig 8.

Both measures suggest that women and men collaborate with a similar number of
peers. However, when measuring the network size with respect to the time line
instead of the total number of publications, then Fig 3 suggests that the
networks of women are even smaller than those of men, at least when looking at
an early career stage, since women publish around 10% less articles than men
within the first 5 years of their research [19].

Bozeman and Gaughan [12] statistically analysed collaboration patterns based
on surveys of STEM researchers in the United States. In contrast to the
authors’ expectations, women had a slightly (but not significantly) larger
collaboration network. However, the study did not include information on
publications, and hence could not elaborate on the relation between the number
of collaborators and single-authored publications.

It is a common assumption that a larger coauthor network is indicative of the
visibility of an author’s research. For instance, Bentley [8] shows for
Australian university research that international collaborators were one of
the main factors associated with increased publication productivity among both
men and women. Our findings support the conclusion that men and women
collaborate with similarly-sized peer groups. However, women seem to do so at
the expense of their own single-authored publications, which might undermine
their profiles as fully independent researchers.

### Topical distribution

We study the distribution of authors and publications in mathematical fields
as represented by the MSC 2010 (see subsection The zbMATH corpus). We focus on
the first and second MSC levels; the first level represents mathematical
fields such as “Algebraic Topology” or “Dynamical Systems”, whereas the second
level allows for a more granular view of related mathematical communitites. We
restricted to the primary MSC code assigned to an article since this usually
captures the main content of the research.

#### Women’s distribution across research fields is not homogeneous

Women publish in all of the 63 mathematical fields represented by the first
hierarchy level of the MSC; out of the 528 topic-based subfields at the second
MSC-level, there are only three in which none of the women in our data set
have published either alone or with a coauthor. By restricting our search to
single-authored publications, we find 13 second-level classes in which women
have not yet published, such as “$K$-theory in number theory” (19F) or
“Function theory on the disk” (30J).

However, women are not equally represented across mathematical areas. Using
hierarchical maps as displayed in Fig 10 we visualize the share of women resp.
women’s publications across the MSC classes on level 1 and 2: each rectangle
represents a mathematical class, its size is proportional to the number of
authors resp. publications in that field, and the darker the color, the larger
their share.

Fig 10: Distribution of women authors across mathematical fields and
subfields. Mathematical subjects are represented by MSC classes as a
hierarchical map. Data includes publications of all mathematicians classified
as women or men. An intense green color stands for a relatively high share of
women’s publications, an intense yellow for a relatively low share. The size
of the rectangle is proportional to the field size. Under
https://doi.org/10.5281/zenodo.51147, the detailed numbers are shown when
hovering over the rectangles. Clicking on a rectangle shows the distribution
on the second MSC-level in that field; a right-click returns to the first-
level view.

This confirms the results by West et al. [1, 33] who showed an uneven
distribution based on publications from JSTOR. Unfortunately, we cannot
compare the results in detail since West et al. did not use a classification
schema such as the MSC but instead employed an unsupervised hierarchical
clustering approach to assign publications to topics.

In subsection Perception of quality we showed that the presence of women in
three of the most renowned mathematical journals—the “Annals of Mathematics”,
“Inventiones Mathematicae” and the “Journal of the American Mathematical
Society”—is low, and reveals no significant improvement over the last three
decades. The three journals, despite aiming to cover all fields in
mathematics, display a bias towards certain fields. For instance, the five
areas “Algebraic Geometry (14)”, “Number Theory (11)”, “Differential Geometry
(53)”, “Dynamical Systems and Ergodic Theory (37)” and “Group Theory and
Generalizations (20)”, already cover more than 50% of all publications in
these journals. On the second MSC level we see a similar dominance of certain
subfields, leading to a coverage of more than a third of all publications by
only 12 classes which are shown in Fig 11. To investigate whether the
selection of research areas might be responsible for the underrepresentation
of women in these journals, we checked for correlation between a particular
field’s presence in the three journals and the women’s share in this field. It
turns out that women are well represented in the top 12 level-2 classes
($\sim\\!9\%$ above the average when considering all publications and
$\sim\\!13\%$ when restricting to single-authored publications). When looking
at publications in those fields instead of authors, the numbers even out
($\sim\\!-3\%$ when looking at all publications and $\sim\\!4\%$ when
restricting to single-authored publications). Most level-1 fields with strong
dominance in the three journals show an average or even higher presence of
women, with the traditional field of “Number Theory” being the most
significant negative exception.

Fig 11: Single-authored publications in twelve research fields. These second
MSC-level subjects dominate the articles in the analyzed three top journals.
The bar chart on the left shows the deviation of the share of women’s
publications from the average, on the right-hand side is the size of the
research field in terms of the overall number of single-authored publications.

#### Women’s distribution of research topics is narrower than men’s

As shown in subsection Perception of quality, women and men collaborate with a
comparable number of peers when measuring against groups of authors with a
similarly-sized publication record. Taking the point in time as scale instead
of the total number of publications (see Fig 3), the networks of women are
smaller than those of men. We see a similar pattern when considering the
variation of topics: as shown in Fig 12, publications of women spread across
less MSC classes than those of men, while keeping the overall number of
publications per author fixed. Their stronger focus on a smaller set of
research topics could potentially be another drawback for women in academia,
since it reduces the already low number of possible faculty positions suitable
for applying to.

Fig 12: Diversity of research fields for women and men with 2 to 5
publications in total. For a fixed total number of publications ranging from 2
to 5, the same number of female and male authors has been sampled and the
number of different MSC classes per author has been computed.

## Discussion

Our study is based on comprehensive data from publications in all areas of
mathematics research between 1970 and 2013. Backed by a statistically
significant data corpus and scanning a rather broad set of determinants for
scholarly productivity, we audit the status of women mathematicians in the
publication landscape and identify research questions which would provide
additional substantial insights.

We have split all authors in our data set in cohorts according to the year of
their first publication and have investigated their progression 5 and 10 years
into their careers. We have looked into variations in publication patterns
between men and women regarding presumed quality of the journals they publish
in, their coauthorship networks, and the topical distribution of their
scholarly output. We report statistically significant differences among
genders in all the aforestated aspects.

The share of women mathematicians who have been active for at least 5 to 10
years has roughly tripled since the 1970s (see Fig 2). However, women abandon
their academic careers within a decade of having started them at a much higher
rate than men (see Fig 4). This indicates the existence of a “leaky pipeline”
that slows down the inclusion of women in the higher ranks of academia, and it
invalidates the hypothesis that, given the steady increase of women entering
mathematics at the undergraduate level, their incorporation to higher academic
ranks should simply follow suit. Furthermore, the so-called productivity gap,
stating that women produce less publications within a fixed period of time, is
clearly visible in every cohort. However, it has been narrowing down
drastically since 1970 with a visibly positive trend in recent years.

The perceived quality of the journal in which an article is published is one
of the most common means of evaluating a researcher’s academic output. There
is legitimate and compelling criticism of this approach. Beyond all objections
to particular shortcomings of these measurements, what they all have in common
is the impossibility of providing any information on individual articles.
While we believe that journal rankings are no proper means to evaluate
scientists and their work, they are still widely adopted to measure research
quality. With respect to such a measurement scheme, women are extremely
underrepresented in top-ranked journals. A negative correlation exists between
journal rank, measured using the ERA ranking or the journal impact factor, and
the percentage of women among its authors, a pattern that remains fairly
stable over time. A further investigation of three highly renowned mathematics
journals shows an unusually low percentage of published women, with almost no
improvement over time. Several explanations may be proposed for this fact,
from biased editorial boards and reviewers to lack of strategic publication
choices on the part of women. Using our data, we were able to exclude the
choice of the research field as possible reason, since women are well
represented in the fields favoured by the considered journals. Certainly, it
would be worth to further investigate if and why women simply submit less
articles to prominent journals or whether their papers are more often
rejected. Nonetheless, our findings uncover a specific phenomenon correlating
journal rank and scarcity of published women, and the reasons for these
differences need to be studied in more detail.

With respect to collaboration through coauthorship, our results indicate that
men publish far more single-authored papers than women. Since a solid record
of single-authored publications seemingly shows one’s ability of independence
and creativity and is hence associated with “scientific autonomy”, the
disparity could have a negative effect on women’s career perspectives, in
particular at an early stage. Considering that their network is not
significantly larger, this suggests that women regularly collaborate with the
same researchers and begs the question of with whom women and men collaborate.
Are the most frequent coauthors the doctoral advisor and close collaborators?
Likewise, an analysis of the coauthors’ gender could help understand whether
gender induces distinctive publication dynamics, e.g in an all-female versus a
mixed-gender collaboration. Additionally, it would be interesting to explore
if factors such as the academic position or the country/internationality of
the collaborators have an effect on the collaboration patterns.

It seems sensible to consider the aforementioned questions also in a field-
focused setting since the presence of women strongly deviates across research
area, as shown in Section Topical distribution. It would also be interesting
to explore in more detail which factors motivate women to enter a certain
research area. What constitutes an inviting “atmosphere” within a field, what
is the importance of role models, mentoring, etc.? How does this relate with
the age and interdisciplinarity of a field? Do new and emerging areas produce
a different mind-set and are hence more attractive for women scientists?

We note that our analysis is robust with respect to the counting scheme. In
certain cases, e.g. when papers authored by men have a larger number of
authors than papers by women, it might be more suitable to analyse
distributions of fractional authorships where an authorship is weighted
reciprocally to the overall number of authors of the paper [10, 9]. For our
data set, however, both full and fractional counting lead to very similar
results. This is explained by the dominance of single-authored publications in
mathematics and the relative balance of women’s and men’s network sizes. Since
women in our data set have, on average, more coauthors than men, the gender
gap is even slightly stronger in terms of fractional authorships.

Our findings support the thesis that gender-related publication patterns exist
and are one of the factors that lead to an underrepresentation of women in
mathematics. Our analysis cannot give a definite answer to the main motivating
question, i.e. why the gender gap in mathematics. The differences in research
productivity according to gender are by no means trivial to measure or
explain. Likewise, research productivity alone does not fully translate into
career success, however defined. Various studies, including those cited in
Section Related work, have looked at the factors that might contribute to a
higher or lower research output, including demographics, family-related
circumstances, working environment, etc. Furthermore, academic excellence is
an inherently gendered concept [18], with several aspects contributing to its
fabrication. Even if the publication and collaboration patterns of men and
women showed no significant differences, a completely gender-blind approach to
promotion in mathematics academic positions is unfortunately not to be
expected. Hence a thorough discussion on the topic must necessarily expand
towards further aspects. Perhaps a first one is the question of who or what is
setting the pace and norms of scholarly publishing. In the work of Brink and
Benschop [18] the concept of “masculine career path” (p. 513) is put forward:
every researcher (man or woman) whose publishing record deviates from the
traditional trajectory, maybe due to career interruptions or periods of part-
time work, is at dire disadvantage for promotion. A similar remark is found in
Bentley [8], which mentions the institutionalization of male dominance by
associating merit primarily with scholarly output, an activity for which men
receive greater patronage and support. The lack of encouragement that many
female doctoral students perceive when it comes to applying for funding or to
collaborate on research projects already sets back their careers. Women are
forced to either “catch up” later or, or are driven out of the field
altogether at a higher rate than men, as evidenced by our cohort analysis. The
fact that in many cases the number of publications is the main factor in
defining the quality of research constitutes a drawback for the numerous women
with nonlinear career trajectories or less research time.

Using one of the largest metadata sources on mathematical publications we have
shown that the collective actions of all actors in mathematics publishing
result in significant differences between two gender groups regarding key
factors of academic careers. A more thorough and detailed analysis of single
aspects would clearly help to explain the observed disparities between women
and men. For this, additional data such as affiliations, acceptance and
rejection statistics from journals, or the country of origin would be very
helpful; the latter could also be used for an improvement of the gender
assignment algorithm which constitutes the base of our study. In fact, we
would prefer not to use such an assignment schema at all but ask the authors
instead how they identify. Our analyses have unveiled significant differences
which may already foster individual takes on publishing, hence career
decisions, and inspire institutional measure. We believe that the gained
insights will deliver input for further discussions within the community for
potential collective and/or individual strategies to overcome the current
situation.

## Acknowledgements

We gratefully acknowledge the support of FIZ Karlsruhe for granting us access
to their publication data. We thank the European Women in Mathematics network
and specially its former convenor Marie-Françoise Roy for feedback in the
first stages of this project and useful comments on an earlier paper draft.

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