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MATHEMATICS OF EXCLUDED WOMEN -A PERSONAL
NARRATIVE
A. Mani
Department of Pure Mathematics, University of Calcutta
9/1B, Jatin Bagchi Road, Kolkata-700029, India
Exclusion definitely affects a women’s mathematics. Some classification of the factors
that shape the unique features associated can definitely be specified. .On the basis of
these considerations I propose a new partial theoretical model for accessing the
connection between a woman's attitude towards and practice of research in
mathematics, and the discrimination faced by her. My approach to the subject has
been very non-standard and unique with much focus on representing reasoning and
knowledge. In this narrative research (or reflective paper), I try to explain the shaping
of my mathematics at the research level over many years in the clouds of many
exclusions in the perspective of the model mentioned.
INTRODUCTION: BASIC FRAMEWORK
Exclusion and its consequences have their hierarchies that vary with one’s perception
of sociological context and related assumptions. Women as a class are uniformly
excluded relative to a level of exclusion. Trans women and lesbians face much higher
levels of exclusion at all stages of their life. These exclusions affect most aspects of
life, learning and creative activities of all kinds and in particular research level
mathematics.
In feminist and sociological studies, it is well known that women react to
systemic discrimination and suppression in different ways (by way of becoming door
mats or slaves, door mats that play with the contradictions of capitalism-
patriarchy nexus, through cautious self-centered negotiations, applied feminist
approaches, overt rebellion, activism in the tradition of the personal being political,
uncompromising rebellion, and others). Often their work in fields that involve
intellectual labor are colored by an urge to highlight their suffering or an urge to break
free. A classification of such subtle modes of expression can be computed with words
and will be referred to as proactive feminist attitude . I think that these relate to
attitudes and ways adopted by women in mathematical research as well. Admittedly,
the available studies do not go into the fine details of relatively successful
researchers - because the level of interdisciplinary interaction necessary would be
hard to attain. Most studies on STEM research and gender tend to focus on passive
conditioning attitudes alone (as, for example, in (Leslie, 2015)). Some narrative
accounts (Subramanian, 2017) are available – but these have not been optimized for
illustrating the nature of sexism and discrimination. In contrast, attitude of students
towards mathematics can be accessed by the three dimensional model (involving
emotional dimension, vision of mathematics, and perceived competence) (Zan,
2013).
One can be bold and work within frameworks and problems suggested by others, or
one can be bolder in seeking out newer problems or one can construct frameworks that
question the existing status qua or one can break free from the institutional chains of
the research ecosystem - the possibilities are finite. Attitude of researchers in
mathematics towards research has largely been governed by the whims and fancies of
funding agencies and the limited interests of the people-in-charge. People who try to
work outside the traditional order can be labeled rebellious. Such work may or may not
involve additional philosophical insight on part of the researcher. Most trans
women are women who have endured systemic suppression from society to the point
that they have lost hope of fitting in any way - if these women love research
in mathematics then their mathematics is likely to be rebellious.
The above two paragraphs can be regarded as a new proposal for a partial
theoretical model for accessing the connection between a woman's attitude
towards and practice of research in mathematics, and the discrimination faced by her.
I will refer to this as the Discrimination responsive Attitude modulated Practice of
Research- (APRD) model. The present paper is a contribution to the rebellious category
in the model – Does it relate to the practice of research? Further aspects of the model
will be developed separately.
Narrative research is common in feminist studies, grounded theory and is also well
known in mathematics education research as in (Connelly et.al, 1990). In fact, the
three dimensional model (Zan, 2013) was arrived at through focused narratives. This
paper is in the form of a personal narrative, in which I also seek to find
connections for the APRD model mentioned earlier - am the only trans woman
in mathematics research in the country.
I am a leading researcher in the foundations of rough sets (a formal approach to
vagueness), algebra, logic and allied fields (but my mathematical career has been a
very nonstandard one and am sort of a polymath). I transitioned relatively late and am
also a lesbian. In this brief narrative (with many explanations), I will also try
and highlight important aspects of my development and of being a trans woman
and a lesbian in mathematics at different levels.
Writing this narrative was difficult for a number of reasons. Mathematics is
everywhere and any context that involves enough mathematical insight should qualify.
That in turn includes things like knowledge representation, feminism and related
reasoning. I am not too sure about the boundaries that I have set in relation to
this aspect. Not many readers may be aware of the intricacies of gender transition
and related issues. So I have explained these in the following section before delving
into research in mathematics and related politics.
GENERALITIES ON SEX, GENDER AND DYSPHORIA
This subsection is intended to clarify the terminology and concepts of sex, gender and
sexuality used in this paper. From a modern scientific perspective, the sex (or
biological sex) of a person is best seen as a tuple of parameters corresponding
to hormonal, brain, clinical, chromosomal, physical and epigenetical sex, and more.
Gender is plural term that refers to gender identity, gender expression and gender as a
social construct. Serano (2013) clarifies much on these. It is important to distinguish
between the terms in any discourse.
Gender identity of a person is the person’s innate sense of gender and is intrinsic to the
person in question. There are studies that show that it is strongly influenced by prenatal
development. It has been shown to be hardwired modulo different assumptions
and connections with genetics are also known. There are studies ((Spizzirret
et. Al, 2018), for example) that also relate gender identity to brain structure,
hormones in brain, and other modern biological markers of sex.
A person's understanding of their own gender identity and coherent gender
expression has direct connections with their well-being. But the problem
of determining a person's gender identity is not an easy one due to the machinations of
patriarchal power structures. People tend to develop their own dialectics to different
extents and these share many patterns. Mostly when people are assigned wrong gender
at birth and have sufficient dysphoria do they want to express the incoherence
with their gender identity. The patriarchy and discriminatory power structures try
to interfere even with this process by imposing various strictures on identity, expression
and punishment mechanisms that amount to proactive gas lighting and criminal
oppression. In my opinion, the idea of ‘sufficient’ in ‘sufficient dysphoria’ can
be characterized in terms of possible sets of attributes (Mani, 2014C). Typical
transition procedures for a binary-identified trans woman includes HRT (hormone
replacement therapy), laser treatment and GCS (gender confirmation surgeries).
Recovery from GCS procedures is painful and warrant medical leave for few months.
An alarmingly large percentage of trans women actually attempt suicide at some stage
of their life because of social exclusion, isolation, discrimination and loneliness– this
is indicated in the US survey for example (James, et. al, 2016). I have dealt with the
nature and existence of connections between loneliness, exclusion, sexuality and
suicidal tendencies in a recent paper (Mani, 2016). It is also known that loneliness can
have a number of negative consequences on humans that include: reduced
lifespan, heath problems, lowered level of trust levels in others, feelings of
social incompetence, victim mentality and self-consciousness. A closely related
concept is that of depersonalization (Costa et. al, 2016; Jones, 2017). It can be
regarded as a common symptom of gender dysphoria. A person experiencing
depersonalization would feel that certain feelings and experiences of oneself or
the world as unreal. Depersonalization does not alter perception of reality but
induces a level of detachment from the world and numbing of emotions.
MY TRANSITION IN BRIEF
A dense account of my transition can be found in my blog post (Mani, 2014).
Basically I had gender dysphoria since my childhood. Related symptoms
and depression intensified in middle school. I did well in my school final
examinations though. Subsequently I became severely deviant from prescribed
"course work" - diversifying into higher mathematics, physics, psychology and
politics that did not quite belong to the higher secondary (HS) syllabus. I could not
cope with dysphoria and my performances in the exams were erratic - obtained a rank
in medical entrance examinations and bad result in the HS examination. I
worked with untreated depression for many years – till I discovered the importance
of medicines myself. My B.Sc. results were also affected by depression. Dysphoria
was however not the only reason for my severe nonstandard style of academics – the
system was defective.
I had good access to books, libraries and journals even during those days.
Possibly, because of my problems, I became pretty knowledgeable in psychology and
psychiatry. The limited information about trans-sexuality in “high-quality” journals
that I could find then was not good. The literature on lesbian trans women were not
widely known. But I managed to work out my gender identity and orientation
correctly, and even consulted a psychiatrist for clearances for HRT (Hormone
Replacement Therapy) and GCS (Gender Confirmation Surgery). But could not
proceed because of opposition at home, and the psychiatrist was also not modern
enough. My plans were stalled then. My first suicide attempt happened a few months
after this. My parents have always been of a conservative, highly superstitious,
religious, casteist, bigoted, narcissist and brainwashed type serving the interests of the
patriarchy and capitalism. They have always been a hindrance.
I got into research in mathematics independently after B.Sc. and a PG diploma in
statistics from ISI. I was elected as a member of the Calcutta Mathematical Society
shortly after that. Also I did not accept an offer to join Prof C.S. Sheshadri’s team in
Chennai during the time. More aspects of my research career are in a separate section
in this narrative. Over time I published a part of my rather large amount of my
research in many top grade international journals. I also did a master’s degree
in mathematics after publishing over 150+ pages. As of now the figure is over 1050.
Much later, when I had to decide between suicide and living in late 2012, I
decided to transition fully. My medical and legal transition happened smoothly
in subsequent years. The NALSA judgment (NALSA, 2014) simplified
things tremendously. Social transition was also easy because I had been
introverted and unsocial all through my pre-transition years. My relationship with
my ex-girlfriend and girlfriend was also problem free because we are all lesbians,
feminists and rather mature. The long distance aspect has been an issue with my
girlfriend.
The physical part of my transition was very easy for me as I was already good looking,
femme, healthy, athletic, response to hormones was excellent, had no
complications, a partial class and an Asian advantage. Suicidal tendencies
vanished completely on commencement of HRT itself but am yet to fully come out of
the grips of dysphoria related adaptations of pre-transition period (Mani, 2014A).
I did a late doctoral degree in mathematics during my transition period too. I
faced plenty of bureaucratic delays at various stages of it. The review period for
my~300 page thesis was also extraordinarily long.
As far as my sexual orientation is concerned, during my school days, I was
essentially a lesbian. I have always been sexually attracted to a large spectrum
of femme women. Pre-HRT, I was also attracted to so-called "boys" -- femme
types bordering on butch. So I used to think that I had bisexual tendencies. However I
have always held that "any sufficient aggregation of masculine features in a person" is
a sign of decadence. So much about boys and men. I have always been mature enough
not to translate this into general misandry. My preferences shifted towards larger
classes of women during and after HRT. Overall since my high school days, I
have always identified as a lesbian and being a lesbian is not just about my orientation
but is part of my identity. It did affect socialization, but I am not mixing that up with
dysphoria related reasons.
I never had any real role models, though I have always admired a lot of women (mostly
older) and often abstracted and adapted their positive traits in my own way.
EARLY SCHOOL
I cannot remember much of my days in primary school, but I was an excellent student
with a good collection of merit cards in science and mathematics. There were
five types of exercise books - for mathematics there were ones with small and big check
patterns. The ones with pink big check patterns were more beautiful and easier
to write into. When I was around three years old, I remember studying a number
of patterns found in my surroundings. Things like brick walls without plaster, open
dimly lit spaces, complex objects, and possibly related emotions. I have no
recollections of people or any sound that I may have heard.
I remember doing more of algebra and arithmetic in secondary school.
Collaboration was not really encouraged in schools and it was mainly up to individuals
to understand from the teachers instructions and/or the thing in books and
possibly reflect on them. I have always been introverted and so I liked to work alone. I
do not remember lessons or maybe their physical context. But I do have some
recollections of solving problems. But I am not saying that it was like “I solve; therefore
I am :-)”. All science subjects including mathematics were my favorites and
I did like experimenting beyond what was in the curricula and even at home.
Further I had access to a rather large collection of books on science (especially
physics) and fiction (all in the English language).
RESEARCH CAREER: AN APPROXIMATE ACCOUNT
Initially my research interests in mathematics included analysis, fixed point
theory, summability, semi-group theory and partial algebra mainly. I was pursuing
all this without any formal association with an institute and through self study. I had
access to plenty of journals and books as always. I ended up with a substantially
large and unusual background in research-level mathematics (and philosophy too).
During this time, I had a few opportunities like joining a research group in
algebraic geometry (mainly). But I did not join them. I was not too interested in
publications at this stage and was always working alone. I suffered from
depression, gender dysphoria and suicidal tendencies during this phase - but was not
too clear about life goals. Also I was into part-time teaching in mathematics and science
during the latter part of this phase.
Gradually my research interests shifted to algebra, rough sets, vagueness and
logic. Most of my work is on foundational issues and I invent/use very imaginative and
therefore risky methods and approaches. I have published many excellent papers
before, during and after transition during this phase. One line of research in which I
have been very successful is in formalizing causation in the contexts of formal
approaches to vagueness in a granular way. I will not digress into other subareas and
technicalities here.
That is despite managing two careers simultaneously. I have also been involved in part-
time projects in soft/statistical computing especially after 2004 and have been an active
free software activist and contributor since much earlier. I should also mention that
during most of my pre-transition days, the basic plan was to achieve as much as is
possible before opting for suicide - because I saw no open doors. It was basically a
decision and given the substantial level of dysphoria including disconnect from
the world, it was a reasoned decision rather than an emotional one. I changed this
decision primarily because of an activist mindset and additional knowledge about the
dynamics involved, though it is true that 2012 was also an academically relatively
successful year for myself. Previously I used to think that thirty plus was too
late an age for proper transition under the circumstances.
My productivity rate during my pre-transition period has been less than that after the
start of my transition in late 2012. Transition also involves adjusting one's lifestyle in
puberty-like state - the previous statement stands with or without this statement.
From my experience, I can say that HRT helps one concentrate and think better, and
this holds even during the beginning stages of HRT.
Employment Question
Pre-transition, I never saw anything in full-time jobs in teaching or other sectors.
Working for the corporate sector is death, the idea of working full time in the
corporate sector is based on decadent capitalist values, teaching jobs are ill conceived,
jobs outside academics are less sensible and most importantly "you do not need
the property papers of a building to jump off it in the near future". And there has always
been the need to evolve alternative leftist strategies in the decadent Indian economy.
Somehow the dynamic part-time opportunities in the teaching, short-term project,
freelance academic and statistical/soft computing consultancy sectors fell in place to
an extent. The main advantage was that I could devote more time to research. Yes, I
have always looked down on the slave mentality of the middle and upper middle
classes on the job question.
Post and during transition, I have also been involved with course development
work for foreign universities and massive online open courses. But I do face
mountains of discrimination, and some transphobia.
COLLABORATION AT RESEARCH LEVEL
A researcher can collaborate with others in the research context by way of reading,
reflecting and re-purposing parts of sets of published recent research done by other
researchers in the same subarea and in the context of the same problem with due
acknowledgment .This statement can be modified by possibly replacing
• "reading, reflecting, and re-purposing" with "rejecting", "adapting",
"improving", "initiating" and many other terms,
• "published recent research" with "published research over a long period of
time", "new research" and many other terms,
• "same subarea" with "related subarea", "apparently unrelated area" and others,
• "same problem" with "related problem", "unrelated problem", "orthogonal
problem" and others,
• "with due acknowledgment" with "with partial acknowledgment", "jointly with
some others" and others, and
• "others in the research context" by "specific researchers in the research
context".
In fact researchers can collaborate with others in a number of ways and these
ways form questionable hierarchies based on questionable rationales of evaluation of
collaboration.
In this scheme of things, I have never really collaborated at the level of producing joint
papers (except for a joint paper in an allied field to date). All of my research papers
have been authored by myself alone. This has to do with my style and approach to
research that I have explained earlier. The trans aspect in the sociopolitical
conditions has had a clear influence on this. The latter is very important - there are a
large number of trans women in academia with regular and regular-high-impact
research careers (see for example (Conway, 2005). It is also true that I have been part
of academic groups like the Calcutta Logic Circle and others for many years.
I do not always do research with the sole intention of publishing them and a
substantial part remain unpublished. In the early phase, I was not particularly good in
communicating and interested in publishing and was too independent to collaborate. In
the pre-transition phase after this my collaboration level has been much better
as indicated in publications, participation in conferences, peer review, societies,
workshops and other academic events.
Some people (mostly men) were definitely bigoted, misogynist and trans-phobic
towards me during and post transition. Some others took time to get adjusted to the
facts. While some others were excellent. See my article on trans inclusion (Mani A,
2014C) for more light on these remarks - being a functional feminist is an essential
requirement for survival. I do face discrimination in India in particular, because not
everybody is well educated or rational. Even then I have had much impact on
the mathematics, logic, philosophy, computational intelligence and computer
science communities, So much of inclusive sex and gender sensitive education has
never been seen in the country. Otherwise I have improved on my level of
collaboration.
TRANSITION AND RESEARCH STYLE
Most of the problems/theories that I work on are of a foundational nature, but I do keep
track of possible practical applications. Understanding vagueness involves plenty of
philosophy, related logics and insight in practical problems. This works well with my
approach in which I place much stress on exactness, formalizability and beauty of
proofs and justification. In my pre-transition state, the problems of dysphoria,
depression, a certain amount of depersonalization (that was part of my gender
dysphoria) did slow down my work. I preferred to work in a less connected
way relative to other people's work and simultaneously my work was colored by an
urgency during my pre-transition days. Basically I was simply concerned with the
research in question and nothing much. But it is also true that I substantially
improved my research communication over time.
As mentioned before depersonalization in pre-transition state is part of dysphoria and
related to loneliness and suicidal tendencies. This has also been examined to some
extent in the available literature. Risk in the context of research can be understood in
multiple ways. One useful definition can be in terms of potential reader’s capabilities
to comprehend the research being communicated. Sometimes I become so innovative
that reviewers get floored. At other times, I have taken risk in accordance with
my pre-transition goal to maximize quality of output (relative to myself) because
of 'limited time'.
During and after transition, I had to adjust research strategies, improve
communication and to an extent work harder on connections. This can be seen in my
research work in and after 2013. I have also succeeded in extending my mathematico-
logical approach to subjects like feminism.
Some studies indicate that HRT can be expected to affect brain functions. Many of its
good effects are known, but not much is known about the impact on research- level
mathematics. From my experience, I can say that it improves clarity of thinking, total
volume of both numeric, symbolic and linguistic computations, emotional content
of communications – this matters in mathematics too, imagination (some of my recent
papers involve more imaginative attacks but am also getting mature with time) and
memory power too (this is sometimes reflected in the scale of
interdisciplinary tasks that I have done).
CONCLUDING REMARKS
I hope that this narrative paper helps in understanding some of the inter-sectional
aspects of gender diversity and its impact on women in mathematics. Because of the
discriminatory social order and a history of severe anti-trans discrimination and
genderism, it is trivial that trans women need reservation and additional support in the
education sector – this narrative confirms as much.
The proposed APRD model obviously requires additional work. From the
narrative, it is possible to abstract subjective values corresponding to motivation,
genderism faced, other discrimination faced, quality of work, social attitude, research
style, and other parameters, research-attitude and pro-active feminist attitude. Of
these, the parameters research-attitude and pro-active feminist attitude have the
potential to predict parts of the others. This is significant.
Acknowledgment: I would like to thank the reviewers Professors Eva Norén,
Beth Herbel-Eisenmann and Jayasree Subramanian for useful remarks that
led to improvement of the original submission.
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