How does one research (pure) mathematics in a more inclusive manner?

Question

Motivation

I don't want my mathematical research to be limited by me being a monoglot, Western, white, and a man; and I'm sure there are other limitations. Diversity is essential.

The Question

How does one become more widely read in mathematical research, beyond boundaries like languages one speaks/reads, one's culture, privileges, upbringing, etc.?

Thoughts

There doesn't seem to be much under my control. I could learn a new language or two. I could try reading from journals from places underrepresented so far in my research.

I don't know what to do.

Surely, we would all benefit from research that casts its net wider …

Answer 1

I am a mathematician who has similarly been intentional about diversifying my research. My PhD training was in algebraic topology and category theory, very far on the "pure math" side of the spectrum. I can think of a few ways you can diversify your research, listed below. I'm going to ignore all the identity politics stuff, because I don't think it's relevant to the actual question of how to diversity your research and cast a wider net.

1. Do some applied math/stats research and choose application areas that stretch you.

I did research related to the opioid epidemic in Ohio (resulting in one publication and one preprint so far), and it connected me to a whole new world of Harm Reduction. As part of my statistical consulting for the organization Harm Reduction Ohio, I met many social workers, sociologists, epidemiologists, journalists, people who use(d) drugs and want to help others beat their addiction, etc. Now I give talks in Ohio and help connect other researchers into this topic.

Later, I did research related to policing and protests and have published two papers from that so far. Through this, I got better at time series models and learned about Hawkes processes from applied math. I also learned about different models of policing, the psychology of protests, collective trauma, etc. I've also done research about Ukraine (one paper in 2015 and one we started in 2021), to understand breakaway movements and civil wars. I learned a lot of game theory, and befriended Ukrainian journalists and sociologists.

Later, I coauthored a paper about wound-healing and diabetes, which taught me a lot about biology, pharmacology, and the lived experience of people with diabetes.

If you are interested in this kind of thing, you might enjoy the research coming out of QSIDE.

2. Teach courses that stretch you in the direction you want.

I developed and taught courses in statistical modeling, time series analysis, Bayesian stats, data mining, and big data. I also taught several computer science courses. In every course, I picked real-world datasets for my students to analyze. As a result, I learned about the world bank, racial disparities in median net worth in the USA, how climate change impacts vulnerable populations, racial disparities in criminal sentencing, and what factors predict for high salary, long life span, long-term happiness, etc. I remember learning about the John Henry effect from this. I'm working to develop a course that would teach statistics via social justice applications. It would be called "Statistics for Social Justice." There's already a book "Mathematics for Social Justice" and I look forward to reading it and teaching that material at some point.

3. Study the scholarship of teaching and learning.

After observing some trends in test scores in my early years teaching, I read up and learned about "stereotype threat." I then changed how I taught and reduced the impact of stereotype threat. Around the same time, I read up on fixed vs growth mindsets and again changed how I teach. These changes led to several publications in the scholarship of teaching and learning, e.g., a paper in PRIMUS, another in the Annual Review of Statistics, and a couple in the Journal of Humanistic Mathematics.

4. Intentionally read papers by authors from under-represented groups, that might be under-appreciated and under-cited.

I tend to believe that papers by mathematicians from developing countries tend to have a harder time getting published, achieve less visibility, and get less citations, than the same papers would get, if written by a mathematician in the USA. So, when I find such papers, I make sure to read them and to cite them if appropriate, because I feel many others in my field will have chosen not to read them.

Let me give you a concrete example. This past fall, I wrote a paper about coalgebras over comonads. As part of this, I wanted to do as full of a literature review as I could. I stumbled upon a paper by a mathematician from Burkina Faso. Despite being written around 2016, this paper had fewer than four citations, and the author had returned to Burkina Faso rather than getting a research professorship in Europe where he'd done his PhD. I might have said to myself "well, this paper is not highly cited, so it's probably not very important or everything in here was well-known." Instead, I read the paper fully and carefully, understood the main result, included a discussion of it in my paper (a bit of an advertisement to the reader that they should read his paper), and cited it.

5. Travel to research centers in developing countries, and establish collaborations with researchers you meet during such travels.

I travel every chance I get. Often, I reach out to universities as I go, and they invite me to give talks. For example, I taught a week-long course about model categories to a bunch of Moroccan PhD students in 2015. I gave talks in Argentina and Uruguay in 2018. I gave talks in the Middle East in 2022. My CV has a list. I've not counted but feel confident I've done this in at least 20 countries. It's led to some wonderful collaborations and lots of math I would have never learned about on my own. If you are interested in this kind of thing, you might consider visiting the AIMS centers in four African countries.

6. Go to seminars, colloquia, and conferences on topics you are interested in.

I go to the seminar in my main research area religiously, and every week I try to go to at least one other talk, whether in the colloquium, or a different seminar (e.g., topological data analysis applied to neuroscience data), or an interdisciplinary speaker series, of which we have several in central Ohio. Through these activities, I've found lots of new co-authors and expanded my research in lots of new directions. For example, that's how I met the professor who got me interested in the opioid epidemic. Some conferences that helped me a lot include a conference on big data at Wellesley in 2015 (where I met many statisticians and got my start in that direction), an applied math conference at ICERM in 2019 (which led to the policing and protests papers), and a QSIDE social justice math conference in 2021. There's a conference this summer on gerrymandering (specifically, the math you can use to detect unfair maps and to draw fair ones) that seems very interesting. Maybe you can attend.

Answer 2

As requested, I expand my comments to an answer. Much of what I will say applies to science in general, not just mathematics, but I will limit myself just to math in the answer.

1. Your main question is:

How does one become more widely read in mathematical research, beyond boundaries like languages one speaks/reads, one's culture, privileges, upbringing, etc.?

What limits your mathematical horizon has (almost) nothing to do with "languages one speaks/reads, one's culture, privileges, upbringing" or "being a monoglot, Western, white, and a man."

Your main limitations come from your specialized mathematical education. In your case, as I know, your initial math specialty was combinatorial group theory and, later, theory of algebraic groups. This is your "zone of comfort," these are the areas where you have read and are able to read current research papers. At the same time, there is a good chance that you will be unable to read current research papers in, say, probability, PDEs, algebraic geometry, analytical number theory, etc. Very few mathematicians can currently move with ease from one area to another (very few of us can imitate Terry Tao in this regard). I will make suggestions based on what worked for me. The main rule is to move only to adjacent areas of math. In your case, moving from combinatorial to algebraic group theory is a perfect example. There are two ways to move (both learning and proving new results) from area A to the adjacent area B:

(a) In order to solve a problem in area A you realize that some tools from area B might be useful. Thus, you learn enough math from area B in order to achieve what you want.

(b) You learn (either from talking to somebody, or listening to a colloquium talk or reading a paper in Notices of AMS) of problems in area B that seem to be amenable to tools from area A that you are comfortable with. Then you either find a collaborator from area B or do some reading, or taking a graduate class if this is an option, and, maybe, it will work out.

After that, maybe you move to area C adjacent to area B, etc. How much of math from the new area you have to learn in order to succeed, of course, depends on too many factors to give a more specific advice.

What never worked for me is learning a new area of math just for learning sake (and not for the lack of trying).

2. "Diversity is essential." Well, yes and no. What is important is diversity of mathematical knowledge and thinking. What is unimportant: What's currently known as DEI, that focuses on race, gender, sexual orientation, etc. With few exceptions, you do not need to go to another country to learn and do more math. (Up to a point: If you have a collaborator who works in a different country, this is another matter. If you want to learn, say, condensed math, you might benefit from going to Bonn.) What's detrimental when learning and doing math is thinking in terms of ethnic, socioeconomic, geographic background that you have.

3. Regarding

I could learn a new language or two. I could try reading from journals from places underrepresented so far in my research.

Learning languages is, of course, a nice thing to do, but it is primarily useful if you want to visit a country. Almost all first-rate math these days is written in English and, to much lesser degree, French. (There are also some older first-rate papers written in Russian, they are all translated in English by now. Also, sometimes I have to read old papers written in German, but this happens very seldom.) As a native English-speaker, it should not be difficult for you to read math papers written in French, you may need to learn a bit of grammar and vocabulary, but that's all. Reading journals from other areas of math will not be particularly useful for expanding your math horizon. Most likely, you will be simply unable to understand what and why the authors are doing. A better option is to go to colloquia, to read articles, for instance, from the Notices of AMS which are intended for general mathematical audience.

4. In case (which is what might be underlying your question) if you want to do some math related to various social issues. My suggestion is to proceed as in Part 1 of my answer. For instance, if you are familiar (from studying combinatorial group theory) with Rips complexes, you can consider reading papers on mathematics of gerrymandering, where Rips complexes appear as one of the tools.

5. If you have time and energy and are determined to do something socially good as a mathematician, the best thing, in my opinion you can do is guest lecturing in middle and/or high schools in the city you are in (no need to go far). Here is a story told by two of my Mexican mathematical friends: They decided to organize a "math circle" in one of the local high schools. To their great surprise, many students came, even ones who were not interested in math. When asked why, these students replied that it was the first time in their life, they had teachers who really cared about the subject they teach. Sigh...

Answer 3

If you wish to help the countries where math research is not as developed, single out a conference or two in such countries, and travel there to report your results. Talk to the people there, exchange ideas, facilitate collaboration. Take note of talented students, advise them on how to get to graduate studies in the West.

My close friend, a prominent astrophysicist from MidWest, has long been cooperating with a couple of universities in the South-East Asia and a couple of universities in the Latin America. There, he is co-supervising MS students. Some of them later come to his department, to read for PhD or as visitors. The guy is doing a great job, helping to create new scientific schools. At the same time, he emphasises that his work has nothing to do with race, sex or other parameters irrelevant to science and knowledge. The only kind of diversity that he respects is the diversity of ideas. I gladly agree with him, because the promotion of diversity based on sex or colour or other irrelevant factors is discriminatory -- and therefore harmful.

Answer 4

As someone who comes from an underrepresented minority group to this field, here is what helped me:

1. Keep lecture talks and seminars open to public on a known platform like youtube. Also promote it so that people know about it.

2. Publish notes online.

3. Make discord groups/ mathstodon channels were peopl can participate.

4. Make it so that people who are also not in the university you study at be able to involve themself and talk about research. It is a minority, but there are some people who are very very interested but unable to contribute to the public mathematics place due to not being affiliated with a university.

5. Keep a blog where ideas are discussed at a more informal level than books.

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Those are some tips how to concentrate people who are interested into a single place. The next step would be bringing those who are interested actually into the physical places like the university you conduct research. That could be achieve very simply by offering scholarships. However, this is not an individual thing but rather an institutional thing.

In the case of Germany, I know very many students from countries like India and Nepal who are very interested in the subjects that they do, then came here cause this country funds them (about 1.3k euro per month).

Answer 5

The Question

How does one become more widely read in mathematical research, beyond boundaries like languages one speaks/reads, one's culture, privileges, upbringing, etc.?

Mathematical research is already a bit restricted w.r.t. privileges (esp. educational opportunities), geographic region and institutional culture.

At the same time, it's not as restricted language-wise as other fields and neither is it as funding-sensitive as you don't need expensive lab equipment and expert technicians, etc in math.

Previous responders have offered many ideas on how to embrace more diversity within your work if the issue is simply external.

Yet I feel that your quest for diversity is mainly a reaction to the social limits experienced while in graduate school. This is a problem for all doctoral students: no one wants to fail or even do poorly so we tend to rob time from other life activities and invest it in our PhD project. Most PhD supervisors do little to ameliorate this tendency as hard-working students are likely to benefit them too. Now that the doctorate is over you must take care to recover your own self from the institution to which you committed years of time - otherwise you will be instutionalised in your perspective.

Major changes can only begin with oneself. It's naive to think that a new hobby or exposure to a new reading source will passively transform us. So the first thing I would do if I were you would be to do a life reset for myself. Simple yet personally fundamental things like sharing a house with researchers in other fields (and indeed practioners!) and learning from their viewpoints and rationales could provide a more effective spark to a new modus operandi and momentum in your work.

This form of engagement won't radically alter your own natural aptitudes, cf. Moishe Kohan answer. But it will give you a clearer vision as to how to use other perspectives methodically. These other perspectives may be relevant in other branches of mathematics that professionally you should at least appreciate.

The real benefit of such heterogeneous engagement will be to your own motivation and sense of usefulness to humanity.

That's the beginning for you as I see it. If you can do it "at home", you can try it anywhere with a good hope of success. There is benefit in learning another language: it helps us to be understood by non-English speakers of that tongue and also teaches us - now as adults, not children - to express ourself more effectively in our own mother tongue.

An overseas job's main benefit would be in giving you a deeper sense of what culture is and how it impacts on so much of what we do and think about. Once we conceptualize the problem we are living with it is far easier to develop checks on its impact on our own work and even begin to construct - with others, of course - a culture of diversity in our own workplace.

Answer 6

Publish as open access. Otherwise you might exclude non-academics and people at institutions that cannot afford to subscribe to all the expensive journals.