Follow Your Heart, by Jeff Weeks

Throughout my seven years as a math grad student, there was a constant struggle for attention between “what I was supposed to be working on” and “what my heart was into.” This theme played out in different ways over those seven years.

When I first arrived in Princeton in 1978, I discovered that I was the only one in my entering class who hadn’t already taken graduate-level courses as an undergrad. Worse still, the Math Department, catering to its typical clientele, offered no introductory graduate courses. None at all. Our mandate was to learn—or, for my classmates, review—the basic stuff on our own, and then dive into the research-level courses that the various professors offered.

I was adrift. What should I have been doing? Studying even harder about Noetherian rings, the Radon-Nikodym theorem, etc. etc., all at a level of abstraction that I found neither useful nor interesting.  What was my heart into? Learning some concrete geometry and topology, along with some general relativity. You can guess what I spent most of my time doing.

As you might imagine, my qualifying exams did not go well. On my first attempt, they let me off the hook on the basic topics with a humiliating but welcome remark that “you can learn this stuff when you teach it.” But for the advanced topics, they wanted me to try again the next year. They weren’t impressed then either, but they decided that I should start working on a thesis anyhow.

By then, I’d signed on with Bill Thurston as my advisor. I don’t remember what problems I was supposed to be working on, but I made no progress with them. What was my heart into? By that time, my fellow grad students, colored chalk in hand, had introduced me to the beautiful world of low-dimensional topology, and I’d fallen in love with it. I’d also noticed that all books on the subject involved a lot of graduate-level algebra and analysis that really wasn’t needed to understand and appreciate the core concepts of geometric topology. So, I decided to ignore my thesis problems and instead took it upon myself to write the “missing book,” something that would welcome everyone—from high school students on up—into the magic world of multi-connected spaces.

That project took several years, with the book, The Shape of Space, finally completed in my fifth year as a grad student. My grad student stipend ended that year, so during what would have been my sixth year, I taught at Stockton State College and saved up enough money to return to Princeton and write a thesis in the seventh year. I don’t remember what I was supposed to be working on, but while Bill Thurston was away for the winter holidays, I decided to grant myself an indulgence to investigate some especially simple 3-manifolds and write a little computer program to find hyperbolic structures for some of them. I was lucky enough to stumble onto the smallest closed hyperbolic 3-manifold. During my first meeting with Bill after the holidays, I figured I’d briefly mention this little discovery. Bill responded with some ideas for how I might move forward with these investigations and how I might extend my little computer program. He said not a word about my old boring thesis topic, so by the time the hour was over, it was clear I had his blessing to do a thesis with my software for putting hyperbolic structures on 3-manifolds. “What my heart was into” had finally become “what I was supposed to be doing”!

Throughout six-and-a-half of my seven grad school years, I’d always felt that I would have been better off with a different advisor at a different school, with a firmer hand to guide me. But in retrospect, Thurston’s approach was exactly the right one: he let me find my own path. By the end of those seven years, I had some research software (SnapPea) and a book (The Shape of Space). In my heart, the book was my true dissertation. Even though it did nothing to satisfy Princeton’s Ph.D. requirements, it set the tone for my whole professional life, both in content (geometry, topology, cosmology) and style (exposition for the general public).

As for my advice to current students, I dearly wish I could say “follow your heart” and leave it at that.  But, of course, it’s not quite that simple. One needs a paying job. So, my advice is: follow your heart, and find a way to turn your passion into your livelihood. I wish you good courage and the best of luck.

Jeff Weeks is a free-lance geometer, topologist and occasional cosmologist.  His favorite successful projects are the third edition of his book The Shape of Space and the Geometry Games software.  His favorite unsuccessful project was collaborating with cosmologists to deduce the topology of the universe from the cosmic microwave background.  Support over the years has come from the National Science Foundation, a MacArthur Fellowship, lectures, and occasional work for science museums.  In his spare time, he enjoys biking (spring, summer, autumn) and cross-country skiing (winter) with his wife, and learning foreign languages.

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Invisible struggles – when the mask stays on at work, by Mikael Vejdemo-Johansson

It has taken me a long, long time to recognize my own story as one of resilience and to recognize my own experiences as a struggle. It is still at times difficult for me to fully embrace it. One core reason for this is that we value work very highly – and I rarely struggled as a student, postdoc, or professor. Instead, the energy I expend masking my issues raises my stress level and brings the pent-up emotional storm to bear at home.

I grew up in Stockholm, Sweden, in the 1980s and 1990s – I’m at the very cusp of the “Millennials.” We had computers at home as far back as I can remember, and my parents both worked with computers already in the late 70s and early 80s. It was a household that encouraged academic endeavor and seeded it with a lot of literature – literature that I devoured as soon as I could read.

I always dreamed of working in academia. We have a family story from when I was four and was asked by a man I was talking to what I wanted to be when I grew up. “Researcher,” I lisped as precociously as I possibly could. Since that day, my plan has not changed noticeably – it has merely become more precise year by year.

I was precocious. I was odd. I was a rampant geek. Kindergarten through 9th grade was a period of constant exclusion and bullying at school. Grades 10 through 12 came with some specialization in the schooling, and with that selectivity came relief.

Selectivity as relief is something I have noticed through my years. Even when bullying was particularly bad, my extracurriculars have always provided me with a haven. Scouting, orchestra, theatre and the Young Scientist’s Association all took their turns as a place of refuge and safety. Selecting peer groups for shared interests rather than shared geography has always led to better outcomes for me.

As far back as my family remembers, I have always had problems with my mood, with my emotions going haywire on me. I am still right now digging through the why and how, and I am finding diagnoses and letter combinations along the way that may explain parts of it all. Certainly, there is some sort of PTSD from the years of bullying, but my family has told me stories of mood swings from before Kindergarten.

I am pretty good at masking, though: keeping stable while out among relative strangers and forcing my mood to stabilize. It is something paid for dearly once I let go of the force. As a result, I tend to have more and more severe mood swings at home than in school or at work. My colleagues could have gone for years without knowing that I have any issues whatsoever, because I stay stable and balanced during the day. Instead I will crash at home, reacting with anxiety, tears and sometimes freezing up completely at the slightest of causes.

There are some particularly noticeable crashes I can remember because they caused me to go and seek help. The first time I got started with psychiatrists and psychologists was thanks to my wife. During her first family dinner with my family, she got to witness my meltdowns firsthand as I crashed out, fled the dinner table and hid in my room. She came after me and encouraged me to seek help. A few months later I was seeing a psychiatrist, taking Lamictal for mood stability and seeing a psychologist for therapy.

Another time – earlier than this – during a postdoc in Scotland, my wife was enthusiastically looking forward to my cooking a lamb curry for dinner. I did not want to, but I could not bring myself to tell her that I did not want to cook the curry. Instead, I froze up in the middle of the frozen foods aisles and then broke down. That’s the first time I got restarted on mental health care.

During a research semester in Minneapolis, a car turned in front of me at a crosswalk and the world just … slowed down. I froze up on the sidewalk and stood just still and shaking for several minutes. Once I managed to get myself to move again, I could not push myself beyond an extremely slow pace. Once I got home and inside, I cried so hard the muscles in my face hurt from it. A few days later, I sought out the student health services and saw a psychiatrist for advice on the antidepressants I was taking and a psychologist for a sequence of therapy sessions.

There was a time period when the hacker / security research community faced a sequence of high-profile suicides. Almost all of them were of people who were very close to one of my close friends. Feeling the impact of these deaths, the community stepped up and organized conference panels, support groups, and tried hard to increase visibility and support for mental health issues. I was watching this as it happened and looking over to my academic circles where I could see no visibility, no support, leaving each of us feeling alone and isolated in our struggles. I wanted what the hacker community built for my academic world.

At one point, people were posting texts “coming out” with their own struggles – to put a spotlight on how widespread issues with depression and anxiety were in the community. So, I wrote up a text about my mood stability, I put it on my website, and I tweeted about it. A day later I got an email from one of my colleagues during my postdoc in Scotland. He told me he had depression, and that he had not noticed me struggle at all. I told him about the hacker community and their work – so we founded a group blog for “depressed academics”:

Since then, I have been consciously choosing to be open about my mood instability. I write online under my own name about moods, medications, therapy. Sometimes very personally. I tell people early on about my mood disorder – for instance I often weave a mention into my teaching early in my courses. As a result, people open up to me. Students come to me with their own struggles instead of hiding them.

Just because it was not visible in the workplace did not mean I did not struggle. Now, I am making it visible.

Mikael Vejdemo-Johansson, Assistant Professor of Data Science at CUNY College of Staten Island, started out in computational homological algebra before moving into topological data analysis (TDA) a decade ago. After a MSc at Stockholm University and a Dr rer nat at Friedrich-Schiller-University Jena, he went through 8 years of postdocs at Stanford, St Andrews and KTH before settling in New York at CUNY. Beside TDA and running the blog, his interests are wide and varied – touching on linguistics, necktie knots, and psychology as well as most recently mathematical art (exhibited at JMM, Bridges, ICERM and the AAAS) and the Illustrating Mathematics research semester.


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Recovery, Like Mathematics, Turns Out to Be Fun! by Anonymous

Thirty years ago, I expected to die from alcoholism. Suicidal ideation gave way to a complacency that I would just drink myself to death. Mired in hopelessness, I went through the motions of life, pretending to teach, pretending to do research. Despite my every instinct, I managed to ask for help. Today, I am a happy, successful member of Alcoholics Anonymous with a lively career in mathematics. I share my story hoping to help even one person who is now in the place I was all those years ago.

In school, I was that student who could solve all the problems quickly and showed a natural gift for mathematics. How poorly that prepared me for the actual practice of mathematics, where we must learn to spend most of our time feeling confused. Indeed, in college, I think that my strongest motivation for doing mathematics was to earn praise and make myself look good, rather than a sincere love for the subject. As I started drinking and smoking marijuana more and more, my life started to break in two: an outer persona who won academic prizes and an inner one who became increasingly insecure. However, for a few years, it was all great fun.

Going off to a top-tier graduate school opened my eyes to the reality that having a knack for mathematics was just one possible starting point for study, not a free ticket to success. Among my colleagues were people who knew how to face challenges and work hard when things did not come easily. I felt increasingly out of place and turned to self-medication to avoid the reality of my situation.

My gift got me through a PhD, but without distinction. I took a post-doctoral job that I felt I didn’t deserve. My drinking became heavier and I started to accumulate the subsequent embarrassments that I will leave you to imagine. Suicide started to seem like my best choice. Hanging on by my fingernails, I started a tenure-track job at a nice university. As my outer façade became increasingly difficult to maintain, I squeaked through the tenure process.

One summer, I supervised a brilliant student’s summer research. It made me cry to realize that I had once been just that promising, but my prospects for success in mathematics were now few. I encouraged others to think that I was just a mediocre mathematician who spent too much time working on teaching (I didn’t), which was better than being known as the drunk that I was. It was during this period that thoughts of suicide gave way to the idea that I could simply keep drinking and be dead in some small number of years.

Some part of me did not want to die. For those last years of my drinking, I would make plans to stop, try to stop, pray and beg to stop, but not stop. My health started a serious decline. After about ten years of heavy drinking, I finally called my health care provider to say that I thought I had a problem with alcohol.

When the voice on the phone told me, “We have a drop-in meeting that you could attend today,” I said something akin to, “Don’t you know who I am?” Alcoholics build up narratives of sweeping grandiosity and unreasoned pride. I was no exception. I drank for two more weeks while awaiting a one-on-one intake appointment. The doctor helped me learn about alcoholism, explaining the difference between abstinence and recovery. I knew that I wanted to recover, but did not believe it possible. I asked, “How can I go home and not do the thing that I have done every day for ten years?” He answered with a question: “Do you think you could go to an AA meeting?”

Primed by the doctor’s information, I thought I could give it a try. The people in the meeting seemed energetic. They read through a lot of stuff that I didn’t understand. Then a woman at the podium addressed the whole crowd and said, “I don’t know you, but I love you.” This is not any famous cornerstone of AA, but that was what broke through my shell. I was desperate for help, ashamed of myself, and all but certain I did not belong in that room; here was someone willing to say that she loved me just for being there.

Through that crack poured the light of recovery, though very, very slowly. I was extremely reluctant to embrace what I was told. Don’t mathematicians, with our pride in rigorous proof, always think that we know best? Over time, I’ve learned to listen for a match between the voice of my best inner self and the voice of the loving community of people in recovery. That combined wisdom leads me to discern my next right action, the most basic of which is not to pick up the next drink.

By grace (identified by Francis Su in his wonderful writings as “good things you didn’t earn or deserve, but you’re getting them anyway”), I’ve been sober since my first AA meeting. Relapse is very common and I don’t look down on people who experience it; my continuous sobriety is a reflection of the depth of my desperation when I finally was able to ask for help.

What has all this to do with being a mathematician? For one thing, I would have been helped by a different mathematical education that was less about my talent and more about the things I did not understand. It seems to me that we invite young people into mathematics only when they measure up by the same old yardsticks of speed and innate comprehension. It seems to me that we reward people who chase after mathematics, the way I used to do, solely to show themselves powerful and bright. Can’t we encourage that student who’s good at explaining something to a friend; who thinks about ideas after the test is over; who enjoys drawing a picture to illustrate ideas? Rewarding innate talent set me up in a game I was destined to fail. I’m sad to think that others are being taught the same way.

My greatest gift in sobriety comes on the days when I feel what a friend taught me to call “right sized.” I am not puffed up by a paper that I’ve written nor driven to self-abasement by a mathematical error that I’ve made in public. I am not riding on an imaginary wave of brilliant accomplishment, nor led to wallow in suicidal ideation because I have not measured up. I am just me, one of many, participating in a mathematical community that more and more values the variety of our members. If you are having trouble with drugs or alcohol, please ask for help. Mathematics can become much, much more fun.

This story was written by Anonymous. Why do I write anonymously? In Alcoholics Anonymous, we say that “Anonymity is the spiritual foundation of all our traditions, ever reminding us to place principles before personalities.” In order to maintain my own practice of this simple program, it is better if I do not step forward as myself, but rather as one of many whose stories are like my own. This story is not really about me, but about the help available to anyone who, like me, has experienced “incomprehensible demoralization” from drugs or alcohol.

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I’m Living Proof, by Danielle Amethyst

In one way or another, mathematics has been a partner in my life for as long as I can remember. Sometimes as a progenitor of crisis.  At others, as a savior.  And even as a fixed point when all else was shaken.

My first crisis in mathematics came in sixth grade. In my current language (as an adult 25 years later), I now understand that I had a hard time accepting that the multiplicative and additive identities for the field of real numbers were not the same number.  Back then, I really wanted 0 x n to be n, not 0. I don’t know why, but it really seemed wrong to me. I remember crying in the closet area in the back of the classroom, throwing a veritable tantrum. Thankfully, my teacher, Bob Stanko, consoled me and worked to convince me, patiently, through tears and protest, that it’s 1, not 0, that is the multiplicative identity. I finally accepted it a few weeks later – crisis resolved. I wonder what would be different in my life if Mr. Stanko had gotten angry with me, had shouted at me or belittled me. I probably wouldn’t have gone on to become a mathematician, but instead turned away and never come back.

My multiplicative identity crisis provided me an important experience. I learned that I can be frustrated with something yet continue to work on it and through it. This has been invaluable as I’ve moved further into the world of mathematics as a numerical algebraic geometer. I call on this lesson frequently when programming. And I even tap into this tolerance in interpersonal relationships; it’s ok to be frustrated!

A very different set of circumstances really *made me a mathematician*. I had breezed through all the available classes in high school and earned a minor in mathematics accompanying my Bachelor of Liberal Arts (yes, that was my major in undergrad, it doesn’t get any more generic than that). But in 2004, I found myself working at a grocery store selling fish, utterly unable to communicate with my coworkers about the things that kept me up at night. Awake at 2 am, I kept coming back to my analysis book, my abstract algebra notes, thinking about proof and reason. I realized I was unhappy not being around others with my interests.

My unhappiness was much deeper than not having mathy friends. I was struggling with depression, which I now know stemmed from gender dysphoria (I really couldn’t have labeled it at the time at all), and I became fascinated with the altered states afforded by psychedelic drugs. I moved with reckless abandon into a dangerous underground world, nearly losing everything.

It was late at night in a moment of clarity that I decided to become a mathematician. I realized that I needed something to challenge me, to lift me from the hole I was digging for myself – that I would keep self-destructing if I didn’t do something *hard*. I reasoned with a friend: what’s more difficult than earning a PhD in math? And, thus, it was decided. Math would save my life.

Having not earned a major in math, I was ill-prepared for a graduate program in mathematics. I signed up for a second bachelor’s program at my university, with only the intention of taking enough classes to be able to handle graduate level work. I took the GRE in December 2005, and I officially started graduate school in January 2007.

Finally, I was surrounded by a community of people who were as passionate as I was about the wonderous world and surprising connections of mathematical theory. I had permission to go as far as I wanted. And I did, earning my PhD in 2012, enjoying several postdocs, and obtaining a permanent position at a university.

The mathematical community has embraced me as I have embraced it. This provided crucial support to me during gender transition and through the debilitating depression that came to a head while I worked as a postdoc at Notre Dame.

Earlier in life I had tried – several times – to transition, not knowing what I was doing, lacking the language to describe what I was feeling, and thinking I was utterly alone in what I was experiencing. Attempts to come out were met with strong resistance, and I would repress again – pushing down the feelings, throwing out the garments, stopping the conversations, replacing the thoughts with unhealthy behaviour. This cycle finally led me, in the summer of 2016, to search for answers; Google was my tool. The primary question I was afraid to ask was, “Why do I want to be a girl?” To my surprise, I found that I was not alone. I learned, with the help of so many strangers on the internet, the words I was looking for: “transgender”, “gender dysphoria”, and “transition” are a few.

I shed a lot of my identity once I started to work on transition. I lost my name, wandering namelessly. The nature of all my relationships changed. I questioned everything. But through that was a love of mathematics, an unrequited love born of persistence and wonder. I used math as a pivot, as a fixed point in the map I was living through as I moved toward becoming a woman.

I am so happy that I have found allies and friends in math and that my colleagues and students have allowed me room to be my true self. I wouldn’t be myself without my identity as a mathematician. When everything else was crumbling, mathematics was solid. When I needed a way out from a dark place, mathematics saved me. And when I didn’t even know I needed a lesson to guide me, mathematics taught.

Now that I’m mostly through transition and back to a nearly steady state, mathematics beckons me further. Here I go…

Danielle Amethyst is an assistant professor of mathematics at the University of Wisconsin-Eau Claire. All three of her degrees are from Colorado State University. Her research is in algorithms and implementation of numerical algebraic geometry, and visualization and computation of real algebraic varieties. She is absolutely enthralled by 3D printing on her own machines, both for mathematical art and practical problem solving. Emails from the broader community bring her joy. Danielle also enjoys bicycling and gaming.  

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Welcome to the Living Proof blog!

Welcome to the Living Proof: Stories of Resilience Along the Mathematical Journey blog! We are so happy you’re here. 

Living Proof is a project that was borne out of interactions Matthew Pons had with a number of his students. One semester, Matthew had a strong cohort of women in his Analysis class. He was impressed with their work–their ability to grapple with the course material, try problems, learn from their failures, and seek help when they needed it. From his perspective, they were succeeding. Unfortunately, from their perspectives, they were failing. They felt like mathematics shouldn’t be so hard, that the fact that it was difficult for them must mean that they aren’t intelligent or aren’t cut out to study math. Matthew tried to reassure them that everyone struggles–that he himself struggled with the subject as an undergraduate–but they brushed aside his encouragement. Perhaps they assumed that he was being dishonest just to make them feel better. Perhaps they assumed that his struggles couldn’t have been as bad as their own. In any case, Matthew thought, “If they don’t believe me, who would they believe? Maybe they can’t identify with me because I am not a woman. Maybe they can’t hear what I am saying because I am their professor.” This gave Matthew an idea. He needed to collect stories from a wide variety of mathematicians about times that they faced crises of confidence when they were in school. So, he got to work assembling an editorial team and reaching out to people to ask them to tell their stories. 

With tremendous support from the AMS and the MAA–especially Steve Kennedy, MAA editor and the project’s biggest cheerleader–the Living Proof dream became a reality. Stories of struggle and resilience, told by 41 mathematicians, were shared in a book that was made freely available by both organizations. But there are many more than 41 of us in our community. And people aren’t defined by a single story–there are so many stories we can share. This is why we felt it was important to start the Living Proof blog. We need to continue sharing our stories. We need to hear new voices and hear about different types of struggles. We need to hear more people talking about the same struggles so that people who are just now beginning to live through these experiences know that they are not alone. Our ultimate hope is that someday–perhaps years from now–someone tells the story of how what got them through their biggest challenge on their own path to becoming a mathematician was reading the stories of so many others in Living Proof.

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