My Living Proof Story, by Michael Dorff

In 1987, I was married with two children and was teaching math at a U.S. military high school in Germany. Two years later, in November 1989, the Berlin Wall fell, and with all the political changes, I expected that the U.S. might cut back on their military bases in Europe and that would mean fewer jobs for teachers at U.S. military high schools. So, my wife and I decided to return to the U.S., and I would start a PhD program in mathematics education. This was before the Internet, and I only knew one university that had a PhD program in mathematics education. I applied by sending in a hard copy application though the mail (no email at the time). I got accepted, but was told that they did not know if there would be funding for me until after the application deadline. So, I waited until after the deadline and called the director of the graduate program. He told me that he still wasn’t sure because there were two really good students who were thinking of applying but hadn’t yet. He said that I should come, and something would work out. My questions were, “Isn’t the deadline passed?” and “I guess I am not considered a good student?” but I did not ask them. I was naïve. We decided to do what he said and come.

When the high school year was over and I was done teaching in the spring of 1990, my wife Sarah and I moved our family of four with a third child on the way to that university, which was in a part of the U.S. where we had no family. I arrived at the mathematics department and met the director of the graduate program. He informed me that the good students he was waiting on did finally apply and there was not a TA position for me. In fact, they did not even have a scholarship for me, and, since I had moved from Germany, I would have to pay out-of-state tuition. I thought it would have been helpful if he had told me these things earlier. Also, he let me know that during the first two years of the PhD program in math education, I would have to take standard mathematics courses to earn an M.S. degree in mathematics. It had been several years since I had taken a math course and for my undergraduate degree the math classes I took consisted of calculus 1, 2, and 3, linear algebra, abstract algebra 1, and number theory. In a casual way he mentioned that I was probably not good enough to earn an M.S. in mathematics. I wasn’t feeling very confident in myself.

I went back home and talked with Sarah about the situation. I looked for a local high school math teaching position, but the K-12 schools were starting soon, and I couldn’t find an open position. So, by default I started the graduate program. The first semester I took graduate classes in real analysis, abstract algebra, and topology. I also sat in a class in calculus 2 since I had forgotten much of that while I taught high school. Because we needed money, I got some part-time jobs doing construction and grading free-response questions on standardized high school math exams in the evening.

One day after class I learned that there was a room in the math department where graduate students and the professors could go to talk and get snacks.  No one had told me about the room, but I decided to go. When I entered another graduate student told me I wasn’t allowed in the room. Later, I realize that she did not know that I was a graduate student. But with all that had happened during the past few months, I did not have a lot of confidence in my math worth and I silently left the room. During that first semester, I had little assurance that I could pass my math classes let alone do well in them, and there were times I was ready to drop out of the program.

At the end of the first semester, I ended up earning A’s in my three graduate math courses. The graduate director told me that a scholarship was available for me for next semester so that I wouldn’t have to pay tuition, but there was not a TA position for me. During the second semester I also received A’s in the next three graduate math courses, and I was offered a TA position for my second year in the PhD program. At this point I met some professors in the department who were very supportive. By the end of the second year, my confidence had grown and I transferred to another university where I earned my PhD in mathematics. In thinking back on this experience, I know that I could have easily stopped studying math. There were a lot of reasons for me to stop.

My story is not the only one like this. Too many others have gone through worse than I, and unfortunately there are some who are still experiencing dispiriting and demeaning situations, including those who want to studying math education instead of mathematics, work in industry instead of academia, those who are female or from underrepresented ethnic groups, and those who are LGBTQ. The book Living Proof: Stories of Resilience Along the Mathematical Journey (edited by Allison Henrich, Emille Lawrence, Matthew Pons, and David Taylor) shares a collection of such experiences and helps bring these elephant-in-the-room stories out in the open. We need to do a better job of supporting students and colleagues through their challenges, enabling everyone to flourish in mathematics. Let’s work to be more encouraging and empowering of all people in their mathematical journey.

I would happy if you sent me an email at telling me your thoughts on this article or sharing your own personal struggles.

© Mathematical Association of America, 2020. All rights reserved.  This piece first appeared as the President’s Message for April/May 2020 issue of the MAA FOCUS magazine. We would like to thank Michael and the editor of the FOCUS, Jacqueline Jensen-Vallin, for allowing us to republish it here.

Michael Dorff is the current President of the Mathematical Association of America (MAA). He earned his PhD in complex analysis at the University of Kentucky and is currently a professor at Brigham Young University. He has five daughters, the oldest of whom has three children and is working on her PhD in mathematics. In the picture to the left, Michael is with Sarah and their three daughters (Becca, Lizi, and Hannah) while Michael was in his first year of graduate school.

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Teaching Using Living Proof, by Allison Henrich & Matthew Pons

Since Living Proof: Stories of Resilience Along the Mathematical Journey was released by the AMS and MAA last summer, we’ve heard from colleagues all over the country that they are using the book in their courses. By using the book, faculty members aim to achieve a variety of goals. For instance, some want to foster a growth mindset in students where productive failure is acknowledged as a helpful learning tool. Faculty who work with future teachers report that they use the book to help their students learn what types of teacher behaviors can limit a student’s development, and which mentoring practices can enable students to flourish. Many among us are focused on creating an inclusive environment for math students of all types by showcasing successful mathematicians from a wide variety of backgrounds. And some professors aim to highlight the unequal treatment of mathematicians from different backgrounds in order to encourage our students to help us create a more just and equitable math community. Whatever the goals of a professor may be, Living Proof has provided another tool to help them achieve these goals.

So, in which classes have our colleagues used the book, exactly how have they incorporated the book into their classes, and what has the response from students been? To find out, we’ve gathered information from seven faculty members.

First, we were surprised at the variety of classes represented in this small sample. Living Proof has been used in a quantitative reasoning course for non-STEM majors called “Multicultural Mathematics” (Jim Humphreys, Seattle University). It has been used in a “Math for Elementary Teachers” course (Scott Zinzer, Aurora University) and a course called “Methods for Teaching Secondary School Mathematics” (Angie Hodge, Northern Arizona University). Christine von Renesse (Westfield State University) has used Living Proof in a Linear Algebra course, while Dana Ernst (Northern Arizona University) and Allison Henrich (me!) have used the book in an Introduction to Proofs course. The book was also used in a senior capstone course for math majors (Brian Birgen, Wartburg College).

Several of us used versions of the following prompt for the assignment.

Read the foreword, the preface, and two stories in Living Proof. For each story, write a short reflection. For instance, you might respond to one or more of the following questions. 

  • Did you identify with the author of the story? If so, in what way?
  • How does the author’s experience differ from your own?
  • What surprised you about the author’s story?
  • Did this story make you think differently about mathematics?
  • What about the story inspires you?
  • What about the story bothers you?

Some of us only assigned this once, and others of us required several similar assignments, each time having students choose two stories to read. Sometimes, which stories students could choose would be restricted to a certain part of the book. Other professors made recommendations about which stories might particularly interest students. For the most part, however, assignments involved student choice and open-ended reflection.

Christine von Renesse gave even more structure to her Living Proof assignment by incorporating videos into a more substantial reflection assignment in Linear Algebra. Here is her assignment.

Please watch one of the following video clips:

 1) (Mindset – Alia Crum)

2) (Getting stuck in the negatives – Alison Ledgerwood)

 Then choose 3 stories to read from the book Living Proof. They are all written by different current mathematicians in the US. Write a 2-page paper (double spaced) addressing at least the following questions:

  • How does the video clip relate to your learning experience in this class? What does it imply about learning mathematics in general?
  • Describe at least one new idea from the video that you believe has great impact on how you learn and what you need to work on as a student of mathematics.
  • How have the stories you read influenced your thinking or believes about “becoming a mathematician?”
  • How do the stories support the idea that you could be a mathematician if you wanted to?
  • What are you curious about after watching the video and reading the stories?

So, what has the response to these assignments been? All of the professors we gathered data from felt like most students got something meaningful out of the assignments. Jim Humphreys had this to say about student responses in several sections of his “Multicultural Mathematics” class:

“It was highly successful in engaging the students. Students eagerly found articles by writers they could identify with: students of color read articles by mathematicians of color; queer students read articles by queer mathematicians; students interested in art or in athletics read articles by artist/mathematicians or athlete/mathematicians. One very common theme in the student essays was surprise over the emotional pull of mathematics for the authors; it had never occurred to the students that mathematics could have an emotional appeal. Another common theme was surprise at the fact that many of these professional mathematicians had had to struggle to understand some of the mathematics — many students assumed that mathematics just came easily to everyone who would pursue it as a career.”

Allison recognized this last theme as being a common one in student reflections from her proofs course, while Brian Bergen’s capstone students came away from the assignment thinking that every mathematician has to overcome feeling stupid and having someone tell them they couldn’t be successful. His students learned that their thoughts and feelings were normal. Christine Von Renesse’s students (particularly the future teachers) indicated this as an important theme as well.  One of Scott Zinzer’s students reflected, “Sharing stories like these helps others relate to mathematicians. Seeing and hearing about others’ struggles may inspire you to fight through yours.” A student in Allison’s course wrote, “Reading this story inspired me to keep pushing for what I want, even if there are others who expect me to fail.”

In addition, several students responded to themes in the book related to inclusion/exclusion. One of Dana Ernst’s students wrote:

“This story made me think differently about mathematics. Sometimes I forget that academia was not built by people of color or by immigrants, and I have to remind myself that there may be more obstacles for people who belong to those groups. Not only this, but reading this story reminded me that math and science fields contain disparities among minorities, and that being successful in mathematics is not only the consequence of hard work, but also of privilege.”

Christine Von Renesse noted that her non-STEM majors all commented that they could see a place for themselves in the mathematical community. A student of Allison’s wrote:

“I know that most of the successful people in my prospective field look like me, but there’s a clear divide between the success of Caucasians and people of color that should continue to be addressed until it no longer exists. This story makes me think differently about my place in mathematics and the place of others around me.”

Several of the students in Scott Zinzer’s Math for Elementary Teachers course also spoke about the inclusion/exclusion theme.

“This story showed me that the people behind math can be anybody.  It shows me that we probably do not even know who the most powerful mathematicians are because of the people that did not get the opportunity. It shows me to never give up on any kid that does not understand.”

“A lot of times students see their teachers as experts.  If they do not see a teacher who looks like them teaching in a specific field, they will often internally decide that they must be unable to succeed in that field.”

When we began the Living Proof project, our goal was to share stories from all corners of the mathematical community.  We believe that sharing our experiences with each other is crucial to making our community more diverse and inclusive.  A diverse and inclusive community will enable us to tap into far more sources of creativity and innovation to take mathematics so much further than we have been able to take it in the past.  However, if we cannot reach the next generation and assure them, regardless of their background, that there is a place for them here, our capacity for innovation will be limited. The evidence given in this post is hopeful. In the ten months since Living Proof was published, instructors have found innovative ways, across course levels, to use the collection as a resource to help students understand some of the highs and lows inherent in the mathematical journey.

We acknowledge that this is just a small sample of faculty and student experiences with Living Proof, so we would like to think of this writing as a catalyst for generating more conversation about how these stories have been and might be used. We suspect that many of you have either used the book or have colleagues who have, or perhaps you’re thinking about using it in the upcoming academic year. To contribute to the continued sharing of ideas related to teaching and mentoring with Living Proof, we invite you and your colleagues to fill out the following survey:

Let’s keep the conversation going!

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Remember Why You Started, by Allyson Hahn and Vien Ho

With the rapid spread of COVID 19, our junior year of college went from collaborating with our friends, in-person, on a daily basis, filling up whiteboards in the Math Resource Center, and stopping by our professor’s office to gain clarity, to sitting at our desks and attending class from our respective homes. As students, we’ve been faced with many challenges over the past semester while acclimating to the remote learning environment. The learning curve was steep, but over time we developed strategies to become successful and overcome these obstacles.

We were eager to start the remote learning journey with Abstract Algebra II, but we encountered technical issues right away. Our first class period was difficult, as we struggled to hear our professor through the digital platform. This left us discouraged and we wondered whether we would meet the learning expectations we set for ourselves. But this just meant that we had to work harder. We spent hours reading the textbook and trying to understand concepts from notes and PowerPoints. Office hours were available virtually and via email, but it was challenging to communicate the mathematics. Thankfully, the audio was better after the first class, and we began to adapt to this way of learning even though other technical difficulties, such as suddenly getting disconnected from the digital platform or being unable to view the screen the professor shared, had become commonplace. Despite the challenges we faced, what motivated us to meet the expectations we set was our interest in the content, our belief in ourselves, and the reminder of why we fell in love with math in the first place.

This semester, we were also both in a small independent study course. In the first half of the semester, during class meetings we presented the proofs to theorems and lemmas; this helped our understanding of the material, as we explained it to our classmates and received feedback and further explanation from our professor. Outside of class, we would collaborate in the Math Resource Center to work on problems and ask our professor for guidance. However, we lost these opportunities when we switched to remote learning, which made it even more difficult to comprehend the material and tackle the practice problems. We felt that the first homework assignment due during remote learning was impossible, and we would never be able to finish it. After panicky texts back and forth, we decided to use Skype to discuss the homework and content. In the coming weeks, our calls would last for hours as we poured over the material and completed the problems. Math is incredibly visual, so we had to change how we collaborated. Since we couldn’t see each other’s work in front of us, we had to hold our solutions to the camera or send them via text. We didn’t have the luxury of working side-by-side to point out theorems and errors in each other’s work. However, this “video collaborating” experience made us better mathematicians because it forced us to be clear and concise in our work and discussion. This experience taught us not to be afraid to reach out to our friends and peers for assistance and guidance even if it might expose our weaknesses. But we wouldn’t have been as successful without our professor’s support during the remote learning journey.

As juniors at a small liberal arts college, upper-level mathematics courses are typically quite small, which can make remote learning difficult. With only 6-10 students in a class, we tend to foster a more informal environment when it comes to participation. This natural flow of learning and discourse, which we thrive on, was broken in remote learning. When a professor asks a question during remote learning, it is hard to jump in and answer. Not because we don’t have an idea of what the answer may be, but because when “in person”, the fear of being wrong was so diminished. In the remote setting, there is a new set of fears, that we would say something wrong or talk over someone. In addition, a student’s body language is telling, but without video, it is impossible for someone to pick up on those cues.  This is what causes the “Does this part make sense?” question to have an awkward silence, which we’re sure a lot of professors can relate to. In-person, a head nod would usually suffice, but in this new setting, it was somehow uncomfortable for us to say “yes.”

Since remote classes started, our learning process has been hindered by the numerous distractions in our homes. It is hard to admit, but there were days where we did not feel motivated to work on homework or try to understand new concepts. We learned that we had to structure our days with allotted times for classes, homework, and breaks in order to create a healthy mindset and a productive environment. Even little things like putting on jeans every day, turning off news notifications, or listening to music lightened the mood and helped increase our focus. Not only did we gain skills from learning how to navigate our classes and collaborate with peers and faculty during quarantine, but we also learned how to help ourselves mentally, by reminding ourselves of why we started.

This journey through remote learning was unexpected and left students and faculty to face numerous challenges as we all worked through the remaining weeks of the semester. However, it brought us an experience we will never forget and taught us many lessons. It taught us to be more independent but unafraid to lean on each other. It taught us how to adapt to a new environment and to find ways to work things out. It taught us to not take anything for granted and appreciate the time we had before the remote learning period. More importantly, it taught us to remind ourselves (and always remember) why we started our journey during difficult times. Remote learning ultimately was not a bad thing as it brought many lessons, and time to reflect and be grateful for every day that we get to spend with the people that we love. We are thankful to be safe at home and able to remain connected with our family, professors, and friends, while others are fighting on the frontlines to save lives and restore the world.

Allyson Hahn and Vien Ho are Pure Mathematics majors whose continued passion for mathematics was shaped by their dedicated and encouraging professors at North Central College. They share a similar goal of pursuing a Ph.D. in Pure Mathematics and eventually teaching at an institution. 

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To All the Minhyes out There: Walking Through an Unconventional Journey, by Minhye Lee

Like any ordinary immigrants would do, my parents and I followed my new school counselor’s advice: begin school as a freshman instead of a sophomore so that I could have enough time to improve my English. I was 16 but couldn’t speak, write, or understand English. The advice seemed promising. I tried to learn as much as possible, but there was no quick remedy for the language barrier. I would stay up each night until 4 am to translate the material covered in class with a giant English-Korean paper dictionary. Yet even knowing the material, I would still get lost in all of my classes. My Korean class, which was taught in English, sounded like a half mystery story. I was often marked as absent in my PE class because I couldn’t hear my name when my PE teacher took attendance. In my early math classes, I was able to follow lessons using my previous knowledge from Korea, but this didn’t last long. As I moved up, new concepts and new terminologies got tougher to understand. But I had a belief that I could learn if I continued to work hard.

After two years of struggle, my family decided to move to a different county in California, hoping that I could have a better education there. Despite all the hard work I had done, I was rejected from high school. The decision was made in less than 10 minutes. The school official said, “You are too old to be admitted, and your English isn’t good enough. I don’t think you will be able to graduate on time.” After this unexpected change to the plan, there weren’t many options left for a student like myself who was off track for completing high school on a standard timeline. Two options were given: either move to a different district or attend a continuing education school. We couldn’t afford to move again and didn’t have any relatives or family other than ourselves. So, I decided to attend the Centennial Continuing Education Center, an adult school where I earned my high school diploma through self-paced study.

The self-paced study setting works via an exit/entry system, which is not the same as the GED test. If you are ready to take an exam for a lesson that you signed up for, you schedule the exam and take it. To prepare for each of the exams, I would enter a study room, sign in, and study alone. I continued my study routine as before. Although learning was exciting, studying different subjects written in English alone was challenging. I used the same giant dictionary and gradually transitioned to an English only dictionary. I was getting better at reading, yet I struggled to articulate my thoughts in spoken words. Being an introvert and a language learner made it even harder to make friends or open a simple conversation, especially in my mostly independent self-teaching learning environment.

As soon as I earned my diploma, I entered a community college and was faced with a new challenge: I didn’t know what to do with my life. I knew one thing for sure, which was that I didn’t want to be judged and rejected again. So, I couldn’t allow myself to make mistakes. As a result, I decided to do everything on my own instead of asking for help. It took a very long time for me to figure out what I wanted to do. Starting from Intermediate Algebra, my desire to learn mathematics steadily grew as I continued to take more math classes. What attracted me to mathematics, at that time, was that it helped me challenge myself when I needed it. To this day, I believe that mathematics is the subject that most rewards hard work, and it invites anyone who is willing to learn. I eventually discovered what I wanted to do: I was determined to become a math major. However, my lack of confidence in myself and fear of being wrong still held me back.

My educational path brought me to a four-year institution, where I enjoyed being surrounded by various math topics and problems. Spending hours studying alone and learning to teach myself in my previous schools helped me learn what I wished to learn. The bigger issue was that I didn’t know how to interact with classmates or professors. Even when I had an idea or a question in class, my fear of making a mistake made it hard to try it out. I detached myself from others as much as possible. But isolating myself required a lot of energy—I got sick almost every semester. The only reason I survived was that I didn’t mind spending hours studying, even if it was to find the solution to a single problem. And most of the time, I was eventually successful in understanding the concepts I was being taught. Although a painful process at times, I enjoyed learning mathematics.

But the pain gradually became greater than the gain. Towards the end of my undergraduate degree, I took Real Analysis II. As usual, I worked alone. Of course, I was constantly sick. I didn’t worry too much about my ability to succeed since I loved the prerequisite course, Real Analysis I. But I struggled and struggled. At times, I desperately wanted to ask for help, but I didn’t know how to start. I barely managed to pass. The excitement of learning dissipated rapidly in only one semester. Finally, I realized that I needed to change. I had to overcome my fear so that I could enjoy math again.

Two years ago, I became a math graduate student. When I started the master’s program, I promised myself that I would not repeat the same mistakes that I made during my undergraduate program. Adapting to change takes time, and I may be uncomfortable with change. However, I have never stopped trying, since I’ve learned that trying is the only way I can improve. I now know that it is okay to ask for help, to be wrong, and to say “I don’t know” because these things are just part of learning. By going to office hours, I have listened to what others asked, learned how to use new terms, and attempted to ask a few questions. I have made countless mistakes, but surprisingly, my professors were very kind and patient enough to work with me. By working with classmates, I learned to express my ideas and articulate my thoughts in words more effectively. In 2019, I attended my first math conference, the Pacific Math Alliance Conference. By attending, I learned that there are people who love to talk about and share their passion for mathematics. I can’t say that I’ve completely overcome my weaknesses at this point. I know that trying new things isn’t always pleasant, and learning math still requires hard individual work. However, what I have learned in the past two years is that this math learning process can be more fruitful and powerful if I’m ready to adjust the way I approach it.

Life does not bind itself to a carefully constructed plan, and sometimes life brings complications, which, in my case, includes political, economic, and cultural complexities. These things have had an immense impact on my life. Indeed, my perspectives have changed over the years. However, I know that these social issues will not diminish my desire to exercise my passion for mathematics fully. Most importantly, I have learned to stay healthy and flexible to unforeseen changes. Now, my story has become a substantial asset that I can share with others to help those in similar situations feel less alone.

Minhye Lee obtained her master’s degree in 2020 and her bachelor’s degree in 2018 both from California State University, Fullerton. She strongly believes that anyone can learn mathematics, regardless of one’s economic, academic, or social background if provided with adequate support and resources. Minhye enjoys studying patterns and proofs as well as solving problems. She is considering a Ph.D. program in math education. Minhye desires to expand her knowledge and understanding in mathematics and to serve and encourage students to expand their own interests in mathematics.

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Persevere and succeed, by Jeanette Shakalli

I had always been a straight A student. Everybody at the Episcopal School of Panama knew that I had the highest GPA in my class. In particular, I was really good at math since I inherited a passion for mathematics from my dad. At the beginning, I would get frustrated with my dad since he would teach me advanced material that I did not need to know at the time. I was only interested in understanding the math concepts that would enable me to pass the next math exam. However, when my math professor would explain a concept in class that I had already seen with my dad, the ideas made sense and I started loving the feeling of being ahead. Soon enough, I challenged myself to solve the most difficult math problems in the textbook on my own. I even participated in and won a medal at the National Math Olympics in Panama… twice! Furthermore, I was trained by the Panamanian Math Olympics Foundation at the University of Panama to compete internationally while I was in high school. I never actually travelled to represent my country in an international Math Olympics since someone somewhere had spent the funds for the program on something else, which is sadly pretty common in Panama, but at least I knew that I was above average. Therefore, failing my first calculus exam during my undergraduate studies at the University of Notre Dame was appalling!

“Was I capable of failing?” I started panicking. “What did that say about me as a person?” I desperately tried to find a somewhat reasonable explanation. “Or does this failure simply mean I am not good at math after all?”  A sense of despair took over me. It was my first failure EVER, and I had a choice to make: I could either succumb to it, quit, and return to Panama, or I could do something about it. Option 1 involved me giving up and never knowing what would have happened if I had stayed. Option 2 involved me taking a risk. Since I have always loved a challenge, I decided to do the latter. I emailed my calculus professor and asked to meet with him one-on-one. He was a very patient man and we went over all the problems of the exam one by one. He explained what I had done wrong and I redid the entire exam, making sure that I understood the material profoundly. His kindness and my perseverance helped me get through my failed exam.

As a result of this experience, I learned that failure is not the opposite of success. If you would rather not fail, you will probably never succeed. However, I did not have experience with the concept of failure while I was growing up since I always had good grades. Hence, facing my first failure on an exam on my own while I was living by myself in a different country definitely shaped the future me that I was meant to become.

It turns out that I later found out that failing your first exam is pretty common among international students when they study abroad while they are adjusting to a different environment. I was lucky that the University of Notre Dame was aware of this issue and my professor was understanding. Nevertheless, I share this story every time I am invited to give a math presentation to young students in Panama because I want them to know that just because you fail a math exam, it does not mean that you do not belong in math.

Math is all around us. You can find math in magic, mime, music, art, movies and more. I am blessed now to belong to an international math community with whom I can share the richness and beauty of mathematics, regardless of gender, race, religion, or nationality. Thanks to these connections, I created a Program on Math Outreach in Panama in 2016 with the purpose of inspiring Panamanian youth to study math and to convince the general public that math is not only fun but it also has many interesting applications. Moreover, this coming April 2020, I will officially launch the Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT), a private non-profit Foundation that I created with the goal of promoting the study of mathematics in the Republic of Panama. Therefore, my advice to you, who are reading these words, is to never give up since you never know what adventures await you.


Born in Panama City, Panama, Dr. Shakalli attended the Episcopal School of Panama. She won a Gold Medal and a Bronze Medal in the Panamanian Math Olympics. She obtained her Bachelor of Science in Mathematics and Chemistry from the University of Notre Dame in 2007 and received the Senior GE Prize for Mathematics Majors. From 2007 until 2008, she was recognized with the W.E. Coppage Fellowship in Mathematics by Texas A&M University and obtained her PhD in Mathematics from Texas A&M University in 2012. From 2012 until 2019, Dr. Shakalli worked at the National Secretariat of Science, Technology and Innovation (SENACYT) of Panama. 

Dr. Shakalli is currently the Executive Director of the Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT), a private non-profit Foundation which she established with the goal of promoting the study of mathematics in the Republic of Panama. Since 2016, Dr. Shakalli has organized more than 50 math outreach events in the Republic of Panama, including Math Carnivals, MathsJams, Julia Robinson Mathematics Festivals, Celebrations of Mind, Origami Workshops, and presentations open to the general public given by international mathematicians on topics like “Magic and Math,” “Music and Math,” and “Origami and Math.” Since 2017, she has been the International Mathematical Union (IMU)’s Committee for Women in Mathematics (CWM) Ambassador for Panama. Dr. Shakalli was recognized as “One of the Twenty Faces of the Mathematical Association of America (MAA)” in their magazine MAA FOCUS in the April/May 2017 edition. Furthermore, she was promoted as IEEE Senior Member in 2019. Her unique career profile appears on the fourth edition of the book “101 Careers in Mathematics,” pages 203-204, and her story was highlighted by Lathisms on October 12, 2019. Dr. Shakalli currently serves as Director of Admissions of the Panamanian Association for the Advancement of Science (APANAC), Secretary on the Board of Directors of IEEE Panama Section, and Secretary on the Board of Directors of the J. Thomas Ford Gift of Life Foundation. Moreover, she is the Executive Coordinator of the Panama Pod of 500 Women Scientists. She is also a member of the American Association for the Advancement of Science (AAAS), of the Mathematical Association of America (MAA), of the American Mathematical Society (AMS), of the Association for Women in Mathematics (AWM), and of OrigamiUSA.


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Finding my niche, by Allison Henrich

When I interviewed for my tenure-track job at Seattle University, I admitted to the chair of the department during my on-campus interview that I was really much more interested in teaching than in research—I would do what research was required for the job, but it wasn’t my real passion. She said to me, looking around to see if anyone else was in the hallway we were walking down, “Don’t let the dean hear you say that!”

Sometime during my preparation for this on-campus interview, I looked at all of SU’s math faculty webpages. Some faculty had research records that were completely terrifying to me. “Are those the publication standards they expect of tenure-track faculty??” Fortunately, some were less terrifying. One faculty member in particular had a research track record that looked like something I might be able to match. This faculty member happened to be an acquaintance of mine, so I contacted them—off-the-record—to ask about research expectations for tenure. They reassured me that the expectations were at a level I could achieve. So, when offered the job, I took it with a bit less hesitation that I could actually be successful in it.

Up until that point—in my first tenure-track job, my first year out of grad school—I had been fairly successful at publishing. The problem was that I felt like the heavy lifting in my research projects had been done by my advisor or collaborators. I felt dumb most of the time in research discussions, and I didn’t feel confident that I could contribute in a meaningful way to research. My advisor and collaborators could easily have done our work without me. I expected that once everyone figured out that I was a pretty worthless collaborator, they’d drop me, and I’d make no progress at all on research.

That all changed when I started mentoring undergraduate students in research. The summer before I began my job at Seattle U, I was given a chance to lead a research group in the SMALL REU at Williams College. I worked with four very bright, hard-working students, but throughout our process of doing joint research, I felt that I was an important contributor to the project. I got to choose the problems we worked on, which came from ideas that I was excited about, not what I “should” be working on. I got to feel like the expert on many of the tools we needed to solve our problems. I was able to answer questions and offer ideas for how to get unstuck when my students hit a roadblock. Making such meaningful contributions completely turned my relationship with research around. For once, research was actually fun! During the last week of the REU, my team submitted two papers for publication, both of which were accepted by well-respected journals.

From then on, I decided to focus on finding problems I found interesting, collaborators that were fun to work with (including many more undergraduates), and supportive research communities to be a part of. I now know to look for mathematicians who get along with each other—people who enjoy sharing a meal together and talking about things that may be totally unrelated to math. I have found people who don’t see a difference between doing math and playing; people who are doing exciting things not only in their research, but also supporting their students and contributing to an inclusive environment in the math community; people with whom I can share successes in order to celebrate, not to impress; and people with whom I am comfortable admitting my failures. There have been hiccups along the way. I have worked on research problems that I didn’t enjoy, where doing math didn’t ever feel like playing and where I wasn’t sure my contributions were meaningful. I have gone to conferences where I felt worthless—conferences where people were doing highly technical mathematics and working very hard to impress each other. The important thing is that I figured out that I don’t have to go to those conferences. Those research questions don’t have to be my research questions. My scholarly agenda can be driven by my mathematical interests and people who I love to be around.

Now, I am 12 years out of grad school. I have co-authored 17 math research papers, four pedagogical papers, two books, several articles, and I’ve co-edited two more books. I earned tenure, and I became full professor as soon as I was able. I wish I could have told that scared young faculty member that everything would be alright. I would have saved her so much anxiety!

Allison Henrich, Editor, is a Professor of Mathematics at Seattle University, where she has been a member of the faculty since 2009. She earned her PhD from Dartmouth College and bachelor’s degrees in both math and philosophy from the University of Washington. Allison is passionate about teaching, and she is active in research in knot theory and recreational math as well as the scholarship of teaching and learning. One of the most rewarding activities she engages in as a professor is working with undergraduate researchers. Through knot theory research, Allison mentors students—many of whom are unsure about their career goals—to help them learn what may and may not excite them about a career involving mathematical research. In general, she gets the most enjoyment out of supporting students to do their best work as they learn about the beauty of mathematics. Allison recognizes that she would not be where she is today without the inspiration and encouragement of several of her own undergraduate professors.


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Grad School and the NICU, by Julie Skinner Sutton

“Why are you here today? You need to go home and rest. Let’s catch up in a few days.” Those words from my supervising professor for my mathematics PhD were so comforting. The words may not be exact, but the sentiment is. I can’t remember who asked me first if I was OK; was it my advisor, or someone on my committee? I remember walking into the seminar I was helping with; then I was in the hallway with my advisor; it was early July and campus was pretty much empty. “I had a miscarriage.” Just saying the words were hard enough. The compassion and kindness that I was met with made all the difference. Not that I expected anything less; I had been very open from the beginning that I wanted to have kids and I was already 34 entering my 4th year of a BS-to-PhD mathematics program. The plan for Fall 2013 was to interview students in an undergraduate calculus class (some of whom were in a special program working on more intense questions in a group setting) and to teach a large section of pre-calculus. I found out I was pregnant on a Sunday, and by the next Sunday we were in the ER because I was having cramps. By that fateful Wednesday as I entered the seminar, it was over. I went home to rest, as instructed. Then, we went to one final appointment. “There’s a heartbeat.” I remember being shocked. My husband found his voice before I did, “How is that possible?” Within a few minutes a nurse was handing me a prescription. “Take these and start tonight. It probably won’t be enough. The heartbeat was too low.” This is not at all how I pictured pregnancy starting. I took the progesterone, afraid to tell anyone what was going on, and we waited.

At MathFest that summer (how was it hot in Hartford?), I was miserable. I slept so much. Thankfully, a dear friend was there, and I could confide in her. She brought me lunch more than once when I couldn’t muster the energy to leave the hotel. As classes began that fall, it seemed as though everything was working out. When I told my chair about the pregnancy, he exclaimed, “This is wonderful news!” He told me that in the late fall, we could figure out how to handle the spring semester. People kept asking how we managed to get Pi-Day as a due date. I didn’t realize the rarity of my having such a supportive department. I assumed that people would be accepting because women have babies all the time, and the department that I was in had lots of families and kids. The only time I heard anything negative (from a single, older male), one of our tenured professors corrected the person.

Then, I got sick. I had migraine headaches that the doctors couldn’t control. I was hospitalized over and over again. We had to delay the start of data collection for my dissertation research. It seems like it took months to get everything rescheduled. I came to class when I could (and my amazing officemate covered for me when I couldn’t), and somehow my interviews were completed. We joked that Fall 2013 was the worst time to have a baby. That semester, I had the worst teaching evaluations of my life: “She takes attendance but can’t bother to come to class herself.” Some days, my meds didn’t work, and I would pass out from the pain and end up in the hospital again. But somehow, I made it to Chicago for the PME-NA (North American Chapter of the International Group for the Psychology of Mathematics Education) conference. I remember walking around the city with a friend who lives there. She’s a physician, and I think that’s the main reason I felt comfortable going. It was raining so hard that my maternity pants kept falling down from the weight of the water soaking into the legs. I didn’t look 6 months pregnant, and almost no one knew. My health finally stabilized, and we enjoyed Thanksgiving with my family, talking about the new little one that would join us next year. The day after Thanksgiving, my wedding rings wouldn’t fit, and my shoes were uncomfortable. I met a friend from high school to go shopping and she brushed off my symptoms. “That happens. It’s nothing.”

The following Wednesday was my last interview for my study. Somehow, in the midst of all the pain and exhaustion, I had made it! I remember walking up the steps to the building, feeling winded. I was tired and looking forward to the break. A faculty member saw me walking in and asked how I was. I will never forget her telling me, “You look puffy,” before I reassured her that I was fine. “Let’s do lunch,” she offered. After that last interview, I caught up with my dissertation advisor. He was also concerned about me, but I had a doctor’s appointment that afternoon and promised I was fine. I would start transcribing my interviews over the break and into the Spring. The department had offered to let me be a grader for a few classes and I could teach a special seminar until I had the baby. We had meetings scheduled to finalize the plans.

“Get back on the scale again.” I looked at the nurse, confused, but I did as she said. “Your doctor will be right in,” she told me as I sat on the cold table, my husband playing on his iPad. In less than 30 seconds, the door opened and my doctor entered. “You’re going to the hospital. You’re going to stay there until you have the baby.” Shocked, it was again my husband who first recovered enough to speak, “That’s 15 weeks!” She just nodded. I had gained 35 pounds in less than 4 weeks and had high protein in my urine sample. I had preeclampsia. I remember trying to tell my husband what to pack in a bag because, of course, I hadn’t packed one yet. It was a balmy 70-degree day in early December, and somehow, he found the rattiest nightgown and holeyest pajama pants I owned. And he forgot the shampoo. The nurses and my doctor did their best to comfort me as I moved into the hospital’s ante-partum floor, “You can have your baby shower downstairs if your blood pressure is low enough,” and (my favorite) “You’ll make friends on the floor!” (I did, in fact, meet a woman two years later who had been on the floor with me). That night I cried, alone in a hospital room. As soon as it was ‘decent’ to text someone on the East Coast, I reached out to a math professor I knew who had had premature twins. She had also had preeclampsia. I remember the care in her voice as I apologized over and over again for calling. “This is what we do – we support each other.” Word got around that I was going to be in the hospital for a long while and people texted and called. My doctor friend from Chicago called – she’s a pediatric hospitalist and I was her sounding board throughout her NICU rotations in residency. When I said I was 25 weeks, she responded, “Oh, Sh-t!” I hung up. We had so much stacked against us. Then it snowed. (Remember the 70-degree day?) Well, in fewer than 48 hours, the DFW airport had turned into a hockey rink. They cancelled exams at my university (which doesn’t happen in Texas!). All day, my blood pressure kept rising. I finally called my husband. “Get here, I need you.” He hemmed about the weather but came up. I ordered dinner and got in the shower. There was a nurse with an IV waiting when I got out and, at 9:01pm (so, technically AFTER classes ended in 2013’s Fall semester), my 640g (1.4lb) daughter was born via c-section. Our families couldn’t get there because of the weather. It was just us.

A few days later, my department sent out an email saying that I’d had a baby and I received so many congratulatory emails (and some saying, “We didn’t know you were expecting!”). My advisor and his wife (who is also a math faculty member) came up to meet my daughter in her little isolette in the NICU.

And this is where I thought the story would end: with me and a Master’s degree. But that wasn’t the end. My department let me grade and coordinate a set of classes, and there was a grant I could contribute to as a research assistant for the next semester. I kept in touch with my advisor, but most of the contact was when I initiated it. My daughter had complications, and we moved to a children’s hospital. She had more surgeries. After 173 days in the hospital, she came home on May 28th. I taught a class over the summer, and I did eventually get my transcriptions done. We had to navigate the world of in-home nursing instead of daycare and nanny shares. Throughout all of it, though, I knew that my department was behind me. In fact, after my daughter was born, it seemed like there was a baby boom among the graduate students! We all finished our PhDs. They instilled in us that we were worth investing in, and then they did just that. I’m not saying that everyone got a semester to grade instead of full teaching duties—mine was certainly a special case—but no one was made to feel like they had “messed up” by getting pregnant during their education. Even now, when I go back to my Alma Mater to have a meeting or teach a class, people ask first about my family. It’s been 6 years, and they still think I’m worth investing in. And, I am.

Julie Skinner Sutton is a researcher in Undergraduate Mathematics Education who teaches at The University of Texas at Dallas in the department of Mathematical Sciences and is affiliated with the department of Science & Math Education as a Senior Lecturer. She has found a passion for teaching those students who choose a path into the liberal and fine arts disciplines and considers herself an ambassador of mathematics.

Julie first attended The University of Texas at Austin with plans to become a Chemical Engineer, but quickly determined that life in a cubicle wasn’t for her. In fact, after a tenured faculty member commented (to her father) that she would “be a fine entertainment director on cruise ships,” her dreams of even attaining a Bachelor’s Degree became dark. Eventually Julie decided to continue the chase – this time at The University of Texas at Arlington – to obtain a teaching certificate and teach high school math. However, a faculty member took an interest in Julie and invited her to apply to graduate school. After receiving a GAANN fellowship at UT-Arlington, Julie also worked on a large NSF-DOE grant researching the impact of group learning on calculus outcomes. Through the Association for Women in Mathematics, Julie was awarded several Sonia Kovalevsky grants with faculty at UT-Arlington and routinely worked with middle school students at events.

After completing her dissertation, Julie took her position at UT Dallas. She enthusiastically teaches pre-service and in-service teachers and those working to obtain a non-science degree. She won a TENSOR foundation grant at UTD and hosted 45 students from a local Title I high school on campus for a day of mathematics fun. Routinely she spends her summers showing students how fun mathematical exploration can be! In 2019, UT Dallas awarded Julie the Non-Tenure Track Teaching Award from the College of Natural Sciences and Mathematics.

Julie and her husband have a healthy (and energetic) 6-year-old now. She went home with a feeding tube and oxygen, but is now just as normal as the rest of us (well, as normal as we can be).


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Helping other women, helping myself, by Amy Prager

One of the most important topics to me in academia and industry is that of gender discrimination. To discuss this problem in the abstract is one thing, however, to actually live through it and have personal experience is quite another. I view this issue through a rare lens, as I am a postoperative transgendered woman.

When I was younger, and assumed to be a cis-gendered male, I let my eyes and ears be my guide to what those around me thought about what the proper role of women and their education should be. My grandparents—on both sides—would actually say things like, “It’s OK for a boy to be bookish or nerdy, but for a girl its very bad, of course.” My mother’s father was actually proud of the fact that he wanted/allowed his daughters to be educated, too, as if this was an unusually progressive attitude for him to take. I remained silent, but I vowed in my mind to investigate further exactly how normative these prejudicial attitudes were when I was older, hoping someday that information would become easier to come by (through a worldwide, interconnected computer system of “webpages,” perhaps?). When I looked at undergraduate colleges, there were still some good universities, most notably Columbia College, that would not admit women. We have come a long way, but in many respects, not nearly far enough.

When I attended university, I took further notice of potentially sexist and other discriminatory attitudes all around me. Some in my family actually said if I did not marry a member of my ethnic group, I would be disowned or worse. These statements are clearly not supportive of an LGBT identity, especially when they were expressed before the legalization of same sex marriage. But these attitudes went far beyond romantic or reproductive relationships—they affected every aspect of my daily life. Dismayed by what I saw happening back “home” and vowing to myself that that place will never be considered my “home” again, I approached my advisor and colleagues about these ideas. My advisor, trying his best to be supportive, told me that, horrifyingly, some women attend college with the goal of obtaining their “MRS degree.” I then queried my female STEM friends and students about their experiences. I was genuinely saddened by what was self-reported. One of my own students lamented that her mother told her she was destined to be a housewife like her and, therefore, did not need an expensive education.  When I tried to intercede on her behalf, I actually got branded as a villain. Tales of parental, familial and societal disapproval were the norm, not the unfortunate rare exception. What was even worse was that the academy, whose very job it was to encourage their students, acted in an even more discouraging fashion. However, I felt more than sadness. I was in disbelief, as I could not have imagined—from my unknowingly privileged vantage point—that such institutionalized discrimination could exist against an entire class, indeed the majority of people on earth. However, all of that was about to change dramatically once I began transitioning.

When I first sought out therapy to help me through my transition, I did not realize that there are religious therapists who believe that their role is to encourage heteronormativity and cis-normativity, and they know that the only way they can do this is by removing the patient (or victim) from other sources of more neutral help. I had my work cut out for me! I had one encounter in my search for a therapist that is amusing in hindsight. A therapist yelled at me that if I did not show up in a business suit, pressed dress shirt, and perfectly tied tie, he would throw me out of his office. His rationale was simple: only these clothing choices would make me at all employable. (He apparently has never been to a tech company office or university campus.) He told me to grow up and get a job, pointing out that he didn’t want to have to pay increased taxes to pay for my welfare my entire life. Oddly enough, he and others like him have inadvertently taught me a great lesson. They made me more sensitive to others’ needs and instilled in me a desire to help.

And it is my need to help others—and especially those who need help strictly because they come from some marginalized group—that has altered the course of my life, my career, and my research. When helping others becomes something you are disrespected and degraded for, you know you know you are dealing with people that have a lot to hide and a lot to lose. These are people that have too much to lose from a fair world, and too much to hide about themselves. As a result of negative experiences, both directed at me personally and those I observed out in the world, my work transitioned from research mathematics and computing to STEM education and, in particular, math education, with a focus on helping women achieve their fullest potential in these fields. In the course of my research and my work in these areas, what I have learned and experienced has been absolutely astounding. I have found that there is a powerful community that uses threats involving educational expenses as leverage to realize their vision for the next generation. It has both encouraged me to continue onward, and it has depressed me so much that I have had difficulty doing exactly that.

I cope and manage to keep going by observing the success stories of my students and mentees. I see the effects on those who have been hurt and those who I am trying to help. Despite the challenges I face on the path I’ve chosen, the positive change I am able to contribute to makes it worthwhile.

Amy Beth Prager is an applied mathematician and computational scientist who has become a STEM Education researcher and passionate advocate for diversity and inclusion, encouraging young women and underrepresented groups in STEM, sharing her love of science and technology to inspire the next generation of scientists and technologists, and people everywhere to embrace learning and education.

In the 20th century, she graduated Johns Hopkins University in applied mathematics and theoretical chemistry, and studied postgraduate level quantum chemistry for 1.5 years beyond her bachelor’s degree, and successfully worked on scientific projects in a wide variety of locations, within Nothern America and Europe.

In the 21st century, her research interests turned towards the disproportionate barriers and resultant income inequality in countries with high education costs such as the USA and UK, that fall on women and underrepresented groups. She entered the doctoral programs in math education and mathematics at Columbia University, featuring additional coursework at Princeton University and IAS, and after becoming ABD at Columbia, completed over a calendar year of post-ABD study at MIT.

She currently devotes herself to these issues in a number of capacities. She serves on the NCWIT Aspirations Team in her native Massachusetts, lectures in mathematics education at Cornell University and other universities in New England, and is an active member and participant of SACNAS, and the Mathematics Alliance. She has served on panels , led discussions, and given keynotes at SWE conferences and similar organizations, and contributed to books and book chapters on encouragement of women and underrepresented groups in STEM.

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I am a Depressed Mathematician, by Matthew Pons

I was diagnosed with depression as a graduate student.  My therapist at the time worked with many graduate students and she understood the external stressors that such programs place on individuals.  She was also well aware of the fact that many graduate students abuse drugs and alcohol in an effort to cope.  I thought that I was just like everyone else. I worked hard, I taught my courses, and I went out for drinks frequently.  I lied to her about my alcohol use as I was embarrassed about how much I drank – not a healthy choice.  However, I’m sure she knew I was not being truthful, and she worked with me regardless of my unwillingness to be honest with both her and myself.  Eventually, she helped me see that my feelings of sadness, worthlessness, and thoughts of suicide were part of something that we could work through.

My therapist helped me to see that I had been depressed since I was around 17.  Throughout college, I had very little self-confidence, was terribly intimidated to speak in public spaces, and thoughts of suicide were frequent. I only made a plan once, and, luckily, I was not determined enough to carry it out. However, math was a place where I felt safe. I understood things quickly in my mathematics courses, my professors were encouraging, and I gained a little self-confidence in that arena. Unfortunately, that changed. As a graduate student and pre-tenured faculty member, math was a large contributor to my feelings of worthlessness. My classmates in graduate school seemed far more intelligent than I was, and I compared myself to them too often. When I couldn’t prove the result I was trying to prove, I felt stupid. Then I questioned my self-worth.  Then I drank. This was a frequently occurring cycle.  I abused alcohol quite a bit throughout grad school (though I would be sure to sober up for therapy appointments). And then there were the days when I didn’t even try because I couldn’t face it—or even get out of bed, for that matter.

What I’ve learned is that I’m not worthless, no matter what my brain tells me or how often it tells me. Fighting those kinds of thoughts can be exhausting and can affect sleep patterns and mood, which in turn, affect how I interact with my colleagues and students.  I have discovered that I can combat a thought of worthlessness by accomplishing something, anything: a load of laundry, an email, preparing or giving a lecture, etc.  This seems simple, but it reminds me that I am a functioning human being.  But that is just one piece of the depression puzzle.  To deal with the bigger issues, having a schedule is crucial for me.  My days are planned pretty thoroughly with meetings, class, and office hours.  I don’t allow myself the time to fall into the trap of thoughts waiting for me, and at the end of the day, I can be proud of what I’ve accomplished.  It’s not about ignoring the depression but on focusing on things that counterbalance those thoughts and symptoms. Where it gets tough is when there are big chunks of unscheduled time. As academics, we have huge breaks in our normal schedule.  Winter and summer breaks are a difficult time, and sabbaticals are completely overwhelming.  In these times, I have learned that I need to be organized and have projects, both big and small, that I can focus on. And for days that I can’t move, I have to accept that they exist and try again the next day.

I’ve also realized that mathematics is actually a great tool for someone like me. Instead of focusing on obsession over proving the theorem, I now end a day of research looking back on what I have learned. It’s about finding the positive.  Ok, so I didn’t prove the theorem, but I learned why my method is insufficient.  Or, I learned about a new result that may prove useful in my research.  Or, I went back to the basics and dug into the foundational aspects of the problem, solidifying my overall understanding. Hell, somedays I just work some fun calculus problems. Learning is one of the strongest tools I have. The fact that I live and work in a discipline that has an endless supply of things to learn is a huge blessing. I know that there is more pressure on graduate students and pre-tenured faculty to “prove that theorem,” but this perspective can still be useful. You are not defined by your mathematics. It’s a cliché, but I wish that we were more acculturated to focus on the journey rather than the destination.

The above change in perspective came about as I began to practice yoga.  My practice focuses a lot on gratitude and has helped me to look for places to be grateful in all aspects of my life. With regard to mathematics, what I know now is that I can be grateful for the mathematics that I do know.  I can be grateful for the mathematics that is still eluding me.  And I can be grateful for my colleagues and students who allow me to discuss mathematics with them. It’s ironic, but many of us communicate the above ideas to our students frequently, and yet we cannot internalize these same messages.  As I continue on my journey, my hope is that I will continue to remember what I’m grateful for and trust myself.

Matthew Pons, Co-Editor, is a Professor and Chair of the Mathematics Department at North Central College, where he has been a faculty member since 2007.  He earned his PhD from the University of Virginia in 2007 and his undergraduate degree in 2002 from the University of North Carolina at Asheville. Matthew’s favorite professional activity is teaching and his approach to classroom learning is shaped largely by his faculty mentors as both an undergraduate and graduate student.  They taught with passion and enthusiasm, and they knew how to push a student to excel all the while providing guidance and support.  As an instructor, it is not always easy to watch students struggle with the challenges inherent in the study of mathematics.  But seeing students overcome these challenges is a constant source of inspiration for Matthew, not only in his teaching but also in his own research.

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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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