Stuck in the South of France

The Calanques, where I hiked and swam every day during the conference.

Valentijn Karemaker and Marius Vuille talking math outside the lecture hall at CIRM.

I love the variety of beautiful places (physical and intellectual) that math takes me.  This week math has taken me to the south of France.  What a wonderful place to do math, or really anything!  Not least because France has recently taken the extraordinarily cheering step of electing a Fields Medalist to Parliament.  I was at the Centre International de Recontres Mathematiques (CIRM), a math center near Marseille.  The conference: Arithmetic, Geometry, Cryptography, and Coding Theory (AGC^2T), a biannual conference which began in and has been held at CIRM since 1987. I hate to go overboard, but it might have been the nicest conference ever. It wasn’t just the daily hike to the nearby Calanques to swim in the Mediterranean, though that was incredible. The talks were great, which I say with full information because I went to all 35 of them. Even more, though, I just enjoyed talking with these very interesting people. The conference organizers, and really all the participants, deserve a great deal of credit for creating an exceptionally relaxed and positive atmosphere.

In graduate school, I spent a lot of time reading Algebraic Curves over a Finite Field, by James Hirschfeld, Gabor Korchmaros, and Fernando Torres.  James Hirschfeld was a member of the scientific committee for the conference, so I got to meet him for the first time this week. We started chatting at a coffee break, and I didn’t realize at first that I had spent so much time in the company of his work. He was very personable, and I eventually told him that I had in fact purchased three copies of this book over the years (losing one in a move across the country and another in some unknown way). I asked how he came to start writing books, and he said that in fact he started his first book because his research wasn’t going well. He thought that writing a survey of the field would help him regroup. I’ll quote here something he had earlier written about this: “In 1972, when my research was going poorly, I decided to write a one-volume survey of the field of mathematics that I had been working in, that is, the combinatorics of finite projective spaces. … As the book was supposed to be a survey of the field, I decided to begin the book by compiling as complete a bibliography as possible.” He said that in compiling the bibliography, he read many papers and had a lot of ideas that helped him move forward with his research.

I found this narrative, well, not exactly surprising, because it makes sense—writing a deep survey like this would be incredibly enlightening. I would love to do it, and I do like writing survey/expository pieces. It seems impossible, at this juncture, that I will ever have the time and focused energy to do such a thing, but he had only been out of graduate school for 6 years at that point (the same as me, now). Ahem. Anyway, it was not surprising that writing the book worked, but it was somewhat unexpected and inspiring to me that he freely stated that his research had been going poorly.  Nobody ever says their research is going poorly in public! It is so rare! The market, the culture of the field, and our own dedication to positive thinking all encourage us to accentuate the positive. And greatly fear the negative. Because when things aren’t going well, it becomes very easy to think that we actually aren’t smart enough and we probably shouldn’t be doing this after all. For those of us that are trying to get tenure or get the next job, it seems like an act of self-destruction to send the message that you are stuck, or struggling in any significant way. So, I guess it really struck me to hear someone that I respected casually mention that their research had been going poorly!

This is just another shot of the Calanques, because I can’t resist.

Now, poor is a relative term. We are each working from our own vision of what our research life should be, so one person’s poor could be another person’s ideal. But this anecdote, which Hirschfeld just mentioned in passing, really got me wondering what people do when things are going poorly. In particular, how do the mathematicians that I admire get unstuck or find inspiration in their research lives? I often imagine that the “mathematical experts” of the world don’t have this sort of trouble.  But, on the other hand, I spend some time every semester normalizing struggle and convincing my students that the experts struggle too. Students in algebra and number theory classes that I teach are generally assigned to watch The Proof, the Nova documentary about Andrew Wiles and the proof of Fermat’s Last Theorem (based on a book by Simon Singh). There are several reasons I share this film, but one of the things I always point out is just how long it took to prove this statement, and how many brilliant people got utterly stuck on the problem. The idea of being stuck on this scale, of making mistakes and struggling for years, seems to be a bit of a revelation and a comfort to my often-stuck students.

Ask the Experts: Getting Unstuck  

With all this in mind, I decided to ask some really bright, successful mathematicians about being stuck. What I wanted was to ask about times when they had really struggled, and felt that their research was going poorly. But, in the end, the specifics of this seemed too personal to ask people to share in someone else’s blog. I just couldn’t bring myself to put people on the spot about this. What I did manage, though, was to talk to some great people and get some more general advice about what some experts  have done when they were stuck or looking for inspiration. And of course, since being good at math means being good at this kind of struggle, they had really good suggestions.

I asked Bjorn Poonen, Clause Shannon Professor of Mathematics at MIT, if he had a good story about being stuck in research. After thinking a bit, he said that he had often been stuck but that there wasn’t really a good story.  He said, “At one point I was stuck for a year, and that was pretty much the story—I was stuck.” Bjorn says that when he has no good ideas to move forward on a problem, he finds it helpful to explain the problem to someone else, “not necessarily to get their advice, but just because the process of explaining it forces me to rethink it.”

Irene Bouw

Irene Bouw, Professor of Mathematics at Ulm University, had an immediate answer to my question of what she does when she is stalled on a problem: “Just leave it for a bit–that is the best thing.  After you have left it alone for some time, you have to go back over it from the start and check every single detail.” Irene is a realist about the situation, though, in a way that perhaps those looking back at the comparative wealth of time of graduate school can relate to. “There is no recipe that always works. Also, this method worked better when I was a PhD student and I had more time. I don’t have time to be stuck anymore. Now, maybe I come back to it, and I decide it is not so interesting, and leave it. Of course, this is more possible when you have tenure, and maybe you have more problems than you have time to work on.”  She gets to one of the hardest questions for a pre-tenure person—still there is no time, but there is great pressure to produce results. When should you push through on something that is less interesting to you now, for the sake of salvaging a publication, and when you should just cut your losses and move on?

Everett Howe

Everett Howe confirms that he, too, has been stuck, and in particular has sometimes felt stalled by a lack of inspiration.  He said that he has found that going to a conference and just talking to people about their problems has actually been a good way to find direction.  “When a friend or someone that I meet at a conference asks me something that they would like to know for their own research, and I have some ideas on how to answer, it gives me the incentive to work on their question. The personal connection provides the motivation.” I found it really interesting to hear Everett elucidate one of the ways that generally meeting people and building friendships within math, and particularly going to conferences, can be so worthwhile—these things can open up a whole new world of questions to care about, and maybe you actually know how to solve some of them!

Thank you very much to everyone who talked with me at the conference, and especially to James, Bjorn, Irene, and Everett.  Your thoughts on research setbacks? Conferences in the south of France?  Please share in the comments.


I should mention here that I was thinking about some of the ideas in this post weeks ago.  In an earlier comment thread, I asked Joseph Silverman some questions about his math life and how he dealt with being stuck in his research.  Just in case someone out there doesn’t read all the comments on every PhD + Epsilon post, I’ll share an excerpt here:

Me: “What do you do when you are stuck, and you may not know anyone who is interested in your problem? Is it strange to cold-call an expert, or to impose on your advisor? If you ask an expert for advice, is it your responsibility to add them to the project? ”

JS: “There are lots of strategies when stuck. Try to work out an example or a special case. Try to find a counterexample (which often leads to a proof). Try to read something that seems relevant to your problem. Talking to your advisor is fine. Put the problem aside and work on something else for a month or two. Cold-emailing an expert probably should be saved as a last resort, but talking to experts at conferences is a good idea. (Then, when you email them, they know who you are.) If there’s a specific fact you want to know, MathOverflow is good, but before posting, write out your question locally,read and re-read, wait a day or two, re-read again, then post. Also first search MO to see if your question has already been asked and answered. It’s amazing how much stuff is there.

“Generally, if anyone offers you advice, you should acknowledge that advice in the acknowledgements of the paper. But it has to be pretty substantial before you ask someone to be a co-author. There’s no hard and fast rule.”

Thanks again to Joe for taking the time to read the blog and answer my many, many questions!

Postscript: A few more thoughts from an expert

James Hirschfeld

I had such a good time taking with James Hirschfeld about his mathematical life that I wanted to share a little more of our conversation here. I asked him a few questions about how things had changed in mathematics, his early career, and how he found problems.  For your enjoyment, here is a sampling of things that that I found particularly interesting from his answers:

“Considering my career, I always remember that in my early career I was particularly fortunate: in the mid 1960s, if you had a PhD you could get a job anywhere.  There was a great post-war expansion of the university system.  So, I know that my experience is extremely different than it is today.

“But when I think back to the start of my research career, my MSc supervisor suggested a very particular problem—working on the double six theorem over the field with four elements. When I moved on to a PhD program, my supervisor didn’t suggest a new problem; he said just continue your previous work, with the double-six over larger finite fields. I did this, and of course it’s very nice to have a specific problem to work on.  The fault with this is that there is a larger context to consider. What I should have done is more wider reading.  Algebraic geometry has been through so many phases.  After the classical stuff, there was Andre Weil doing it more abstractly, then Grothendieck even more abstractly.  As a PhD student, it’s good to have a particular problem and get somewhere with it, but it’s important to acquire this broader knowledge, rather than just doing some calculation.

“And how do mathematical problems arise, anyway? Of course, there are a very few people who are doing something truly original. Otherwise there are two ways. You can generalize something or connect to similar problems. But equally well, we get problems from other subjects.  Physics or social sciences or biology. And there is an interconnectedness to look for within the fields: In my area of finite geometry, for example, it was the 1980s before geometers and coding theorists realized that they were working on the same problems.”

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MAA Section Meetings

Hood College has been heavily involved in the MAA for years and years, and our whole department always attends – and sometimes runs chunks of – the section meetings. Thanks to Project NExT I’d at least heard a bit about what the MAA does, but I didn’t really know much about how the meetings went. So in case you – like me – thought of these meetings as primarily for undergraduate students, I wanted to take you on a little tour through the latest meeting I went to of the DC/MD/VA section at Frostburg State University. And I’ll hope the AMS allows a little cross-promotion.

In our section, the meetings begin on Friday afternoon with a minicourse for faculty. This spring’s workshop – entitled “How to use as much inquiry as you’re comfortable with in your calculus class” – was run by Cassie Williams of James Madison University, Amy Ksir of the US Naval Academy, and Mitch Keller at Washington and Lee. I had to miss this one due to a late class, but I’ve enjoyed past workshops on everything from how to use Magma to how to teach Euclid’s Elements in a liberal arts math course.

Laura Taalman on the ubiquity of productive failure in mathematics

After the workshop is a reception and dinner, with the after-dinner talk given by Laura Taalman from James Madison. I’d seen Laura speak on the difficulties of 3D printing at the last JMM, but this talk put a different spin on it. Her talk “FAIL: A Mathematician’s Apology” discussed the long strings of failure that every mathematician has to learn to deal with in order to ever get anywhere. Not only did Laura share some of the more impressive failures she’d encountered, she gathered letters and videos of some other famous mathematicians to share the biggest time they did something dumb. I’m sure it was comforting and supportive for the students, but I know I wasn’t the only faculty member who appreciated the sentiment as well.

Saturday is the typical conference mix of short talks by students and faculty, a student poster session, and longer plenary talks, with a lot of games and activities for the undergrads. Paul Humke of St. Olaf gave a talk called “A Voyager from the Fourth Dimension,” followed by Alissa Crans at Loyola Marymount who spoke on how to divide cake so that everyone got the same amount of cake and frosting. If only all speakers had visual aids that the audience got to eat at the end! And one of our students even took second place in the poster session.

This was my last year as a Section NExT fellow, which is a kind of mini-NExT that’s run through the sections. We meet for a workshop in the fall on topics suggested by the fellows, we sit together at meals so we can meet new people in the section, and in the spring we help with the undergraduate activities. I’ve enjoyed judging the talks and the posters, as it gives me a better sense of how to prepare my own students when they go to conferences. If you’re interested in Project NExT but aren’t able to participate for whatever reason, I strongly recommend checking out what your section has to offer.

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Talking Math Life with Ken Monks

This is the second in a series of interviews with early-career mathematicians, with the goal of providing snapshots of a range of jobs and early-career experiences.

Ken Monks, killing it on guitar when he’s not busy killing it as a math professor at Front Range Community College.  Of his job he says, “I see myself at Front Range Community College forever!  Hopefully in my old age working here, they can give me some Front Range Community Collagen.”

I met Ken Monks (who goes by Kenneth M. Monks professionally) in graduate school at Colorado State University. He was a year behind me in coursework, but was way ahead of me in general mathematical knowledge and pun-making ability. People went to Ken for help with homework, teaching questions, and general mathematical stuck-ness, and to soak up his distinctive kind-and-caustic, pun-filled banter. He is also a great cook and excellent guitar player (check out his band Mama Lenny and the Remedy), but I always assumed that research mathematics would be at the center of his work life because he is just really good at it.  However, Ken surprised me and many other people by choosing to stay on the front range of Colorado after his PhD, accepting a position at the Boulder County Campus of Front Range Community College (FRCC).

Ken comes from a mathematical family—his father Dr. Kenneth G. Monks is a Professor of Mathematics at the University of Scranton, his mother Gina Monks has a degree in math and teaches at Penn State Hazleton, his sister Dr. Maria Monks Gillespie has earned a huge number of mathematical honors and recently finished her PhD at Berkeley, and his brother Keenan Monks studied math and computer science at Harvard and is now a software engineer at Facebook.  Together they founded Prove It!, a summer math camp for talented high school students, which takes up a lot of Ken’s spring and summer energy.  He is also working on an open-source calculus textbook built around active learning techniques. It wasn’t easy to find a good time for an interview with Ken last few weeks, between the book, getting ready for the camp, and his double commencement duties: he played guitar with a jazz quartet for the ceremony, and was also the keynote speaker after being named Master Teacher for the year (here’s a video of the commencement, if you want to check out Ken’s speech at 48:11 about how Good Will Hunting is a mirror of FRCC life). I caught up with Ken recently by email to ask him some questions about his math life.  Let me just get out of the way and let Ken take over from here…

Me: Thanks for agreeing to do this!  First, I want to write a paragraph about you and your path in math.  Maybe a few stats would be helpful.

Ken: I never took stats.

Me: I should have seen that one coming. Where did you go to undergrad, what year did you graduate from CSU, and how would you describe your research there?

Ken: In middle school/high school my math was homeschooled by my dad.  Undergrad was at University of Scranton where my dad taught. My mom and I went through the math BS pretty much together there (took Discrete, Algebra, Complex Analysis, etc. together).  Scranton is a small Jesuit four-year liberal arts school.  Graduated in 2006, moved to CSU and got my Masters in 2008 then PhD in 2012.  My research was in combinatorics/group theory since my advisor was Alexander Hulpke. Tim Penttila also put in an unbelievably generous amount of time mentoring me.

My research in my Masters was just to compute the Möbius number of the subgroup lattice of S12 (symmetric group on 12 points).  Möbius numbers in essence are just the “plus and minus ones” that you use on subsets of a set when you do Principle of Inclusion/Exclusion, except generalized to substructures of any structure.  There was lots of Richard Stanley-esque combinatorial trickery and lots of group theory that played together in really nice ways.  My PhD was a continuation of this thread, further studying Möbius numbers of symmetric groups.

Me: Tell me about your job.

I teach a few classes per semester, usually one or two sections of Calculus 2, a section of either Calculus 3 of DiffEq/Linear, and some mix of a section or two of Math for Liberal Arts or College Algebra.  I do a lot of college service in the form of committees within our campus, college, and the Colorado Community College System.  I also run a student Putnam Club where students can train to take the Putnam.  I have a lot of freedom to run Independent Studies whenever a student is interested.

Me: Can you tell us a bit about the choice you made to teach at a community college instead of looking for a research career?

Ken: Ha!  Ok that’s an interesting question. Yeah, because I did have an option.  I got a job offer at University of Wyoming and I turned it down to take the Front Range Boulder gig.  Location was one factor… I was living in Fort Collins, didn’t want to leave, and Longmont is way easier of a drive than Laramie, especially in the winter.  But that wasn’t the only reason.  I LOVED the fact that at the community college there was really no attitude there whatsoever regarding academic chest-pounding or totem-pole climbing or status or prestige or anything like that.  The only thing anybody cared about is student success.   If someone with minimal resources or external support walks in the door and says “I’d like to improve my position in life,” we are all obsessed with how do we collectively help them do that.  There is a ton of interaction at every level, constant conversations, initiatives, and innovation involving faculty, adjuncts, advisors, deans, VPs, and our president Andy Dorsey himself.  This collaborative caring and nurturing aspect of it was extremely appealing to me.  You get to see it first-hand.  We take tons of fast-food employees and help them become nurses, machinists, etc., and enormously improve their lives for themselves and often for their families.  We also take students who are not quite ready to jump into an academic program at a place like CU Boulder and give them an inexpensive first two years with a big sense of community.  They choose us sometimes for financial reasons, sometimes for social reasons, sometimes for reasons involving childcare or location.  A lot of times that option to do the first two years with us makes the difference between someone pursuing a four-year degree or not.  So, we have a mix of quick two-year degrees to get people in the workforce in skilled jobs, and then students looking to transfer to a four-year school.

I love this mission because it seems very selfless and very genuine.  It is super rewarding!  I feel like I make a huge difference by being there and being warm, comforting, accessible, and providing excellence and expertise in a place where it is needed.  Geography might have been the single biggest reason I tried the job out in the first place, but the values and mission of the institution are why I’ve stayed rather than search for a position at a four-year school.  I haven’t even visited MathJobs once since going to FRCC BCC, and it is sure going to stay that way.  Unless something drastically changes, I see myself at Front Range Community College forever.

Me:  Wow. Awesome. Besides all that, what’s the best part of your job so far?

Ken: I think my biggest accomplishment has been getting three students to get positive scores on the Putnam.  Being that they’re two-year college students, and the fact that frequently even junior and senior level math majors at four year institutions get zeros on the Putnam, I was very proud of them and very pleased with this.

The best part of my work environment is how supportive administration has been.  Basically, if you have any idea that genuinely will impact student success, they have your back all the way.  My department chair the last five years, Christy Gomez, was a fantastic mentor.  Our president Andy Dorsey was very supportive and offered me an Innovation Grant when I pitched the idea of writing an Open Educational Resources Calculus textbook designed for Front Range (emphasizing our competencies and Active Learning/Learning Assistant use in the classroom).

Me: What are some big issues or challenges in your math life/career?

Ken: I think the biggest is just managing my own time.  I tend to want to take on so many cool projects at FRCC that I can spread myself too thin or get super sick because I haven’t been sleeping enough!  Fortunately, my fiancé Faith Mata is good at making me actually sit down and go to sleep when she can see that I look a little worn thin.  I’m also lucky that she’s a spectacular personal
trainer, so she keeps me from getting hunchy mathematician posture from too much typing and grading

Me: Have you realized anything surprising in the last few years of your math career?

Ken: Yes, the biggest surprise for me is how ineffective of a teaching method traditional lecture is. I always loved lecture-based classrooms and had no problems learning from it, but eventually I had to be honest with myself that I had a very unusual and fortunate background, being homeschooled by my math professor father in math. So, I had to trust the volumes of research out there that unanimously show that Active Learning is so much more effective and just let go of my beloved lectures! I still lecture a little of course on some topics here and there.  But by and large my courses have been redesigned to reflect that best practice.

Me: Any other questions I should have asked you? If so, what are they and what are the answers?

Ken: Hmmm, yes!  Maybe if you were going to ask me what makes my classes special or unusual, I’d say that I include a lot of math history in my classes, even when it’s not a history of math course.  My students always comment that they love the context it gives the material, and they never fully realized that math was not a system of rules imposed upon us by our alien captors to torture us, but rather a language invented by people to solve problems and to study for its own sake!

How does this compare with your math life?  What would you want to ask people about their math careers?  Let me know in the comments.

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