Beth Malmskog

Math etc.

Colorado in Context

A visualization of the precinct dual graph for Colorado, created for our paper by Jeanne Clelland.

My news this week: I have been working with a great team for the last couple years to study fair redistricting in Colorado, and we just posted a new paper on the arXiv!

The basic idea of ensemble analysis is to first use a computer to create millions of random valid congressional districting plans for a state. These plans are created using only the legal parameters for valid plans, with no partisan information included, so are inherently free from partisan bias. We then use real voting data, like the votes in the Secretary of State or Governor’s race, to model elections in these possible districts. We create a histogram of how many seats a given party wins under each of these districting plans, which gives a baseline of what we could expect for plans drawn without partisan bias given the human geography and real voting patterns of the state. If we have a proposed districting plan for the state, we can then see how many seats the party would get under that plan with the same voting data. If the proposed map gives an extreme outcome that gives the party many more or fewer seats than we expect from the baseline, we can identify that map as unlikely to be created without partisan bias. This can be interpreted as evidence or quantification of gerrymandering–or at the very least a sign that the proposed map gives a bad political representation of the state! This simple and powerful idea has shown up recently in many court cases and shaped public policy outside the courts.

Some cool features of this paper: we study the interaction of partisan baseline and two of the fairness criteria in Colorado law–minimizing splitting of counties, and maximizing the number of competitive districts. We also apply statistical techniques to determine the sample size necessary to achieve a desired level of empirical mixing. We are hoping to spread the word about ensemble analysis within the redistricting community and the general public here in the state, so give me a shout if you’d like to talk about this :).


Today I am on strike from mathematics, responding to the call to ShutDownSTEM and spend the day working to create a plan for and carry out anti-racist action in my life and work. My collaborators and I have cancelled all meetings.  I am not writing or reading  academic email.  Instead, I am reading and learning. I am writing to my state legislators about how a police reform bill and broader criminal justice reform are essential steps against systemic racism in our state.  I am thinking hard about how my research, teaching, and way of interacting in the mathematical and academic communities can help to dismantle institutional racism instead of perpetuating it.

Until today, I hadn’t updated my website since 2017, and I haven’t written much publicly in the last few years for lots of reasons. Writing is hard and takes a lot of time. There are other important, often marginalized voices telling their stories. I want to take the time to listen and learn from others, and to honor them. I feel rusty in writing now and it’s hard to know exactly what to say in this post.  But this is my website, which definitely qualifies as my own tiny sphere of influence, and one of the goals of #ShutDownSTEM is for each of us to take action within the spaces where we have influence. So here it goes.

I’m outraged by the killing of George Floyd, and it is devastating that so many others have been killed and hurt by police brutality, racist policing, and other forms of institutional racism and oppression. This is wrong. White privilege makes it possible for white people to avoid engaging with the reality of racism in America, but this avoidance is also deeply wrong. We need to do the work of anti-racism every day.  Saying something here, so anyone who wants to look me up on the internet must at least see this sentiment, is one tiny part of it, but there is so much more we need to do. I’m working on it, and if you are too, I want to work with you.

I am sending my love and deepest sympathy to the family of George Floyd today, and to every person who has been impacted by all of the tragedies of racism.  I’m grateful to the hundreds of thousands of people who have kept George Floyd’s name on the front pages of local papers across the country with their protests. I’m thankful to every person who has ever talked to me about anti-racism and tried to teach me how to help.  I’m angry that Black people and other people of color in America are in danger all the time, and have reason to fear those that are meant to protect us all. I am angry about the unequal opportunity and the thousand additional burdens borne by people of color in America. We should all be angry about this.

Everything Old is New Again

You know: grunge, vinyl, Twin Peaks… In particular, my old home is now my new home again.  I am back in Colorado, starting a new/old job at Colorado College.  Classes started Monday (Linear Algebra for me), so of course it’s a little crazy right now.  But in a good way.

So many good parts of being here: love my new/old colleagues and students at CC, love the giant mountain, love having many of the most important people in my life a whole lot closer.  I am also sad; I miss Philadelphia, my students and colleagues at Villanova, and some of my other most important people, who are now much too far away.

Other news: In teaching news, this spring Katie Haymaker and I co-taught a Core Mathematics course at Graterford Prison.  It was an intensely positive experience, and I wrote a bit about it on the PhD+Epsilon blog.  I also had really good Algebra and Number Theory classes this spring.

Research projects are moving along.  Functions for solving the S-unit equation over general number fields have been submitted to SageTrac and are almost ready to be incorporated into Sage! We still need a few documentation fixes, but the code works well and we’re close.  I have computed bounds for about 80 small degree number fields with the code, which will be available soon in a table on my Research page.

Other milestones or near milestones: The quilt problem paper, which started as a post here, seems like it’s maybe been kind of accepted.  Meaning, I submitted revisions, but haven’t heard the final OK.  A paper on a variation of the McEliece cryptosystem will soon appear in the proceedings volume of Algebraic Geometry for Cryptography and Coding Theory.  Revisions are nearly done on a paper about locally recoverable codes using fiber products of curves.  About to submit a paper with psychology department collaborators about using graph theoretic algorithms to help determine what cues people use to recognize speech sounds.  And finally, I can’t believe I’m even saying this, but part of my work on Suzuki curves could be drawing to a close.  This particular piece of the project began in 2012, but it seems like we have been working on it actually forever.  Can’t wait to let go of this very interesting but long-simmering project, so I can then go get stuck on a new problem, or a new part of this same problem.

I went to some wonderful conferences this summer, too.  So perhaps I will end here with  some pictures, of conferences and other good stuff that has happened since December:

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Chris Rasmussen, me, Christelle Vincent, Mckenzie West, Alejandra Alvarado, and Angelos Koutsianas hard at work during an ICERM working group on implementing an S-unit equation solver in Sage.



Katie Haymaker and I at the AMS Southeastern Spring Sectional at the College of Charleston. We rode a train 12 hours each way for this meeting, and it was great.


Villanova math students Amanda Brady and Shantel Silva, showing off their original proof that any 4 erasures can be recovered by a locally recoverable code with 4 disjoint recovery sets.


Great signs at the March for Science in Washington DC.  I walked a hole in my shoe that day.  


 Museum of Math in NYC with Villanova AWM Student Chapter.  We also visited Google that day!


Above Lake Louise, during the conference on Diophantine Approximation and Algebraic Curves at Banff International Research Station in July.


Our Lake Louise adventure, human side.

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Les Calanques, near Luminy, France, during the conference on Arithmetic, Geometry, Cryptography, and Coding Theory in June.


With math friends, headed back to the talks after a swim.


Field with thistle and sunflower, outskirts of Denver, July.


Bonding with the Jackalope–my favorite magical creature–at Death Valley’s Little Brother, a Jackalope-themed coffeehouse and whiskey bar in Waterloo, Ontario, during the AMMCS conference.  The special session on Computational Number Theory was great, as was the local escape room!


The view from the Math and Computer Science Department at Colorado College.  I work here again!

DC or Bust, and Other News

New paper submitted and up on the ArXiV!  All about locally recoverable codes from fiber products of curves.

Also wanted to share a couple of my recent PhD + Epsilon posts:

Join My GA Math Book Club continues the book club posts (1) and (2) on this blog!

DC or Bust is about my recent trip to Capitol Hill with the Villanova Student Chapter of the Association for Women in Mathematics and some other awesome AWM members.  Great adventure.

Got to get back to writing final exams now!  First some pictures, though:


Here’s the whole AWM delegation!


Velveteen Rabbit Syndrome

I was the kind of kid who felt really bad for neglecting any particular toy.  Maybe I should blame The Velveteen Rabbit, but I definitely thought my toys had feelings and I was very worried about hurting them.  I’m having those same feelings right now about this website.  I mean, I am old enough to know that websites don’t have feelings.  And I managed to let go of my Myspace page without any twinge of guilt.  But I have definitely been neglecting this blog in favor of PhD + Epsilon, the blog write for the American Mathematical Society.  They do pay me, after all, and those two posts pretty much scratch my blogging itch every month.  However, I did want to stop by here and at least say: check out my posts at PhD + Epsilon!

I guess I can add some more news, because there are many things that I haven’t written about there.  One exciting math thing that happened is that I was awarded an NSA Young Investigator grant to support some of my research for the next two years.  That is really exciting for me!  The support begins this summer and I hope get a good chunk of time to spend on some other neglected projects, a.k.a. some hard research problems.

Here are a few non-math related pictures:



30th Street Station #2: During the SEPTA Strike


30th Street Station #3: Protest, November 10, 2016


When I was growing up in Wyoming, my idea of “New Jersey” was basically “urban-suburban-industrial wasteland.”  Clearly I had no idea.  This is from the Jersey Shore back in September.


And here is a picture from my last trip back to Wyoming, which is still so dear to my heart. This is not the best picture, I admit, but I just love this truck, which is not mine (I just walk by it a lot). Maybe weirdly, looking at it now makes me homesick.


More Blog!

Yes, I totally painted that chain rule picture.  Don't everyone order their print at once.

Yes, I totally painted that chain rule picture. 

Hello from my office at Villanova!  I just rearranged to more easily get my students at the blackboard, so look out students.  After being away so much this summer, it feels great to just sit at my office and work on the syllabus for my class.  Except I’m putting off working on the syllabus for a few more minutes to write here…  But I wanted to post here to let you know about my other blog life, which is really just starting today. I just made my introductory post as part of PhD + Epsilon, the early career blog sponsored by the American Mathematical Society.  I’ll be posting there every other week about early career life.  Sara Malec will do alternate weeks.  This blog was started 5 or so years ago by Adriana Salerno, so there is already a huge back catalog of great stuff there about pre-tenure math career issues, in which some of us are of course very interested.

Home for a minute

Back in Philly now after about a month away. I was in Colorado and Wyoming mostly, with a few days up to Ontario for the Computational Number Theory session at the AMMCS-CAIMS meeting. I’m heading out for another trip in a couple days. I’ve been in Philadelphia for about two weeks since the semester ended, and I spent most of that moving from one apartment to another. In the spring and fall I traveled a lot, too; conferences and trips to visit my family and friends, (friends that are spread out all over the world now!). This is great, in a way, but I’m sad to be missing out on my still-kind-of-new home. I want to settle in and look out the same window every day for a few months straight, to find a rhythm of working and feel like I have a routine (if only so I can deviate from it sometimes). I want to practice my accordion! I am dying for what some people think is boring.

Not to say I don’t want to go on any one of these trips. I feel really lucky to have freedom in the summer, not to mention so much flexibility during my school year. And from some perspective my life fits together really well—I can go work on math in Colorado, see my family and friends, then head out for GREAT conference, constantly going from thing that I like to thing that I like. Even the actual transportation has some good points. I read a ton in the airports (twelve Patrick O’Brian books down, nine to go…) and got to take a three-day road trip back to Philadelphia with my parents.

So what is this longing to stay home? Is it just another kind of FOMO (fear of missing out has earned its own wikipedia page)? I don’t know exactly how to reconcile this with all the things I am excited about.

Instead of addressing that difficult question, how about some pictures!?

Did I mention that I learned to solve the cube this spring?!  I am still VERY SLOW.  This is what I did on the train for a while, and boy do the other people look at me strangely.  Nicely, but strangely.

Did I mention that I learned to solve the cube this spring?! I am still VERY SLOW. This is what I did on the train for a while, and boy did the other passengers look at me strangely.


Did I mention that I spend a huge amount of time on the train? Here’s my platform at Villanova, looking kind of cold and lonesome this spring.


Did I mention that I ran the Pi-K (actually a pi mile race) at Villanova this March? Here are the student organizers and a few of my competitors. I almost beat them on the home stretch!


A window in the library at UPenn. I have had a great time attending the Math Department seminars there (and even gave one, very nervously!).


Spring in Philadelphia was so damn lovely.


Ben Franklin is my hero these days. Best founding father, hands down.


Dr. Katie Haymaker and I, on our way to commencement at Villanova. It was SOOOOO HOT in those robes!


Waterloo, Ontario had a jackalope-themed coffeeshop and whiskey bar called Death Valley’s Little Brother. Did I mention it was really great? Oh wait, it was obviously great given that it was full of JACKALOPE art.


Crossing the Mississippi at St. Louis on my road trip back to Philadelphia with my mom and dad. Yes, those are dead bugs smeared not the windshield but I actually liked the effect–almost like a sunset!


My parents at Rodin’s Gates of Hell in Philadelphia.


My craze of the summer, the Aubrey/Maturin novels.

Math Book Club: “How Not to Be Wrong”

I love book clubs, especially as an idea. I love talking about books, and watching whole new worlds open up from a different reading of the same text. However, absent a really good guide or leader, book talk can be: “I liked that book.” “Admiral Harte is sure a jerk!” “That was boring.” This is actually pretty fun; chatting lightly about shared experiences strikes me as a pretty major human need and creator of community.  I get a spark from realizing someone else heard the same song on the radio as I did, let alone experienced something as lengthy and sometimes heavy as reading the same book. The problem is exactly that, though: some books have a lot in them, and it’s frustrating to stay on the surface of something that feels very substantial. But who knows where to even start? Hence the need for awesome English professors. Plus in some book clubs, coolness prevails in that it is somehow a little shameful to talk about meaning in public. Even though you’re in book club, ostensibly to talk about the book, saying anything heavy is just slightly in bad taste, pretentious, oversharing. Why is it so weird to talk about meaning?!? Maybe because it’s hard, and so we find ourselves saying things that aren’t quite what we want to say. Which is kind of embarrassing. Or maybe we are all kind of insecure and afraid we didn’t really get it. I am in awe of how really good literature teachers can work a discussion, both in providing ways to look at a text and in overcoming all of this social crap that we put in the way of talking about meaning. Anyway, my experience in book clubs has been that people talk for a few about characters they liked and didn’t, and then everybody has some wine and book club becomes essentially planned social drinking! Which is always cool with me. Sign me up for book club.

However, I don’t have one now, and I have been reading a lot of mathy books lately. If it’s hard to find a great book club, how about a great book club that wants to talk about math? So, I guess that’s one reason to have a blog—it can be your pretend math book club! Perhaps we should all pour a glass of wine. Okay, all set on this end. This week we are (um, I am) discussing Jordan Ellenberg’s recent book How Not to Be Wrong.

Some of my recent math reads.  Wine not included in photo.

Some of my recent math reads. Wine not included in photo.

First, the quick and surface pre-wine book club version of my thoughts: “Super awesome book! Math is cool! Jordan Ellenberg is freaking smart.” Okay, now in case you didn’t read the book, (also a hazard of book club), HNTBW is sort of like a tour of great mathematical ideas (subtitle: The Power of Mathematical Thinking). It goes everywhere. Like, scatterplots, the Baltimore stockbroker con, philosophy in mathematics and statistics, error correcting codes, game theory, perspective, voting paradoxes. Picture a book that picks up where Darrell Huff’s How to Lie with Statistics left off and then tours through the country of Burger and Starbird’s The Heart of Mathematics, with the historical color of E.T. Bell’s Men of Mathematics, but with the advantage that the history (I’m pretty sure) is all real. Ellenberg sketches out ideas and stories that are essential to modern scientific thinking. The anecdotes and examples are contemporary, bizarre, funny, and very relevant

The most important thing I learned: statistical significance is shady, shady business. Statistics is how we make sense out of data, so statistics lies at the base of all science.  I think of myself as a logical thinker, a scientist, and I like to use scientific studies to help me make decisions. So how is it that I have never thought carefully about this business.  When I gleefully read  read the aforementioned How to Lie with Statistics as a kid (yeah, I was pretty nerdy), I thought I knew all the tricks and pitfalls.  So wrong.  The second section of HNTBW, entitled “Inference,” was a lesson in what p-values really mean.  If we gather some data from an experiment, and compare two quantities (like height and shoe size), we would think it likely that they could be connected if as one quantity changes, the other seems to change in a predictable way as well.  We are “allowed” to say that the quantities are correlated (the data shows a statistically significant correlation) if there is a probability (p-value) of less than 5% that we would see this relationship in the data by chance if the quantities were actually totally independent (the null hypothesis).

That sounds pretty good—if the two quantities are not correlated, there is less than a 5% chance that we would say they were statistically significantly correlated by looking at a particular data set. But I never really thought about it in this light: say we gathered data on a lot of entirely uncorrelated quantities. Out of every hundred pairs of uncorrelated quantities, five of the pairs of data sets would show statistically significant correlation entirely by chance. Of course if we gathered more new data on these the two seemingly-correlated quantities, there is only a 5% chance this false correlation would show up again. So our false correlation would very likely be debunked. But first there might be a news story about it, because positive results are exciting! And then, when another scientist could not replicate our result, there might be a follow-up piece, but then again maybe not, because negative results are boring. Their non-replication might not be published at all, even in a scientific journal. In fact, it could be that someone else had done the same study years earlier and found no correlation, which would be sort of a pre-non-replication of our study, but we would never have known because this earlier group couldn’t publish their negative results.

Now, despite the beauty and validity of the butterfly effect, I believe that most pairs of quantities in the universe are not meaningfully and predictably correlated. So I’m ready to dismiss claims (based on fMRI images of one out of many, many scanned “subjects”) that dead fish can correctly assess human emotions from photographs (Chapter 7), even though the correlation was statistically significant, based on, well, yeah. However, with complicated biological systems, how can we really apply common sense to say two things are not related? A study that finds a connection between Alzheimer’s and a particular gene is exciting, important, and not at all an implausible connection on the surface. One study finds a statistically significant correlation, and millions of people will factor that in to their decision making. The dead fish example is particularly striking given how much people will believe a story if accompanied by fMRI images.

My mind was totally blown by this previously unconsidered pitfall. Apparently people who were not blind to this have been advocating for the publication of negative results for years. It appears that the advent of open-access online journals may have finally made this possible.

The last part of this book is called “Existence.” If you had any doubts about whether Jordan Ellenberg is willing to talk about meaning, you can lay them to rest right now. I really like the final few chapters of this book. We get voting theory, slime molds and non-Euclidean geometry. And then, the question: what can we say about the truth, and about being right? Drawing on Condorcet’s paradox, that a group’s preferences for various candidates can result in unresolvably cyclical rankings, Ellenberg raises a question. If there is no one true preference of the people, what are elections doing? What can it mean when there is no one right answer, one correct winner for an election, one consistent geometry? If there is no one right answer, then what the hell is math doing? Is it searching for the truth? What if there is no right answer, or if all of the study and data tells you with great certainty that you can not be certain. What is the point of all this, anyway?

This launches a discussion of what mathematical thinking could bring to every person’s daily struggle to decide what is true, and of what it means to be a creative mathematician. He does not shy away from discussing meaning, both in the careful sense of statistical and mathematical meaning and in the more philosophical sense of questions like, why do we do these things? And, if we can choose how to think about the world, why should we think about it like that? He talks about rigorous uncertainty, the inherent contradictions we face in math and in life, the destructive idealization of genius, and how math comes from a whole community. Math is like football? You mean that in a good way? Yeah, in the team sport way (luckily not in the concussion and sweaty dude way), and this actually gave me a really warm feeling about math. Plus there is poetry, David Foster Wallace, my favorite Philadelphian Benjamin Franklin on how annoying mathematicians are, Terry Tao deflating the cult of genius… also F. Scott Fitzgerald, The Housemartins, and Captain Kirk. This could seem like showing off, or just a ham-fisted attempt to synthesize everything and force a moral into mathematics. It does not. Ellenberg really, ahem, scores a touchdown. This is the best discussion of what it means to be a mathematician, and how that relates to big questions in life that I have read. I think this is a book that we should have our first-year math majors read. Or all the first-year students—which would probably mean more math majors, for better or worse.

The problem of audience—David Foster Wallace brought this up in his essay “Rhetoric and the Math Melodrama.” What reader is this book written for? I can’t un-love math, so I of course I can’t say how this book would speak to people who don’t love math. I would guess that it is aiming for an interested but not specifically mathematical audience, and that it will speak incredibly well. Ellenberg has a great knack for being casual and conversational but never sloppy, and he starts with topics that people care about for their own sake (slipping in the cool math and the hard, unanswered questions after your interest is solid). He comes across as a hell of a guy to have in your book club. If he had time for book clubs, that is, what with a family and a billion speaking engagements and writing for the New York Times and like, proving stuff. But, hey, if he was in book club, we could look forward to more lines like this:

“The moment, early in the Italian Renaissance, at which painters understood perspective was the moment visual representation changed forever, the moment when European paintings stopped looking like your kid’s drawings on the refrigerator door (if your kid mostly drew Jesus dead on the cross) and started looking like the things they were paintings of.”

Conspiracy theories are “like the multi-drug-resistant E. coli of the information ecosystem. In a weird way you have to admire them.”

On a study finding that women were more likely to say they would vote for Mitt Romney during the most fertile part of their ovulatory cycle: “I was disappointed to find that this study has not yet spawned any conspiracy videos coming that Obama’s support of birth control coverage was aimed at suppressing women’s biological drive to vote GOP during ovulation.  Get on the stick, conspiracy video producers!”

“It’s not wrong to say that Hilbert was a genius. But it’s more right to say that what Hilbert accomplished was genius. Genius is a thing that happens, not a kind of person.”

“If I’m going to pay a college kid to superimpose dancing cutlery on all my pages, I want to know not only whether it works, but how well.”

“Here, ‘Swedishness’ refers to ‘quantity of social services and taxation,’ not to other features of Sweden such as ‘ready availability of herring in dozens of different sauces,’ a condition to which all nations should obviously aspire.”

And all good book clubs, as well.


A few of the many varieties of delicious fish that I sampled at a smorgasbord at the European Women in Mathematics summer school on Apollonian Circle packing in Stockholm last summer (2014).

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Anna Haensch and Amy Feaver, who also marveled at Sweden’s incredible wealth of smoked fish.

And did I mention we saw James Blunt in Sweden?

And did I mention we saw James Blunt in Sweden?

Both Math and Not

I’m pretty much in a constant, random walk-type state of reading Both Flesh and Not, the collection of essays by David Foster Wallace. As has become a pattern for me with hip things that turn out to be truly amazing, I’m somewhat late to the party.[i]

The problem with taking this long to catch on to David Foster Wallace (he died in 2008, Infinite Jest came out in 1996) is that I missed out on those years of having his voice in the mix inside my head. His work is so goddamned smart, funny, sad, and ultimately generous, and has lately taken such a space in my mind and heart, that I feel I must hurry up and tell everyone about it so they don’t miss out too. I’m trying to hold my evangelism back in daily life, because I don’t think anyone wants to hear about it. I mean, I read a lot and like to hear about books, but there are only a few people in my life from whom I enjoy unsolicited book tirades.

But that’s one of the good reasons to have a blog. It’s all about just saying what I want!  Nobody has invested anything in this piece, or is obligated to read about it any longer than they want to.  But then, would anybody read this unless they already knew? Or would the reader just glaze over and click on something else? Who would actually read this blog entry about David Foster Wallace and (as you can guess) math unless they were already pretty into either DFW[ii] and math, and probably a friend of mine as well (or my mother—she reads these things too, hi Mom!)? So am I not writing only for an audience that either doesn’t care, or one that not only knows everything I am going to tell them but will probably think I am mangling something that is legitimately beautiful and very close to their heart? This kind of writing has an audience problem.

This dilemma of audience is the crux of the problem of fiction about math, as DFW points out in “Rhetoric and the Math Melodrama” which originally appeared in Science in 2000. “Rhetoric and the Math Melodrama” takes a critical look at two math novels of twenty-ish years ago: Uncle Petros and Goldbach’s Conjecture by Apostolis Doxiadis (1992) and The Wild Numbers by Philibert Schogt (2000). Critical in both senses, one pleasure of this essay is sort of like as a really good bad movie review. Plus DFW can be totally hilarious.  Though he doesn’t actually pan Uncle Petros in the end, he does let us savor some weak points. Reaching beyond these two books, DFW takes what he calls the “Math Melodrama”.

Math Melodrama is the pop culture trope of mathematician as “a kind of Prometheus-Icarus figure whose high-altitude genius is also hubris and Fatal Flaw.” At the time of his writing, Good Will Hunting and Pi were still pretty fresh at the video store and the movie version of A Beautiful Mind (2001) would soon appear in the theatres (and then a year later in the VCRs of May classrooms of AP calculus classes across the country). Math was granted laurels as a creative endeavor, and with that came the trage-glamourization (totally made up that word) of mathematicians.

This Melodrama is nothing new for musicians and writers.  The title character of the movie Frank is an eccentric, creative, driven musician who wears a giant fake head all the time. He is talented, exciting, charismatic. The other characters variously value him, envy him, want to be like him, and push him to realize their own ambitions. This is all fun in the beginning but darkens, culminating in an Icarus moment at South by Southwest.  Sounds like Music Melodrama in action, but it’s not Frank who has the Fatal Flaw. It’s the main character, the musically limited but driven keyboard player, Jon, who ignores Frank’s obvious deterioration and in his quest for recognition and winds up humiliated. Frank isn’t in great shape at this point and retreats to his parents’ home. When Jon tracks him down there, he is trying to understand what went wrong in Frank’s life, what terrible event was the key to Frank’s genius and suffering. Frank’s parents offer maybe our one bit of insight into Frank, and something that helps take this film past the easiest answers. Frank’s dad: “Nothing happened to him. He’s got a mental illness.” “The torment didn’t make the music,” his Mom says. “He was always musical; if anything it slowed him down.“ This conclusion asks us to reject the notion of talent or genius linked to insanity, viewing the two as independent.

The two books DFW reviews are similar to Frank in that their main characters are not the undeniable geniuses of the world. These books are not about Ramanujan or Gauss or Archimedes. They are about people who do pretty well but who want desperately to be the best; people who want to win the prize of outside acknowledgement and inner peace that they think will come with solving an officially hard problem or a triumph at South by Southwest. And in all cases this doesn’t work out, because they don’t win. Which makes for decent and worthwhile stories in the case of Frank and Uncle Petros (I haven’t read Wild Numbers), but I am also interested in the case of what happens when people do win. This is one of the plot points not totally at the center of the Melodrama, but is essentially the other half of the same story. Are these people unhappy because they reached too far and failed? Does failure make people miserable? Does ambition make people miserable? Does talent make people happy? Does success make people happy?

There are plenty of places where this is taken on (we could work on this through Frank, for example) but this very gnarly dilemma is touched beautifully in DFW’s Infinite Jest, as the main character Hal contemplates own position in light of his wildly and broadly successful father and his disappointed and embittered grandfather: “Have a father whose own father lost what was there. Have a father who lived up to his own promise and then found thing after thing to meet and surpass the expectations of his promise in, and didn’t seem just a whole hell of a lot happier or tighter wrapped than is own failed father, leaving you yourself in a kind of feral and flux-ridden state with respect to talent.”  This is not the thing that the ambitious characters in the melodrama are thinking about, but it is worth thinking about.

My own thoughts on this problem drift back to the lives of both David Foster Wallace and Jack Kerouac. These were two writers who won. Who succeeded artistically and professionally and had everything any daydreaming writer could hope for.  However, I assume that by the ends of their lives, David Foster Wallace and Jack Kerouac were not happy.  Reading Big Sur hurts because Kerouac has laid it out for us, how winning does not necessarily feel how we think it will feel, or doesn’t feel that way for all that long. Reading “This is Water” hurts too, because it is about the way we are tragically complicit in our own suffering, but also about how we can find at least a little relief. It addresses truth and meaning in life and seems to give a few answers, but when read in the knowledge of David Foster Wallace’s later suicide it can seem like a manual for a hopeless and futile struggle.  I have no idea why DFW killed himself or why Jack Kerouac could not stop drinking.  We could assume that the force that made these two people intensely creative was the same force that drove them to desperation.  However, I have to believe that these are independent.  Everybody struggles in life, but some people are almost randomly struck with depression, mental illness, vulnerability to alcoholism.  Everybody is good at something, and some people are great because they work super hard and/or have talent, and some people are almost randomly struck with exceptional creative vision or intelligence and the drive to pursue it.  Some people are struck with both the creativity and the despair.

This is oversimplified, I know, and I feel like the relationship between ambition, success, and happiness is much more complicated than this.  But these stories remind me in a very concrete way that winning, or getting what I want, would probably not solve my problems or be the key to lasting happiness.  Which is a good thought to have on hand as a mathematician, because I very frequently do not get what I want.  My method fails, my paper is rejected, my students stare blankly at me, my grant application is denied, and on and on and on.  There’s no way I could keep doing this if I had to win to enjoy it.

I’ve gotten away from “Rhetoric and the Math Melodrama” here. The essay says a lot that I won’t re-say, but I do want to go back for just a moment to the problem of audience. The thing about math and mathematicians in novels that a little bit of technical sounding gibberish can lend a mathy feeling which is a legitimate spice for a story. Science fiction math gibberish often serves a real narrative purpose. And if it works there, that means there’s no ironclad rule against math gibberish in a good story, so maybe it could work anywhere. The problem is, though, if math is really central to the plot, there’s going to be this problem of audience. The people who see math as a draw are probably going to know enough math that nonsense or oversimplification is really annoying. But if the story is full of real math, it’s going to lose non-mathematicians pretty quickly unless its also super compelling otherwise.

The movies mentioned above didn’t have any trouble finding an audience—they were good enough or formulaic enough beneath the mathy surface that people liked them. And maybe people liked thinking a little bit in the few places where the math glinted though. But who will actually sit down and read a novel involving math, with all the extra time that reading a book involves? Someone who loves novels, someone who loves math, or, most likely, someone who loves both. Which means your novel better to a really good in at least one of two ways—as a novel (usually a story about people) with math providing some color, or as a study of real mathematics (a story about mathematical ideas) with people providing some color. Or else it’ll be doomed to reach only an unsatisfied audience of people who love both math and novels, and are desperate enough to try about anything to get both in one go, and are very often disappointed by their endeavors. That is totally me.

Writing well about mathematics (fiction or nonfiction) is just ridiculously hard to do well, but there are so many beautiful ideas in mathematics that people just want SO BAD to get them across. So people keep writing about math, and I keep reading it, but only a few writers can really reach beyond the small intersection audience of people who just love to read and who already know a pretty fair amount of math.[iii] Even fewer can use math in a story about people and create something magical, transcendently wonderful writing that talks real math but is so great either you understand the math or, if you don’t, the math becomes like so many of the Spanish passages in Cormac McCarthy’s books—meaningful even in obscurity. It’s a language you don’t speak but it still speaks to you and puts you in the place and mood of the story.[iv]

“Rhetoric and the Math Melodrama” is not about math, exactly, but it is an outstanding piece of writing about writing about math. As a piece of criticism it succeeds beautifully in reaching beyond its raw material, to speak about issues meaningful to people who haven’t read the books and probably don’t even care about math. Regarding Both Flesh and Not, I’m probably the odd one that came for the math narrative criticism and stayed for the prose poems and Roger Federer (not to mention buying a ticket for Infinite Jest) but I’m damn glad I came for something. David Foster Wallace is an Astonishingly Good Writer.

[i] Please enjoy or at least forgive the tribute footnotes. My first favorite footnotes in fiction were Manuel Puig’s in Kiss of the Spider Woman, but David Foster Wallace makes footnotes seem indispensible, like how could anybody write a focused but interesting and layered and natural piece without them? But anyway, another example is Wilco. I mean, it’s been years since loving Wilco was really hip or edgy, but there was a time! And I was behind it. Throwing hipness out the window, that was actually great, like discovering some incredible TV show and finding 4 seasons of it waiting for you on Netflix. Or realizing that there are

[ii] Please forgive the tribute abbreviation of David Foster Wallace as DFW. By the way, I learned recently that these are not acronyms unless they are pronounced as words in their own right. So like STEM is an acronym but DFW if probably not.

[iii] My first favorites in this were Journey Through Genius by William Dunham and The Code Book by Simon Singh. But my favorite right now, which I will write about soon if I get time, is Jordan Ellenberg’s newish book How Not to Be Wrong.

[iv] . What writer can do this for math? Maybe DFW in Infinite Jest? I loved that book but I need to give it a second read to think more about how the math in it works. Everything and More (a book about infinity, and of course more) would also be a natural place to look, but needs another look, too, because I didn’t finish it. My whole fascination with DFW started a few years ago when I randomly read his Kenyon College commencement speech (adapted into the essay This is Water), and I started Everything and More expecting something like the speech and was disappointed. Here was this Great Writer writing about math so I ought to love it but it left me cold. I remember that I was just pummeled flat by the number of words the man could put in a sentence. He seemed to be using way too many words to say things, things that were hard but even harder when he put it that way. That’s honestly what I thought (though I feel funny saying that now because I was completely won over by Both Flesh and Not and Infinite Jest so I figure I must have been mistaken about Everything and More). In the essay, DFW also points to some (he thinks well done) math-heavy narratives I haven’t read—Ratner’s Star by Don DeLillo will be on my next library list, and of course Gravity’s Rainbow.

My favorite math joke and other random notes.

My favorite math joke is:

Three logicians walk into a bar.  The bartender says, “Do you all want a drink?”

The first logician says, “I don’t know.”

The second logician says, “I don’t know.”

The third logician says, “Yes.”

My WIN3 project group, April 2014: Me, Wei Ho, Renate Scheider, Christelle Vincent, Padmavathi Srinivasan, and Irene Bouw, our fearless leader.

My WIN3 project group, April 2014: Me, Wei Ho, Renate Scheider, Christelle Vincent, Padmavathi Srinivasan, and Irene Bouw, our fearless leader.

Our Women in Numbers 3 project group recently submitted a paper!  

Yay! Philly’s theatre scene has math and physics fever, with productions of Arcadia, Proof, and QED this fall.

William Penn, my friend!

William Penn, my friend!