Monday, August 27, 2012


My last post tried to draw your attention to the beautiful writing of Bill Thurston on what mathematics is and what mathematicians do. Near the beginning of section one of his paper on the arXiv, he asks,
It would not be good to start, for example, with the question 
How do mathematicians prove theorems?
The question is not even
How do mathematicians make progress in mathematics?
Rather, as a more explicit (and leading) form of the question, I prefer
How do mathematicians advance human understanding of mathematics?
What an amazing perspective!

Research and teaching We've all heard about some purported level of disrespect researchers have toward mere teachers and expositors. Some make it explicit; G.H. Hardy said "Exposition, criticism, appreciation, is work for second-rate minds. [...] It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done." This attitude is not useful for the advance of human understanding of mathematics.

I'm learning about myself: I want to spend my time creating mathematics, if I'm honest, and then communicating it. But the work of appreciating and communicating mathematics is crucial to our collective mathematical future. We need fans and enthusiasm and the idea that we don't is just the self-justification of a nerd whom no one likes reassuring himself that it's ok that no one like him. 

Teaching and teaching All is not well, though, in the rosy land of lovey-dovey liberal arts teachers and expositors. With the glut of PhDs on the market, schools can demand ever more "research" from their excellent teachers without changing service demands. Why not? Now even the schools that respect teaching the most are putting research on the agenda, whether it be with undergrads or other professional mathematicians. In addition, the job market is ridiculous. Ridiculous! A SLAC can say they're looking for a representation theorist with statistics teaching experience and they can find exactly that -- the geometric representation theorist with statistics teaching experience will be out of luck -- and why not? It is, after all, every school's responsibility to choose the best person for their department. This is moral and right. What is not right is telling the geometric representation theorist they are not qualified to teach representation theory, or telling the person with phenomenal teaching evaluations and three years post-graduate teaching experience at two schools that they just don't have enough experience, or any number of similar things I've seen. Be honest. It's luck and it's a buyer's market. As it is, we on the market feel incredibly disrespected. Fine, it may be a blessing in disguise; the friend who was told he wasn't qualified to teach freshman stats got hired to do statistics for a large insurance company for three times the salary and the friend who was told she wasn't qualified to teach financial math got hired by a finance company to do financial math for twice the salary. They've got very nice financial packages and  far more geographic freedom than academia affords. Maybe I too will leave and do the things I'm not qualified to do for much more money. But it leaves a bad taste in the mouth to have one's strengths and accomplishments belittled as they sometimes are in the job search. Once again, it's the faculty member on the hiring committee coming up for some justification for why things are as they are to make themselves feel better. It's simply not true. 

Economic rewards Our current academic system is, like all systems, primarily interested in maintaining the status quo. Times are changing, though, and the status quo involves economic incentives that will no longer serve us well. Don't defend it: think about. We still reward incredible specialization and high paper counts. We still reward a certain slipshod approach to teaching at some R1 universities. We still reward behaviors that lead to burnout at some SLACs, and we're changing incentives there to reward even more unsustainable patterns. We reward a system that uses people up and throws them out rather than cultivating talent or helping people prepare for jobs in industry and government from the beginning if that's what they want. The disrespect involved in all these relationships and transactions does not advance human understanding of mathematics.

Saturday, August 25, 2012

Endings as well as beginnings

I'll just point you to this: Bill Thurston passed away. I have not read much of his writing although I've heard a lot about his work. I'd particularly like to draw your attention to his note on Math Overflow and his arXiv note "On proof and progress in mathematics." I read this note for the first time this morning. His remarkable humanist approach to mathematics makes me feel better: sometimes the reward structures in mathematics -- for cultural and for economic reasons -- make me feel that perhaps I ought to just do something else. (More on that in the next post.) Thurston's inclusivity, broad view, and honesty about his experiences come through in these two notes and should provide a guiding ethic for our involvement in mathematics.

Monday, August 20, 2012

New Year

It's the academician's New Year in some ways. We're all afluster: classes start Wednesday, or yesterday, or the day after Labor Day, or "soon". Copies need to made. Syllabi need to be posted to Moodle. There are already students streaming through the office to make changes... "Well I signed up for calc because I thought it was like really important for like a liberal arts major to have some like experience with mathematical thinking but then I learned that modern dance conflicts with it and I realized over the summer in my internship I'm actually more interested in like dance and non-profit organizations for the arts and so I'm really sorry but could um like would you be willing to sign my um drop slip? I think I really would have enjoyed calc and I know it's like really important and I'll try to take it another semester..." Yes, I will sign your drop slip. No, you don't have to apologize.

"I'm going to visit my friend in France/Japan in October and I just wanted to let you know in advance and I'll definitely make up the homework for those days and get it in when I get back do you know what the assignment will be?" No, I don't know what the assignment will be. You will turn the homework in before departure or you will not receive credit. Pay attention to this in October.

I'm in a new place doing new things. New people. A new year. Some sort of alternate universe has opened up in front of me; I'm not at a liberal arts school this year. My plans went awry. I started this blog when I realized how truly unpredictable the future was: I'm well-qualified for certain kinds of jobs and didn't get any of them, and instead I'm playing a different role in the math community than I'd envisioned. No calculus prep and no college freshmen. Fate? Economics? Accident?

Time for bed!

Thursday, August 16, 2012


This is a response to Adriana Salerno's post about workshops on PhD + epsilon. She asks at the end, "Do you like workshops as much as I do? Have you had any great results come from a workshop? Are there any others that you can recommend to people?"

Short answers: I love workshops and summer schools!

Workshops give a great chance to really work on mathematics (or coding, if it's a Sage Days-type workshop). The AIM-style workshop Adriana mentions is one of the best. I have attended one AIM workshop and they allow so much time to really get into the math -- I am still working on problems and working off notes that were written down there. (Yes, AIM, when I finally publish the paper inspired by that problem I'll let you know and you can get some credit for it!) They are great opportunities to talk with mathematicians at a very deep level and figure out what needs to be done in your field and whether you could do it.

I think these are best, though, for people who know something about their topic and are ready to dive in. What if you want to learn about a new topic instead?

If you're a graduate student, check out MSRI Graduate Summer Schools in particular and MSRI workshops in general. The summer schools are usually two weeks long and are immersive experiences: you are completely bathed in the mathematical topic at hand. It's a good thing. The best summer schools have homework exercises that you can try to slog through over a beer or something non-alcoholic, depending on your taste; you should always try to do the math you're hearing about. I've had good experiences with all MSRI events I've attended.

The IMA also puts on various workshops, and has trended toward putting on a pure-math computer-oriented workshop each summer recently (Macaulay2 and Sage, for instance, each had a week-long workshop in recent years. IMA workshops tend to bring together people from different areas to a greater extent than AIM or MSRI workshops, it seems to me. Another place that seems to be interested in a certain level of interdisciplinarity is ICERM which looks to have some cool workshops coming up.

I do like workshops with time built in for doing math or doing exercises or discussion better than the conferences that consist mainly of an intense number of talks separated only by thin coffee breaks, but those too have their purpose.

Wednesday, August 15, 2012

Math for all

Today I was on the Greyhound bus passing over the vast heartland of America to get from one place to another relatively cheaply sans car. I sat next to a stoner named Dan who also had a lot of other drugs to sell. (People never offer me drugs, even when they're offering drugs to everyone around me. My face and manner just seem to put them off. This was even true in high school. Is it a hint of my stern and disapproving father coming out?) I was reading about tau-functions and Lax's insights re: integrable systems and Dan took an interest. He asked me, Is that, like, calculus? or is it like about primes? He started explaining to me a question he'd considered that he eventually told me was like the Mobius strip of primes; he also told me his stepsister did math and she'd taken refuge in an insane asylum, using the true sense of asylum -- she needed a break from thinking, you know, thoughts, and numbers, and pressure. I told him I was aware of the danger: history provides us with so many mad mathematician examples. I did not reassure him I was safe.

Dan really likes math: he told me he was into it and either that or linguistics is a field he'd really like to return to. I'm afraid his addictions are too strong to allow that, but one never knows. I've had other conversations like this. At a vegetarian/vegan/punk rock breakfast place I once ended up working through triangulations and Euler's number with another homeless guy who might have been a Wobbly organizer. Part of this is my nature: I am small and nonthreatening and talk with homeless guys now and then, and I'll talk about math with anyone (to a point, and that point does include consideration of personal safety). Now, Dan was into kabbalah and numerology as well as primes and calculus and mobius strips, but he did have an attitude that was refreshingly interested (and he told me several times he wasn't trying to date me and I believed him).

So how could I get that whole Greyhound bus into mathematics for fun? Is is possible?

Tuesday, August 14, 2012

Post college mathematics

Here's something to ponder:

In sports, it can be hard for people to participate in a sport if they're not in the elementary-to-college sports pipeline. Many sports have recognized this and formed recreational clubs: there are running clubs, Ultimate Frisbee leagues, bike groups, master's swim groups. These groups are vital because they contribute to peoples' quality of life in terms of fitness and social contact, and because they provide a community of supporters for the young and the elite in the sport. Community clubs sponsor scholarships for talented participants, provide coaches and staff races or other competitive events, provide economic support to the businesses that sell equipment or training. An enthusiastic community of amateurs helps lift the quality of the entire sport. Sports that don't have this community involvement have trouble succeeding in some aspects above. In the US, for instance, there is not to my knowledge a javelin-throwing and shotput-tossing community on the level of, say, Ultimate Frisbee or soccer. Other countries give a lot more opportunities for track and field and so they are more successful on an Olympic level in javelin and shotput, among other things.

Translate to mathematics. How do we involve and engage adults in mathematics? We have math circles or math team for kids and students. We have math majors for college students, and Pi Mu Epsilon and the Putnam. What about the 30-year-old who likes math but never was a math major or didn't even go to college? What about the 55-year-old who really likes solving certain kinds of puzzles or playing logic games but didn't see math as an option when she went to college and kind of wishes she'd learned more? How can people out of school be engaged in mathematics on a recreational level?

Even more audacious, how can people not in school or academia be engaged in math on a research level, even a small one? A friend commented to me recently that she could not begin to imagine my world and what I do on a daily basis -- she just has no idea what the process of math research feels like, looks like, is like. Maybe that will begin changing as people who have done REUs graduate and go into professional life. That doesn't help the people I mentioned above.

I know people who read all of Brian Greene's books and feel like they get an idea of what goes on in modern physics. They are fans of physics: they support it, are interested in what people do with it, read about the Higgs boson, support physics funding by government entities, staff the physics club at the local high school. They are the community boosters for physics. I have not met as many people who feel that way about math. I feel like there aren't as many math books that allow that "in," with some notable exceptions. How could we open up the world of math research to nonprofessionals to a tiny degree so that we, too, could have a community support network for mathematics?

Wednesday, August 8, 2012


Not quite a math post, but related. This summer I've traveled to three continents, attending conferences geared toward pure researchers, math educators and expositors, and mathematicians interested in using computers to advance their research. I have racked up a fair number of frequent flier miles (which I have decided I love). I have spent time away from my family and friends in foreign cultures and familiar cultures. I'm moving to a new position this fall and am preparing for that. In my travels I've spent a lot of time thinking about what shoes to bring and how to build a capsule wardrobe appropriate to the destination. Now I should think about that for the next year!

I've entered a phase of trimming: I have bags of clothes to give to charity and have thrown away many things that I usually hold on to because I'm thrifty and a bit of a packrat. Moving certainly discourages accumulation of stuff.

At the conferences I went to people greeted each other like old friends. Wait, they are old friends. Maybe they only meet up once a year in Madrid or Madison, but if they stay in the mathematical community they may meet up through marriages, divorces, births, deaths, and of course many moves. Mathematics and the mathematical community provide a certain stability. We move for college, grad school, postdocs, professorships, sabbaticals -- I don't think my undergraduate students or "lay people" understand the mobility that is almost required by academic mathematics. (I say almost required because a lucky few stay in one place forever if that's what they want, but if that's what you want you can't be too picky and you may have to sacrifice a lot.)

But you sacrifice a lot either way. I'm moving away from family because I want to try something a bit different and figure out what my place (if any) in academic mathematics could be. What I've tried doesn't fit, and I have the choice of changing myself to fit into an uncomfortable job or uncomfortably following opportunities that may fit better. Sometimes I wonder why I do this. What does it matter? Why should I have any ambition?

In any case, I'm packing.

Monday, August 6, 2012

Math talks: standing or understanding?

From last week:

I'm at a large math conference; the travel disrupted my internet access this week. Many of the talks are good in that they are understandable to a majority of the audience: audience members learn something mathematical from the talk. Some of the talks are not so understandable. Sometimes in mathematics we give people a free pass on understandability because we think they are brilliant. (This is actually coming up strongly as I attempt to work through an elementary example in a paper I'm reading: authors, I know you're brilliant, but could you define your notation and not leave all the hard work to the reader? If I could do that work I would have written your paper. Seriously.)

So, in your heart of hearts, would you rather listen to a talk at a conference that is understandable or one that is not understandable but might make many people think, "He must be really smart... 'cause I don't understand what he's saying!"

Set out assumptions first: assume you are not a graduate student. Assume you are the target audience for the conference and talk, and are reasonably knowledgeable about the area without being a world-class expert. Do you want the understandable talk or the seemingly brilliant talk?


We all know what the answer should be to the first one; I'm mainly asking in order to check my assumptions. Second question: which speaker do you secretly or unconsciously respect more after the talks?


I have heard some folks confess that secretly if they feel dumb after a talk, they respect the speaker more.... and if they understand, they conclude that the speaker's work wasn't that hard.