School is bulls*(&

Talking recently with a young man who's had a tumultuous path through college; he's through years of classes but has years more. He wants to get out into the real world and do things. I sympathize.

School is bullsh*(. It is a useful form -- good fertilizer, one might say? -- but it should not be confused with its goal. Government was initially formed as people realized they needed to team up for self-defense, for infrastructure, for management of resources. School was formed as people realized that teaching people to read, do arithmetic, converse, and think about abstract topics made business and life run better. Now school is a stamp. A requirement. It still serves many of the purposes it was initially made to serve, but of course we've lost sight of that. That is normal.

I'm trying to pinpoint what makes me happy and what doesn't. Mathematics: the way it describes the real world makes me happy. Sand ripples in a creek, cream swirling through coffee, Moroccan mosaics, pineapples. I'm not an applied mathematician but I love that stuff. I love modeling.

School, though. Calculus. Calculus! Of course calculus was born out of a desire to describe the world -- but do we care anymore? Calculus, like school and government, now exists to perpetuate itself.

How can I teach when I feel my students would be better served by being alive, active, dynamic, questioning? (This is the only way to teach! But somehow it is so hard.) That spirit is often crushed out by the time students get to college. What can I say at the front of the classroom? Should I show Dead Poets' Society? How do I avoid the deadness that sometimes creeps through classrooms and colleges like fog coming off the ocean into San Francisco Bay?

Students, wake up. School is bullsh(&. Use it to fertilize your real dreams.

The artist's struggle

I like the idea of math and art -- symmetry, fractals, perspective, frieze patterns -- but today after a month of absence I would rather touch on math as art. I said something wrong in my NSF proposal, I realized today on a walk, and it's stupid wrong rather than profound wrong. This is incredibly depressing to me. It's not depressing that I made a mistake -- I make lots of mistakes and don't worry too much. It's depressing that it's a stupid mistake that I would hope I would not make. I worry that I can't hold in my head the things that I know. Yes, I can't even remember what I know. I haven't made my knowledge a coherent web, and so I forget that this is also that and then I say that that is a wave and can't be a particle even though if I remembered it was also this I'd remember that in 1992 McGoucher proved a subtle theorem showing that this is a particle, because I myself wrote a paper about the particle nature just three years ago.

(Fine, I'll stop.)

Anyhow. I am afraid that I am not very good at my art, the art of mathematics, because I have some idea what is good and I know that I am not producing  at that level.

What do cellists do when they listen to Yo-Yo Ma and find themselves wanting?

On good days I remember that I do this for fun, for joy, because I love playing with ideas and discovering new things (new to me, at least). On bad days I think I should find something I'm actually good at.

I call this post the artist's struggle because the only other people I hear this from are painters, poets, and musicians, people who struggle against poverty to keep doing what they love, even if they doubt that they are any good at it. In art it seems respectable to doubt your ability or talent. It's part of the path. In mathematics, I'm not sure. Plenty of well-respected people mention that they still don't think they're very smart, but we know the truth!! They are brilliant people unlike us. Evidence: stupid mistakes. The best part about math: they're provably stupid. In cello, the wrong note just floats away.

Whether or not I'm actually any good at this, I have a job lined up for the rest of the year. Guess I'll keep pretending for now.

Old & crochety: job satisfaction

I met a fresh graduate student in English a few weeks ago at an event near a large R1 that is excellent in many areas. I asked her if she was teaching and she said no, and she was very disappointed. She'd really like to get into the classroom: after all with so many bright and talented undergraduates who could ask for anything more fun?!

I tried to smile at her amazing enthusiasm. Why didn't I really smile?

I've heard from some friends who changed institutions this summer that it feels like the same job in a different office. They don't sound thrilled.

I am trying not to be old and crochety without reason. There are genuine thrills to teaching and success stories and other interesting incidents I could go on about for a while (but then I would not be anonymous!). The romantic image of molding young minds clashes so sharply with the feeling of sitting in the room doing calculus for a grade that it's painful, though, and I grimace instead of smiling. It's not unique to mathematics, and we can break through it to some extent in the classroom -- but it makes it hard to be innocently and freshly excited by the whole enterprise.

When I deal with individuals -- real people -- real students -- I feel much more interested in education and teaching. I can figure out if we're focusing on calculus, on anxiety around tests, on learning to learn. When I think about the larger topic of college teaching I get tired quickly. When I deal with many many individuals, a ceaseless stream of unique beings with their unique demands, I get tired even faster.

What allows for job satisfaction in teaching and what makes it feel like living with a nest of lampreys?

Women and research

This post says it all: "Like we didn't know this." Links there to the NPR story on bias that's been making the rounds and the PNAS story that confirms once again that if you put a woman's name on something it's automatically less competent regardless of contents. Old news, old news.


On the one hand, I don't want to talk about it. On the other hand, I would urge men who care about unconscious sexism and racism manifesting in mathematics to read the story on stereotype threat and consider it. It rings true now that I am observing my own interactions with other mathematicians, male and female, and it's brought home very strongly now that it's NSF proposal time. I can't quite believe that I have anything valuable to say and I very strongly feel the need to be absolutely correct about every statement because I feel any incorrect statement is a reason to dismiss everything I might say. These contribute to difficulty writing the thing and a stress burden that is unnecessary -- unnecessary because there's not a damn thing I can do about it and that stress only hurts me. My stomach in particular.

A saving grace is that I saw a collaborator's proposal and saw some of my ideas in print in that proposal, describing our collaboration. They sounded so valuable and interesting coming from someone else! Cognitive dissonance. A kick in the ass. Get writing.

As an early-career mathematician, it's my first NSF. I've written most of it now. It brought up another point quite strongly, which I can't disentangle from this gender stuff: I don't feel like I've ever believed I could be a research mathematician. From another angle, it feels like something I am not allowed to do. Allowed? Sure, the prohibition is some mythical nonsense other that doesn't exist, but I carry the feeling. When I go to seminars and conferences I feel like a guest with a limited-time pass that will expire, and then I will be kicked out of the club. Mathematics is a paradise I cannot stay in. I'm gonna eat that apple and that's going to be it. I keep making plans for the eventuality, in fact.

Mostly written. I feel slightly ill and slightly thrilled.

Does anyone else feel like being a research mathematician is a transgression?

Women and SLACs: internal instincts

Something I don't fully understand is the gendered nature of where people end up professionally. Small liberal arts colleges (SLACs) have a higher percentage of female mathematics faculty than big state university systems; big state university systems have a higher percentage of female mathematics faculty than R1s. There is certainly room to argue for multifactorial discrimination as a cause for women to "slide down" the prestige ladder over time -- the "gender smog" that pervades our air is, well, pervasive, and so if it affects grant funding rates and paper acceptance rates and teaching evaluations and issues of fit* it's not surprising that even if we only consider anti-child career-devoted women who succeeded in postdocs after graduating from Princeton or Berkeley the percentage at high prestige institutions is less than that of anti-child career-devoted men who succeeded in postdocs after graduating from Berkeley or Princeton. Fine. Discrimination sucks; I want to move on to a more interesting discussion from my point of view.

• I noticed at a recent discussion that involved a lot of women mathematicians that a far higher percentage were at SLACs than I would have expected at a research conference. 
• In addition, I've watched some really "famous" women mathematicians move from large state R1s to SLACs over the last five years. (Famous is in quotes because the mathematical community is small -- but they are famous to me!)
• I've watched a fair number of my own generation of early-career mathematicians try out various jobs, and seen a lot of women try SLACs due to their own interest or someone else's encouragement. Several of these efforts have really not worked out and it's taken a lot of effort for these women to get back into research-focused environments. Conversely, I've seen a few guys who really wanted SLAC or teaching-focused jobs just inexorably pushed back toward less teaching-focused schools.
• I have watched my own thoughts and emotions, and have noticed my own internal bias that says "Women more naturally fit at SLACs!" This intellectual bias, though, does not actually fit the evidence that I'm observing. It's caused me a fair bit of cognitive dissonance.

I have no empirical reason to think women mathematicians would do better at a SLAC than an R1. The teaching is hard work, the student evaluations are still statistically unfair to women, and it's a tough job that requires a lot of finesse. I have now gotten to know several women mathematicians at R1s who I can say with confidence would be total failures at many SLACs and are brilliant at what they do in terms of research and graduate students. I know there's a cultural bias that pairs women and teaching or women and caretaking or women and mentoring. What I don't understand is why I would internalize that -- I know rationally that it's not really so. I still feel an internal dissonance when I think about pursuing a research-oriented career. I have a hard time having confidence in myself when it comes to working primarily on research, even though it makes me happier than concentrating primarily on teaching. What? Why? This is so irrational. Clearly something unexamined has happened in my psyche.

Cordelia Fine discusses this in her book, "Delusions of Gender". There are a lot of reviews praising this book for its witty writing and excellent science, but it just made me really really depressed. It's talking about my life. There's a whole chapter on women in mathematics that discussed quite thoroughly why succeeding in mathematics as a woman or man makes you more sexist. We all learn unconsciously from what we see every day. Successful women in math see themselves as a minority, an ever-diminishing minority. Successful men in math see women as a minority. How can you see otherwise? It's a fact. The only place you don't see women as a total minority in mathematics is at some SLACs. Some places women are even approaching -- gasp -- 45% of the total faculty!

I have become more sexist as I've continued in mathematics. (You can test your own unconscious bias at Understanding Prejudice.) I can't help it, and it conflicts with my own interests and the truth of my own life. I anticipate that some troll could come along and tell me I'm just realizing that women are worse at (whatever), but the problem is it's not true. I am clearly, measurably better at some things that are not in the unconscious "female" box in my brain. I am clearly, measurably not cut out for some things that are in the unconscious "female" box in my brain. I'm still female. It's a lot to untangle.


* There are a lot of contradictory and complementary studies on bias: a RAND study says NSF awards don't show gender bias, but other studies show NIH and NSF awards show huge bias against US ethnic/racial minorities; another study says women receive teaching awards at a rate comparable to participation in the workforce but scholarly awards at a rate not comparable to men when prestige of publications is considered; there are tons of studies on bias in teaching evaluations and it seems Asians (whether immigrant or from the US) are discriminated against while women in math get higher evaluations if they're exceptionally "warm" while they're heavily penalized if they are not "warm", while black professors get different messages if the evaluation is phrased as "feedback" or "evaluation"; it goes on and on and on... very complicated!

Bicultural Mathematics (SLAC version)

As you may have gathered, I've spent some time teaching and doing research at a small liberal arts college. I'm at a research conference right now where most of my colleagues have not, and there does seem to be a cultural gap. I feel like a bit of an outsider now and then. On the one hand, I know I'm accepted and people do seem to treat me as an equal. On the other hand, I don't feel like an equal. I've often had to email friends for pdfs of journal articles because the published version differed substantially from the arXiv one or it was not posted to the arXiv, and my library did not subscribe to that journal. I've done less research in a month at my SLAC than I have in a week at this conference, simply because of the demands of teaching and advising and service. I've changed my research to a less technical topic so that I could both keep up and involve undergrads, and it's weird to talk to people here because they want to know about my "old" more technical research. I like the stuff so I'm happy to talk... I just feel like I am back into a big stream after spending some time in the slower side branch for a while.

I do believe that people who have been professors for a while appreciate this bicultural feeling to a far greater extent than postdocs and grad students. Postdocs who have only spent time in the R1 orbit, in particular, have not in general had to appreciate what life would be like in any other world. Professors at all schools feel pulled in many different directions: committees, research, public service, teaching, advising, writing, etc. I guess I feel I have more in common with them than with postdocs who have taught a class or two. On the other hand, I am getting a lot of advice from some of these postdocs on grant opportunities in the research world that I certainly didn't hear about to the same extent while in the SLAC world.

This bicultural feeling is somewhat normal for me, I guess -- in actual culture and the country I'm living in and in being a woman in math. I hope it continues to inspire insight rather than just tiring me out.

Coping with Conference Burnout

I've been at a conference for a bit. So many new ideas! Trying to listen and take notes and talk with people about my own work and theirs and what new things might be possible. Somehow this time was different than the conferences this summer; maybe because a new school year has started my reserves were a bit lower and I was pretty burned out by the end of week one. It's also a fairly lectury conference by some standards. By Friday I was no longer able to cope with processing new information or ideas. What to do?

Everyone's different. Some people partied all weekend, some people watched TV, some people went out on nature walks or adventures in town. I tried to respect my introverted nature and spent a lot of time alone or in small groups. I am feeling much better now: the long weekend was quite a blessing. I will be ready to start again tomorrow, I hope.

Once again, I observed younger grad students wishing we'd quit talking math and older mathematicians keeping up the shop talk through dinner and dessert. As a contribution to our understanding of each other, I want to remind those wishing the math would stop that not everyone gets to talk math that often. To those who always keep going on about the mathematics, look around and decide whether that's what you really want to talk about! Sometimes the answer will be yes, sometimes no, and either is alright.

That's what breaks are good for, as well. I enjoyed the weekend in part because I got a lot of ideas during the conference and I wanted to follow up on them. I don't do well on low levels of sleep, so having non-scheduled weekend time to work on mathematics is important. My new ideas have led me down an algebraic rabbit-hole that I'm trying to work back out of now. Algebraic calculations sometimes take me a while. The time to think was useful.

Disrespect

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.

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.

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!

Workshops

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.

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?

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?

Moving

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.

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.

Talking...

At another math conference. Talk math all the time or only some of the time?

The traditional Wednesday afternoon break is certainly appreciated; I did no math and instead did some sightseeing and a lot of walking. A good change from sitting and writing for hours.

I have some math friends who can keep talking math endlessly: over dinner, after dinner, over drinks, over breakfast, in conference rooms with no food, during hikes. Other math friends keep changing the topic away from math. Part of this is a question of age and concentration: it's mainly my older or more experienced math friends who can talk endlessly and grad students who can't keep it up -- and I remember grad school and being exhausted by the math talk. Another part is personality. Some people are just more one-track than others.

During the school year, while teaching, I was very appreciative of conferences and the chance to talk serious math. It simply did not happen at my home institution much, unless I was teaching someone about this math. This summer I am more interested in a bit of balance but I still have a heightened appreciation of how rare and important these chances are. I don't think my grad school friends understand that. I hope I am not alienating my grad student collaborator by my endless mathematical conversations with others. This grad student, after all, can return to her home institution and be surrounded by research mathematicians who will chat with her and give her feedback and ideas. Things are not quite the same for me, although next semester I will be back in the research milieu. 

"On Tuesday, the female participants..."

Why have these "women in math" lunches or get-togethers at conferences, in grad school, elsewhere?

Oh, how I hate this tired old discussion. It is just like teaching: you may get older, but freshmen are always freshmen. I may get older and wiser, but there will always, always be some guy who thinks he is super-clever saying, "What about lunch for the men?"

Clever, eh? I bet you never thought of that line!

Current response: well, go have lunch!

Now that we're done with that, to the more educational component of today's post. Why lunch for the women? Because it's nice to meet each other and reassure ourselves that we're not freaks and share some experiences. (Why can't I stop being snarky about this?)

Try again. To share experiences and notes and develop effective ways to deal with the usual non-gender-specific thoughts (my research is never going to succeed! I am sooo dumb! I always forget the statistic on tableau that produces the blah function, so how will I ever prove anything again!) and the more-gender-specific (I don't belong here! All these guys won't talk to me and the guy who knows everything about the KdV equations is scared of girls and scurries into a corner every time I try to ask him about remark four in his recent paper! The senior professor who's lecturing on stacks switches to talking about love and beauty instead of orbifolds every time I come near and it is freaking me out! I want to have a baby, or three! I keep getting nominated for committees, so now they want me to be on the women in math committee and the diversity in sciences committee and the undergraduate curriculum committee and the mentoring committee!!!! I just want to be on the funding committee.)

When we talk, we can figure out some of these things that no one else is going to figure out for us. We can learn techniques for gracefully declining those committee nominations, figure out how to shake up conference speaker lists so that speakers don't just include the male organizer's male friends, get tips on organizing our time between work, travel, family, and the rest of life, learn different ways of seeing the world that might free us from our own prejudices. We can make some important professional connections. We can learn from women ahead of us how they made life as a research mathematician or liberal arts college professor work, with or without kids/aging parents/a demanding Ironman training schedule. These models are important because life and society still do demand different things from men and women, and the model that some senior men present (have stay-at-home wife, move anywhere in world for career, work all the time and have wife take care of kids/parents/Christmas cards) is simply untenable and kicks us right out of the picture.

Guys, we like talking to you. Don't be so gosh-darned sensitive. You're fine. But we need a network of women: for advice, sometimes for validation that we're not crazy, sometimes for a tampon in an emergency. You're not qualified for a number of these things, some for understandable reasons (the last, I hope) and sometimes because you are simply unobservant and/or don't experience the same world as we do. The next time I hear some guy saying, "But he never stares at my chest" I'm going to start screeching like a hyena.

Experimentation in mathematics

As mathematicians, we experiment constantly. Just try some shit for heaven's sake!

I'm talking about several different kinds of experimentation here. I'll look at three kinds below. (This is not exhaustive of course, and there are probably other viewpoints to take).

Just work out a few problems. This is what we'd like our students to do most often when we say "experiment." Try similar types of problems and see what happens. Make links between the ideas. Try solving x^2+3x+4=0, x^2+3x+3=0, x^2+3=0, and so on, and see what different kinds of solutions you get -- before asking for the theorem  ("rule") about what kinds of solutions you get.

Why don't students do this? If math is a series of hazily-understood rules, it's safer to just follow those received rules.

Mess with your assumptions. This is a higher level of sophistication but can still apply even to problems like the quadratic equations above. At some point in school we learn that you can't take the square root of a negative number. This is just a lie adults tell us to protect us from something they believe to be scary. All around the world, though, there's some kid every day who says, "Why not?" That's the right question to ask. Why not?

Sometimes there are good reasons "why not." In mathematics eventually one develops a sense of how things "should be" and it is disturbing when violations are found. This is where interesting things happen. But messing with these assumptions is also very useful. Why can't we take square roots of negative numbers? Well, ... um... in the end, no reason -- so we discover imaginary numbers. Why can't we let time go to infinity in this dynamical system and allow negative populations of gazelles, if only in our minds? Well... no reason -- and then we discover something about stable solutions and that our model actually works for an engineering application. Why can't we take the quotient of a geometric space this way instead of that way? Well.... now we develop Chow quotients, GIT quotients, symplectic quotients, stacks.


Gather data like a scientist. Experimentation by hand or by computer can be deeply valuable. Programming the calculations -- often the only way to gather a lot of data in math -- also forces a different point of view that can be illuminating. (Comparing Sage and Macaulay2's treatment and implementation of Schur functions, for instance, is interesting.) The data you get at the end can be REALLY interesting! You can disprove conjectures quickly by finding counterexamples. You can get a suggestion for a new theorem by noticing a pattern (why are these numbers all even? all 0 mod 4? all prime?). You can discover unexpected connections to other areas of mathematics (the results of the combinatorial experiments gave me formulas that solve this differential equation....?!). You can publish things like "this conjecture has been checked for all n less than 17" or "all n less than 16,092,123".

Pure math involves proof: this is what differentiates it from the other sciences. We should not forget, though, that some of the initial investigatory impulses we have share a lot with the sciences. We shouldn't let our students forget, either.

Atlantic article

Like everyone else in the blogosphere, I feel the need to weigh in on Anne-Marie Slaughter's article on women in the workforce and women in leadership. I'm exactly her subject matter: a female in her early thirties trying to figure out work, family, ambition, and what to do with her PhD.

She mentions that academia made it possible for her to do it all for a long time because of its flexible schedule. I agree, if you can live near your work. When I've lived near my academic job I've enjoyed a lot of freedom and flexibility: I can work really hard and still get a haircut, get groceries, go to the dentist, etc. I've also lived far from my academic job in order to deal with a two-body problem + a mortgage. When I'm commuting a substantial distance, living at home rather than coming home only on weekends, and teaching classes in the morning and attending required committee or department meetings in the late afternoon, I too have felt the stress. Hate it. I hate leaving home by 7 am and coming home at 8 pm. If I have to do it again I will quit -- I learned a lot about work-life balance!

And travel is rough. This summer I am spending five weeks on the road. Sure, it's a choice, and one I've looked at closely. (I believe in making conscious choices to the extent that's possible.) I have considered canceling some of those weeks on the road -- but the conferences seem essential to the progress of my career, if I want to have a career, and the family time seems essential if I want to maintain family connections. On the other hand, time at home with my nuclear family seems pretty important too! I want to see friends and go to cool city events and do a triathlon and weed the garden... when is that going to happen?

I am very fortunate: I get to do work that I find interesting and meaningful while being financially supported for travel to interesting locations. Many people I know find the life, from the outside, almost glamorous (crazy to say about a mathematician's life). On the inside, I don't know. What price am I paying in trying to climb this ladder that in the end seems to have little sawed-off rungs every few steps? It's not like I've got a steady job to rely on...

Learning to learn

I've long been interested in learning to learn -- how people learn -- how excellence and mastery are gained. Somehow I ended up reading the book "Flow" by Mihaly Csikszentmihalyi in high school, for instance. Rereading it more recently I'm surprised I got anything out of it back then. (This reinforces my idea that I used to be smarter.) Two of my other recent favorites are "Talent is Overrated" by Geoff Colvin and "The Art of Learning" by Josh Waitzkin. There are similar ideas in all of these. I love "Talent is Overrated" in particular because of its concrete breakdown of different ways of working toward mastery. It is very clear about what deliberate practice means and involves. It ought to be required reading for college freshmen.

One of the biggest frustrations I encounter with freshmen students in particular is that they don't know how to learn. They feel that doing the homework in a half-assed way in the hour before class ought to be sufficient to get them to real understanding, or that reading the chapter before the test is the best way to study. Deliberate practice is a very new concept for most of them -- but it's an idea that they can apply to sports, learning Arabic, economics, pottery, anything! When I teach again I'd like to bring this idea more explicitly into the classroom. I am very conscious that math is not the real thing I'm teaching in freshman precalc or calc. If I can teach students how to approach problems, then I have succeeded. That statement has many levels.

Freshmen come in with these attitudes for many reasons. The two reasons I see as most relevant are the ridiculous waste of time that high school is for many students and current US attitudes toward learning. High school math seems to spin its wheels for years. Students with a good head start due to good education or high socioeconomic class come into high school ready to zoom through calculus on a superficial level. Students with a poor start come in to high school ready to fail to learn how to add fractions year after year after year.

Our attitudes toward education and learning, too, lead us to believe that downloading information into our brains is the primary activity taking place in learning. Consider what some leading politicians are suggesting with regard to education: that brick-and-mortar campuses will be rendered irrelevant by the ability to download a calculus video from iTunes U. We already have these wonderful sources of information and exercises called books -- they're like videos but written down -- and yet I have met few students who have learned calculus from a book alone! Yet students do believe that skimming a book or watching a video is what learning is. The internal work needed is somehow omitted from our cultural discussions of learning.

So go read about learning and how we do it. It's useful in every endeavor!