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!

Time for a real vacation

I think it's time to take a few days really away from math and the web, mostly because I have some pressing family events coming up. Those events need some real attention: I have a lot of family here in the country I'm visiting and am in some sense bicultural, but I have not lived here for any length of time as an adult and so the dance of politeness and family can be less than fluent. We'll see what can be done. Poor introverts! As I learned from the book "Quiet," introverts observe human interactions as keenly and insightfully as anyone, but at times have trouble performing the dual tasks of observing and participating. I need to do both for the next few days.

So, to what extent do complete vacations improve mathematical thought? I am used to keeping a problem rolling around like a stone in a polisher, tumbling into my conscious thought at odd moments. Really setting it aside is a bit unusual. Perhaps during the semester while paying close attention to student needs I did so, but did not notice so much because of the pressing demands of the moment. Maybe it's better to make a real choice to put aside the math for a few days rather than having it be accepted under duress. People say it's good for you. Are they right?

The book "Quiet" also has a lot to say about why I found teaching 3-3 stressful in a way I hadn't imagined. I don't think I made enough time during the day for retreating into my introverted shell after being "on" for 2-3 hours teaching, 2 hours with students, and a meeting or two. This is a drawback of an open-door policy that is taken very literally. I need to mull over this a bit. Dreamed about teaching last night: I had to come up with a bunch of readings on ethics -- good and evil -- for a small seminar class. I was excited about it although rather stressed by the short time frame given for coming up with a reading list, especially since I've never taught a philosophy or ethics class! Maybe my desire to teach is reviving from its wilted state.

June... almost over...

see you in July!

Some progress

Bought a little school-notebook (not too many pages) in which to do some examples. Wrote out a few things -- should now type them up. No ground-breaking mathematics, just writing out explicitly a few proofs that are needed for a project. One of them was very easy and the other needs a few references from previously published papers.

Intended to get to some of that typing today but was pulled away by other projects, weather, and visitors. It's vacation, after all, so I should spend some time with people I only see once a year. Priorities! I enjoy doing some math in my free time. It is for pleasure. (I am certainly behind on the less-pleasurable projects I'm working on.) However, it is also important to go swimming and do some yard work and visit with the neighbors. I am taking time for long walks and that sort of thing too, as well as a run or too.

I had a realization: on vacation in this other country where no one knows me professionally I feel very different. I don't measure myself by my success or failure in the profession of academic mathematics because no one understands that profession or really gives a flying flip about it. To others, I look reasonably successful: I am going to interesting places next year and doing interesting things and getting paid reasonably well. They don't know that I didn't get any tenure-track offers or that getting these positions for next year took some scrambling. And aren't they right?

Notebooks redux

I am in a country thousands of miles away from home -- the annual migration to the land of my ancestors. (As a guy I was chatting with last week said, "You guys are like wildebeests or something!") I forgot my research notebook.

My spouse said, "That's a Freudian slip if I ever saw one."


I did remember my personal journal, and it's been co-opted now for mathematical purposes. This is one reason I know that I'm still in the right field: I can't stop the mathematical itch. Can't stop! Maybe I get tired out by "parenting" students, maybe I get tired out by committees, but I can't stop wanting to know how this combination of group actions acts on my geometric object of choice. I got a nice couple hours in on the plane and have some cool ideas. I can't wait to find out if my crazy insight is correct. There's a nice and clear combinatorial correspondence between the things I'm looking at but I don't know if the geometry will hold up.


Now if I ever get famous enough to have a biographer write my biography they'll read all my grousing about all my neurotic thoughts... combined with math.

The difficulty, though, is that I'm with the family. There is going to be a whirlwind of social activity, from yardwork to running to coffee-drinking. I need a vacation, Lord knows, but I also want to find the answer to my question. How will I find some time? Do I need to beg off with jet-lag induced need for alone time?

Also started reading "Quiet," a book about introversion, which may be lending me some insight into why my last year at a liberal arts college stressing student interaction was, well, rather stressful. Maybe with such information I could do better in the future.

Different strokes...

...for different folks.

I used to be a roller-ball diehard. They were the nicest pens I knew. Now I am an occasional fountain-pen user. I like the fountain pen for taking notes at conferences because they tire my hand less than a ball-point pen and the ink doesn't smear like pencil.

I like having several colors at hand to draw pictures and diagrams with.

I use Bic or cheap pens for much of my scratch work (on recycled paper). Fountain pens don't work as well on some types of recycled paper and I also feel bad about wasting good ink.

I love combinatorists and their endless supplies of colored pens. They always seem to have great colors and some discrimination when it comes to type of pen. They can also always tell you what kind of colored chalk erases best. Some can identify it by the sound when you clink it against the blackboard.

Analysts, by contrast, never seem to think about such banal topics.

Traveling with fountain pen ink is sometimes a bit exciting. One must make sure, if flying in the US, that it will fit into your quart-sized plastic baggie. This is not altogether a bad thing. Once one of my bottles leaked due to the pressure change in the cargo hold. My sunscreen and toothpaste were dyed, but my clothing escaped.

Notebooks

I keep a research notebook. The following issues have come up in conversation with other mathematicians.


To scratch or not to scratch: Do you include your scratch work in the notebook? Some people include everything in research notebooks, but I feel this might dilute their usefulness. I don't include most scratch work. It takes up a lot of paper. I include some done when I'm in a location in which I don't have access to real scratch paper (by that I mean paper that's already been printed on or used on one side). I try to include summaries of my calculations done on scratch paper. Sometimes, the details of the calculation are useful.


Paper thickness: Paper must be sturdy enough that ink does not bleed through.


Hardcover or softcover?: I used to prefer a cardboard cover but I've switched to a lighter notebook. The new kind fits better in my lap than the old kind. I don't like a terribly floppy cover, but I've decided I do not need a very rigid cover.


Wire bound or other?: I really hate spiral-bound notebooks, actually -- the wire spiral always gets caught in my bag and pulls out. I know other researchers who insist on spiral-bound.


What's in there, anyway?: Notes. Research notes -- things I am trying to prove, random ideas I had, snippets from talks with other people. Reading notes on things I'd like to know more about. Every now and then a grocery list or other to-do item. Details of some, not all, calculations. QUESTIONS I need to answer.

I refer back to them every now and then: they're useful when talking to others about old mathematical conversations I've written down, when figuring out what I did last summer or last week, when someone asks, "Did you check (blah)?" I store up some ideas for future work as well.

I don't have a very systematic way of going back over them, though, and I wish I did have a way of doing so usefully. I haven't figured out what's useful yet.

Book of hours

How many hours are enough?

As an assistant professor, during the school year no number of hours is enough (apparently). Besides math, there are the hours and hours of student contact, class prep, committee work, preparation for committee work, learning about pedagogy, grading projects if not grading homework, grant-writing, etc. Sixty-hour weeks easy. A lot of these things have deadlines (some harder than others) and these deadlines pull us into action.

In the summertime there is plenty to do but it is all paced so differently. I can spend all day on math alone if I like. Some people say four hours of good mathematical thinking is enough. I can believe that. I don't think I'm currently putting it in. Maybe if I did that would be enough.

Today I've chatted with collaborators and looked over some relevant papers. I have not proved anything. I should put in another 3 hours to reach my somewhat-arbitrary four hour declaration.

I think I need caffeine for that.

Summertime blues

Well, I've traveled and returned.

Did a lot of math. The agony of defeat and the thrill of victory. More agony than thrill; lots of tearing down of part of a project that was built on slightly incorrect foundations. Dang it.

Now I have all these "free" hours and so much to do. I have done some things efficiently: finished revisions for an accepted paper, for instance. Made some progress on a few projects but zero progress on a few others. Have some reviews to finish. Am procrastinating. Feel bad about it.

Trying to psychoanalyze myself; also trying to figure out how some people are amazingly successful and fairly well-respected while failing to do all the things they are supposed to do. Maybe I can take a cue from them.

Inevitable

Sat next to a nice young man on the airplane. He asked what I was studying, or doing, or... I said I was a mathematician. (I still have trouble saying this with a straight face, and during the semester I used to say I was a teacher. Why is it easier to say that? Why do I still sort of feel afraid I'm lying when I say I'm a mathematician? I've had my PhD for several years and am actively -- daily -- involved in research.) He said, "Oh, wow, I've never met, like, a real mathematician!"

He was not from the US. (Inevitably) he told me he'd never been that great at math; I told him that what he did in school bore little relationship to what we as mathematicians do, in that he was trying to find the answer when he did his problems in school while we are often trying to figure out what the right question is. I was working through a series of examples on a topic that's given me some trouble lately. In that I was simply doing a bunch of computations and looking for the right answer for each one, my mathematics and his school math were similar. However, I was looking to get a feel for the general situation and prove a few consequences of my starting hypotheses and explore what would happen if I relaxed those hypotheses. It is this synthesis that seems to separate research mathematics from school math. He asked a good question: if we switched to base 60 and counted like Mayans would the quadratic formula still hold? I said yes. Then I asked him, if we counted like Americans tell time (mod 12), how many solutions to x^2-1=0 would there be? For instance, would 5 or 11 or 13 suddenly be solutions? What would that mean? He seemed a bit disturbed.

I suppose that some of us do construct some homework sets to lead students to a larger realization about a type of problem or a property of limits... how many of them realize that? What does it take to shift one's viewpoint to "doing twelve problems to explore all sides of a bigger question" from "doing twelve problems as fast as possible"?

Airplanes

Mathematical travel vignettes:

An airport whose location I don't remember. Layover. Reading at a small table outside a pseudo-Starbucks, skylights letting in streams of sunlight, reading about V.I. Arnold's mathematical legacy in the Notices. He skied thirty to fifty kilometers a day on his winter trips and ran long distances too. I can ski thirty kilometers but I can't yet run ten. I love Arnold's mathematics and mathematical viewpoint, to the extent I understand it. Imagining myself at one of his seminars or trips to the countryside... frightening! intimidating! After reading the article I had another hour left to explore some combinatorial implications of the geometry I was thinking about.

A coffeeshop in Berkeley during the free day at an MSRI workshop. I wander in for caffeination and find someone from my master's thesis committee and a half-dozen other mathematicians I recognize even if I don't know them. Laptop lids up, coffee at the ready. I get to ask some questions about a paper I'm stuck on: they have no idea what the author is talking about either. The notation is simply not defined in the paper. Work from first principles -- what must it mean?

The best baingan bharta I've ever eaten was at an Indian restaurant a few blocks from the site of the 2012 Joint Mathematics Meetings.

I missed many of the glories of Marseille because when I visited Luminy I was entirely occupied with a problem that I felt I was finally making progress on. I went on a hike to the coast, twice, and did float in the ocean -- took some beautiful pictures -- but the hikes were almost entirely mathematical discussions. It was beautiful.

I'm packing again tonight. Last time I went to visit this collaborator, I got so jazzed up on the ideas I only slept three hours the second night I was there.

I'll have a layover in another anonymous airport. Better bring some more inspiration.

Fundamentals

I'm working with a student this summer and wondering how to communicate "how to learn mathematics".  We don't have a class, a syllabus, a textbook, and I can tell that this student needs a bit of guidance on what to do. This is something professional mathematicians usually learn through osmosis in graduate school. Can I tease apart some good habits to suggest to this student now?

Many mathematicians have written about this: Terence Tao in particular has some great advice in small portions. On a personal level, his advice to write down what you've done is probably the first item I have on my how to learn new math list. I learn a lot through writing things down. I try to write for others I know (grad school friends, colleagues, students) and then put it aside for a month. When I come back to the notes I am often amazed by what needs to be rewritten to communicate well and reflect my greater understanding -- and the final product is much improved with these changes!

Fine, write down what you've done. But what do you do?

Read a lot -- find some good introductory work on the topic and go to town. You'll get a broad picture of the basics this way.

Write down your questions and subquestions and try to answer them. Write down your explanations.

Find some interesting articles, recent or older, and take them apart. What are the main points? What are the questions people are trying to answer? How did they develop from questions earlier in the area's history?

Why does anyone care about the results? Why do you care?

Prove things. Pay attention to details (this was hard for me to learn). Share with others so that they can ask dumb questions and sharp questions. Remember, it's not personal -- we all just want to understand.

Go back and repeat. It's a great spiral staircase. You go back to the basics of the new area and see them with new eyes because you've looked at the questions people are asking now.

Ok; off to take my own advice...

Math and Computers

What kinds of software do you use? Why?

Mathematica: I just renewed my license for Mathematica through the college I've been working at. It's the best option for creating figures for multivariable and single-variable calc exams, multiplying matrices in a pinch, integrating things to check my answers. I've also done some checks of calculations in research with Mathematica because of the easy entry of polynomials and functions on polynomials.

GAP (Groups, algorithms, programming): Haven't used this in years. Do I vaguely remember that some of my groupy and number-theory-y friends used this?


Magma: I used this years ago in graduate school because they had a license and I was doing some number theory. It is not free. The people I know who do a lot with computer algebra systems all use other programs, so I have not felt the need to buy it. Why is that, though? There seem to be many citations of the program in areas I'm interested in. Is there some geographic clustering of users?

Sage: I know many people who use Sage! It is trying to become the great repository of everything. It's open source and user supported. One of my summer goals is to learn more about Sage and write a few packages that I'd find useful... Even if you don't want to download Sage, you can try it online through their web interface.

Macaulay2: While Macaulay2 is narrower in scope than Sage, it's the program I use the most. I found it to have a steeper learning curve for programming than some languages and I don't know enough about computer science to know why. After a week of working with it I could write crappy programs in M2. After some time brushing up on my general programming skills I could write somewhat better programs. The documentation can be a bit spotty but the folks who are community experts in M2 are very nice and helpful.

Pari/GP: Available as a C library or a computer algebra system and designed for fast computations in number theory. I used it way back when I was still studying number theory but haven't touched it in years. I have a fond memory of it, I suppose.

CoCoA is also a program for computations in commutative algebra, etc., and I found it very very easy to learn to use. I was going to say that I don't think it's actively maintained anymore -- but I guess I'm wrong! A new version was put out just this April! Maybe I will check it out again.

My computer usage goes in waves. I can spend weeks or months never using a computer to do a calculation beyond division (I'm not great at mental division). Then I can decide that I want to do a cohomological computation using the computer and spend a week and a half figuring out how to make it work and checking a bunch of examples. I am no computer expert, just someone who wants to automate certain calculations. I use these calculations for both hypothesis generation and hypothesis testing.

Motivation

To do list:

• email editor about that article I submitted a loooooong time ago
• get two articles out the door involving recent work (small things, but still)
• work on material for meeting tomorrow with collaborators
• finish writing proof for other project
• start reading up on my new area of interest

What do I want to do? Only the last one. New and shiny!!

I don't know why I don't want to do the first two; usually I'm all about the editing.

In the past I have bribed myself into tasks like this with pastries. If I am trying to cut sugar and white flour out of my diet for digestive and health reasons, this pastry does not fit. Cocktails? No... too expensive (and not good for 9 am start). Difficult decisions here!

Freedom

Sitting in a cafe listening to Euro-trance, getting that last bit of grading done... one assignment to go. Let things go later than I usually do in order to decompress and give a bit of grace to one troubled black sheep of a student who might maybe not fail this class now that he got his last assignment in. I am a sucker.

It is so odd to sleep enough, wake up in the morning without the kick of adrenaline that usually greeted me during the school year. I don't know why I get so physical about my job or why I store up stress in my body. I have read a lot about cognitive behavioral therapy and can talk myself out of all kinds of fears (putting my head underwater, eating wierdo foods, trying scary physical adventures) but I can't talk myself out of making my stress incarnate. I also can't quite talk myself out of the stress. I think I am just an introvert on a very physical level: I am so happy being alone about 8 hours a day! Add in four hours of talking over dinner or math tea or Skype and I'm peachy.

So now it's summer. I started this blog because I was stressed out about the job search and my apparent imminent unemployment. I've strung together a few things for next year but am still occupied with the task of moving out of my office and saying goodbye to current colleagues. I have worked with a great department and will miss my colleagues. Right now I'm close enough to the 60-hour workweeks and emotional stress of trying to connect honestly and deeply with students that I don't miss that yet.

(Caretakers are the folks who are most likely to get burned out by their jobs. How do nurses or ministers do it year-round? At least for nurses, there is not less paperwork than I have!)

Since I haven't been done for very long I have not demanded much of myself in terms of research. I have slept a lot, got some paper revisions back to a journal. I need to do some more paperwork for the college before I can consider myself done and return some books. I am starting work with a summer research student (am I a fool?) this coming week. I need to set summer priorities and schedules. Two projects close to completion need to get out the door. I suppose that will be my first main priority..... so much to do!

But I feel free, like I have room to move. Thank goodness.

Conversations

During finals I noticed again a phenomenon that prompts some new ideas (for me) about gender and math. The final exam is a multi-hour affair and students are allowed to ask questions during the final. I often talk with them out in the hallway about problems. At my SLAC students ask many many questions during exams; this was not true at the big R1 I was at for graduate school.


At the SLAC I have often ended up with a young woman frustrated and sometimes near tears who is asking questions about, say, optimization. They are not usually asking about a typographical error or the meaning of the question. Often the student is stuck and "knows what to do" but can't figure out how to do it. I've had so many of these conversations by now that I have a set of stock phrases. Conversations go like this:

Student: "I'm really stuck on this question about optimization."

me: "Talk me through your work so far."

Student: "Well, I have, like, an equation... for... volume..."

me: "Yes?"

Student: "Oh, I forgot (blank) in the formula..." (writing)

me: "Ok? What's next?" (regardless of correctness)

Student: "And then I was trying to put in my constraint... but then I got stuck differentiating..."

me: "Where did you get stuck?"

Student: "Right here.... oh, I see, I need to simplify..." (writes down correct derivative)

me: "Ok? What's next?"

Student: "And then I have to (set derivative function to zero, solve for critical points, use one of various tests to show it's max or min, find dimensions of whatever)."

And then the student writes down the entire correct solution. I didn't say anything but "Yes?", "Ok?", "What's your next step?", "Write things down!", or "Keep talking!"

I hardly ever have this conversation with male students, but with female students it happens at least once per final (sometimes more). I asked one student this year about what was happening in her head as she talked through it, and she said, "It just makes more sense if I can talk out loud about it!"

I am by no means an essentialist: I think most notions of what is "essentially female" or "essentially male" are bullshit. (There are some clear physical differences like the ability to bear children, but even notions of men being stronger than women are obscured by a culture that prizes slender women with little muscle tone. Look at the survey results.) Our cultural baggage obscures any subtle underlying genetic whatever, and epigenetics is changing our whole notion of how genetics impacts life anyway. Given all that, by college we've got to work with what our culture has wrought. My female students seem to really need that processing of mathematics through conversation. I enjoy it myself and am really benefiting from my conversations. I did not have so many of these conversations in graduate school because of a need to not look stupid in front of R1 professors so they would not think poorly of me. Now I figure I've succeeded (gotten a PhD) and failed (gone to a teaching school) and so it doesn't matter anymore!

We got the f(*&ing guns...

Another big secret: I don't give a s$&^ about grades!

I suppose I'd better explain for those sensitive and responsible undergraduates out there. It is the end of the semester and I am putting up grades. I am dealing with late homework (didn't you read that syllabus that says no late homework, and why do you think you're exempt?). I am fielding all the inquiries about last-minute saves. People care so, so much about that grade. But doing all the homework after the semester is over is pointless, don't you think?


Well, no, because my students are focused on the letter that turns up at the end of each line on the main section of the transcript. That's natural, because college selects for people with that focus: such people are more successful in the college application process. It's fostered in high school and emphasized by parents. Why would freshmen think at all differently?

I think differently. Let's use the dreaded sports analogy. To me, your grade is a measure of one aspect of your competence just like the number of pull-ups you can do right this instant is a measure of one aspect of your competence. Maybe you're weak, maybe you're strong, maybe you've got a broken arm, whatever. It's not a moral judgement, it's a measure. You can do some pull-ups or you can't.

You may decide that it's important for you to be able to do more: you're after general fitness or you feel it's a badge of honor or you want to improve your gymnastics or pass some PT exam or you want to be able to save yourself at that pivotal moment when you've just slipped off the edge of a skyscraper in your epic battle with evil but you've caught the edge with your fingers and could pull yourself up... if you had the strength. Or maybe you're just interested in challenging yourself.

So you start training your pull-ups. And then, after some work, you can do more.

No one argues they should pass the PT exam because they worked really hard. They just work to get the number.

Pretty simple. And that's what your calculus grade reflects as well: how well you can do calculus and convey your understanding of it at certain moments in time. I repeat: it's not a moral judgement. It's also not a measure of how much I like you or your future success. It's pretty irrelevant, in fact, to both of those.

Either the material is important or not. You're learning how to think, you're learning something to help you in economics or chemistry, you're learning computational skills, you're learning about the history of intellectual achievement in mathematics -- or you are wasting your time.

If you're fully engaging in this process of learning, communicating, and challenging yourself, you'll get something out of it (and often your grade will be alright as well). This is what life is about, challenge and exploration. Whether you're engaging is actually a better measure of your future success than your grade.

If you're ignoring it, I'll only respect you if you're doing something more interesting and not whining about the consequences at the end.

Codes

In the play "Truth Values" the protagonist ends up dressing "inappropriately" in math grad school as a way of... mmm... acting out? Showing independence? Differentiating herself from others?

My husband once went to an AMS regional meeting and pronounced it a markedly unattractive group of people.

In graduate school I generally wore jeans and t-shirts and sweatshirts. Don't want to stand out.

In undergrad that really was driven home for me, as when you wear a dress at an engineering school all the guys ask, "Hey, is it laundry day?"

My current department seems to have a different code. There are a few more people who had a corporate life, even if only briefly, and so there are blazers now and then and business casual pants and the occasional real suit or even a woman who looks like an Ann Taylor ad. No, I'm not monetizing the blog yet... although their triacetate pants really do last forever (I have a pair that is going on ten years old).

MAA conference attendees are less gray than AMS conference attendees: more likely to wear colors or even ruffles. Maybe it's because there are more women and the women don't feel this American pressure to wear drab colors and a backpack. 

In Portugal and France mathematicians are orders of magnitude more fashionable than in the US. Why is that?


I do try to dress like a professor is "supposed to" look in some freshman's warped view of reality, at least at the beginning of the semester. I am small and female and relatively young-looking at this point. Haha. A student in the library was astounded just a few weeks ago that I got the long check-out period for books -- she said she thought I was a student. This means I can't wear that grad-school uniform of jeans, holey sweatshirt, and Chacos. Looking poorer and scruffier than my students... mmm, just can't do it. But it's rather an experiment to figure out what looks adult without looking matronly or frumpy. Why does it matter anyway? There are plenty of normal fashionable things I don't do because it seems like an absolute waste of time (shaping my eyebrows?). Why do I even care if I look matronly? Maybe if I was more immersed in the mathematical tribe rather than living among the art historians and French professors of a SLAC I wouldn't notice so much.

The conference ramble

One wonderful aspect of the week-long math conference in Europe, in particular, is that while Monday, Tuesday, Thursday, and Friday are entire days of lectures, Wednesday often includes the afternoon hike. Germans especially seem to love the hike, and they have convinced me! The afternoon hike gets the whole group out of chairs and into nature. The group rambles along at a relaxed pace (except for the overachievers at the front) chatting about math, not-math, and everything in between.

It's important to give the brain a little break so that it can do its unconscious work of solidifying connections and giving rise to new ideas.

A walk in the woods has also been shown to increase the capacity to focus. It's as effective as drug therapy for some children with ADD/ADHD.

You get to meet people you may not have talked to otherwise as the group stratifies by walking speed and style.

You get to see the place you're visiting in a new way, as well. I went to Boston for the Joint Math Meetings last January. Boston for the first time... and I saw essentially none of it, for there was no conference ramble. Between interviews and talks and panel discussions I never made it farther away from the hotel than the wonderful Indian restaurants two blocks away one direction and the Charles river. I saw MIT from a distance...

By contrast, on a visit to Oberwolfach I got to meet a goat!

"Break"

My summer is indeed busy. I will be home and non-conferencing for 17 non-weekend days between June 1 and August 31. Perhaps that explains the frisson of apprehension that accompanies the excitement.

I get a little oversensitive when talking to non-academics about the summer. Many believe that it is a vacation. It is in some ways -- I am not lecturing or preparing class syllabi (until August if I'm teaching in the fall). I do get some flexibility in location. But there is a fair bit of pressure to write and research and publish -- Lord knows that at a small liberal arts college that stuff doesn't happen during the academic year yet it's a significant portion of what goes into tenure and promotion decisions.

I don't have to worry about that, though, since I don't have a tenure-track job -- isn't that great?! Well, no; I won't get that tenure-track job if I don't do those things. When I'm being an honest Debbie Downer I say things like, "Sure, it's a vacation if I want to end up unemployed next year! Hahahah!" Responses like this start to step outside the bounds of polite conversation. People don't really want to hear about that -- they want to imagine that I'll spend the summer gardening. That justifies the low pay.

 So, summer. Fewer deadlines. More flexibility. The freedom to concentrate on things I choose rather than reacting to crises and requests from higher-ups in the academic tribe. Some pressure to perform. I do need to give myself a real vacation; the unrelenting knowledge that I could be doing something "useful" is not conducive to real creativity. I will certainly get more sleep at home and therefore be smarter. At conferences, I'll get less sleep and immerse myself entirely into mathematical endeavors like Frederick the mouse soaking up colors for winter.

Outlook

As you might be able to tell from my last post, I'm in an emotional hole. Teaching is hard for introverts and managing the unmanageable is hard for people who like to be competent and in control. Buddhist philosophy counsels nonattachment, simply letting go. Taoist philosophy counsels staying true to your own nature and finding a course through the world that is in harmony with one's own nature and one's surroundings. These currently seem like different paths. Am I to simply let go of my frustrations or change my environment?

It's a moot point anyway. Teaching winds up soon and final exams begin. After grades are calculated and turned in (yes, students, simply calculated -- not given), I am (almost) on "summer break." Next fall I am headed to a different institution, and after that, somewhere else. A peripatetic academic lifestyle, not the one I intended. One which I fought against, in fact, but that's the job market these days: travel or unemployment!

This summer, too, I get to do some travel. I have three conferences and some other trips lined up. Given my recent week I was not seeing the joy involved in 36-hour journeys to exotic locales. Talking with my grandparents on Mother's Day brought back some of the wonder -- they seemed pretty excited about my academic travel. I get to go to interesting locations with some funding help from others and talk about things I love! Thank you, grandparents, for restoring some of my perspective and excitement! It won't all be grading this summer.

In fact, I have two research projects with students very close to completion and two research projects with professional mathematicians making great and intriguing progress. When I think about this summer and the chances I'll have to talk with people (and read all those papers I keep intending to read...) I do feel the stirrings of a battered passion. I am really excited to make progress on these questions, the questions that lead me to talk to myself on the walk back home from the coffeeshop and thus make me look like a crazy lady (more neatly dressed than the archetypal homeless crazy cat lady, but only just). I can't wait to spend all day mulling over them and caffeinating, traipsing from tea shop to coffeeshop to collaborator's office to the back porch. I'm going to read so much and write so much and learn so much and ...!

It is nice to have something to look forward to.

Somatizing

Apologies for the blog break to anyone who actually reads regularly. I had to take time for gastrointestinal distress, two days of migraines, one sleepless night, one evening of uncontrolled crying, and the usual teaching/grading/conversing but unfortunately no research.

It is the end of the semester and plenty is going on. We're not done yet. The department had several large events in the last week or two. The event I was most involved with was of course a team effort, but a lot of the responsibility had been put on my desk as the most junior female. Most of my colleagues were quite helpful and came through when I needed help. The senior colleague who'd initiated the event was not helpful. I got yelled at and told my request for help was unimportant, in front of a student. Sigh. This is why I'm pseudonymous -- who else am I going to talk to about this? Nothing much can be done.

It's Friday. Students are restive. They have tons of work to do and they are freaking out. I also have tons of work to do, but I am not freaking out anymore. Grade 200 pieces of homework in an afternoon? Sure, whatever. At this point in the semester it's going to be graded for completion.

I feel like I've been a somewhat crappy professor this semester -- not up to my usual standards. I still got nominated for outstanding professor by a student group I care about. That makes me feel a bit better.

Grading, editing, organizing the gradebooks and Excel files.... that's my coming weekend.

Juggling 2: How do you learn new math?

How do you start on problems that require learning the basics of another mathematical field? All I know how to do is read. I read the papers I'd like to understand, I follow back through the bibliographies, I try to get back to the basics in the field. Sometimes that is not so easy, as there is no basic introduction. Talking to people seems to be a very effective way to learn the basics of another area of mathematics, but this requires finding a person who knows what you want to know and who is willing and able to explain these things.  I have had particular difficulty with this when I've seen some words that make me think that the ideas from another area might help me out but I'm unable to formulate a good question. "Tell me about how combinatorics might help me with my PDE problem" is awfully vague.

Collaborators are also phenomenally useful in this regard: they are usually people who like you and respect you at least a little bit, so you can ask questions without feeling terribly stupid. I have collaborators with complementary expertise and really enjoy learning from them.

Looking forward to summer -- I have an immense pile of reading I'd like to get to.............

What is love? baby don't hurt me...

In a conversation with a friend I hadn't seen in a while, the friend said he loved his students and wouldn't trade them for anything. (He's at a community college.) I thought that was interesting -- what does that mean? I suppose it means he's happy working with them; I expect it means he respects them and gets some gratification from helping them. (I feel a little Asperger's trying to parse out what this means...)

Do I love my students? I really enjoy working with some of them and I have very collegial relationships with some. I have friends from both the lower-level classes I've taught and the independent research I've conducted. But I guess I wouldn't say I love my students. This is why I'm pseudonymous, by the way -- it seems absolute heresy to say such things out loud. I don't feel like I can be totally honest without repercussions.

I respect them and try to work with them as adults, while keeping in mind that college students are still developing their adult skills. I enjoy working with them overall. Love? I wonder if we have different meanings for the word "love" -- I know that I don't have the same ideas as everyone else on what romantic love is.

Well, this is part of the largest "soft question" -- I don't love my job. Are we supposed to? Our American ideas of fulfillment through career are a little weird and I don't quite buy into it. Part of the problem as I analyze my job satisfaction is that I get very frustrated at not being able to help all students understand and love mathematics. Like any relationship, this is a two-way street. The students also have to make an effort, and not all do: it's a bad relationship in that respect.

But it would be cool to have a job, and students, I loved. Is it possible?

Girl nerd

This is riffing on the post at mathbabe.org on the making of a girl nerd.

I guess I am a girl nerd. Neither of my parents has a science or math background and my dad did not really do college. Cathy O'Neil says that in her experience a mathematical parent is the greatest predictor of mathematical daughters; in my experience an immigrant parent is the best predictor of a daughter's future mathematical success. I know only a few American-born daughters of American-born parents who are mathematical. They are not unicorns -- they certainly do exist! -- but I don't understand how they got there. An AMS article (pdf) discusses some of these ideas as well so I don't think it's all anecdote. Analysis of female performance in the International Math Olympiad also supports the role of culture in fostering female mathematical talent -- and the evidence is overwhelming that being in the US leads to steadily decreasing female math performance over the generations.

Why? Here I'll put my opinions!

• America does not respect mathematics all that much. Many people and politicians are suspicious of any science, as science does not follow morals in evaluating claims of truth. Same for math.
• In the US junior high girls who participate actively in math are often ostracized. It is not a topic for cool or pretty girls. Marine biologist, though.... you get to play with dolphins, and that's alright.
• Having an immigrant parent insulates you from the above attitudes at home to some extent and home is important. You may acquire other handicapping beliefs, but they're different ones.
• The value of an education is stressed more highly by immigrant parents, in my experience and on average, than by American parents. Part of this is self-selection: anyone motivated enough to move to another country to do something is, by definition, motivated enough to do something. At the same time, immigrant parents may be clueless as to how to obtain an education. Some of my students (usually oldest males from a few local immigrant groups) get calls to come home and take care of the family because of a health emergency, even if it's midterms week, because cultural values clash with the expectations of the US educational system. But the parents do keep saying the education is important in a different way from the way American-for-generations suburban parents say education is important! 
• I think the skill of operating in two cultures (or the similar concept of code-switching) actually gives an advantage to female children of immigrants continuing in mathematics. Mathematical culture in the US is different than mainstream culture, and if you're comfortable switching back and forth and talking with both groups you may be more likely to continue. Men and boys are often excused for being socially clueless if they are mathematically inclined, so they can just keep acting according to the norms of mathematical culture while out at the mall, for instance. Women and girls are not excused but rather judged harshly. For girls in particular to have a comfortable existence in the hell-hole we call junior high in the US they must have some facility in switching between cultures. Transitioning between math club or math circle behavior and girl's volleyball team behavior is important and difficult.

As a young woman I found mathematics very soothing once I got proficient at it. This is apparently a common experience for boys and girls -- the certainty of algebra and trigonometry and geometry are an oasis in a confusing adolescent world. I got involved in some outreach activities and learned about fractals and hyperbolic geometry and that sort of thing, which was undeniably cool. (Fractals are still cool!) Eventually I found a community through math team and my accelerated math classes in high school. There were other girls involved; it was male-dominated but not so much so that I was miserable. (I did take a class one summer in junior high in which I was the only girl -- every other boy in the class refused to talk to me at all. At lunch time I either sat alone or found my female friends in the music class to eat with. Only the teacher would talk to me. That was an exceptional experience, though notable.)

Having parents whose attitudes do not mirror those of the American mainstream is one of the most important supports -- that comes through in both my experiences and Cathy's. Why is the US so toxic to mathematical talent, especially female mathematical talent? What could we do to change it?