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...