It’s the Monday morning after spring break.  I had happily forgotten what it’s like to be up at 6AM and start working at 7AM every morning.  But here I am again.

It was a glorious, productive, and restful spring break.  I slept in every day.  I graded a homework assignment. I did some math-reading and had a meeting with my adviser.  I worked on some homework.  I copied some topology class notes from last semester that need to go into my notes-binder.  I put 10-15 hours into a video game (Final Fantasy XIII).  I made some delicious meals because I had time to cook.  I hung out with friends WITHOUT us all having homework or grading in front of us.  I answered a couple of e-mails.  It was great.  I’ve never had a spring break like this in the past.  I should do this every year!  (Well, while I still have spring break… which won’t be too many more years, unless I go into teaching/academia after I finish school.)

My “research” (such as it is, so far) is just finally getting into the good stuff.  For 7 months I’ve just been reading a lot of background material, but now I’m finally learning about the actual definitions and concepts needed to delve into the mathematical unknown.  I’ve written about this before, but I find math research so exciting!  I am in awe of people who regularly walk that line between really advanced concepts and discovery of things no human has ever encountered before.  I’m not at that level yet, but it’s still exciting to be as far along as I am.  And two weekends in April I’m going to math conferences here in Texas, so I’ll get to hear people talk about their research.  A good math talk can be a lot of fun if the person is engaged in what they’re talking about, so I’m looking forward to that (plus I get to travel to places I’ve never been before, which is also fun).

If you’re considering math grad school, I highly recommend having a similar attitude about research.  If you’re coming to grad school just to become a teacher, it is going to be a miserable couple of years for you, because teaching is a very minor part of what math grad students do.  You need to have a passion for the theory and the ideas and the math itself.  Without the drive for the sake of mathematics, I don’t think I would have made it through three and a half semesters, and I’m not even to the real research and writing a dissertation part yet.

In general, life is good.  The weather is beautiful in Texas this time of year (spring and fall are great here because they’re both just like summer back home, and I love that kind of weather).  Spring break has renewed me for the final push of the last month-and-a-half of the semester.  I’m excited to dig into my course work and research and conferences and teaching before the sweet release of summer.  I’m happy in the moment, but I’m also looking forward to travel (short conference trips in April, and a few bigger trips in June).

The only thing getting me down is that my topology class has (finally?) gotten difficult.  The first semester was a “breeze.”  For most of the homework problems, the intuitive approach was the right approach and it was just a matter of writing down the ideas concisely.  Even the first few weeks of this semester were like that.  But as soon as we passed the separation axioms, it became a whole different ball game.  Suddenly the homework problems seem impossible for some reason.  I still understand the definitions, and the proofs shown in class, but I can’t seem to be able to apply the ideas on my own.  I don’t feel as hopeless as when I try to do analysis problems, but it’s not a good feeling to not know how to do something about which you used to have confidence.  It’ll pose a challenge for the rest of the semester and the summer (I will be studying for the topology qualifying exam this summer), but I’m feeling up to it.  I feel like I’m making progress and I have a goal in the big picture of grad school, so I’ll just keep barreling forward with it.

Someone remind me how happy and optimistic I am now in a couple of weeks (or a couple of days?) when I’m bitching about how hard my life is.   I’m busy and I have a lot on my plate, but for some reason today it’s not bothering me.