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Dear diary,

The story so far...

I wanted to give a quick update on a number of things, because I have things to share, things I'm excited about, and good things I want more people to know.

First off, I have been teaching high school mathematics for a semester now, and my contract expires in two weeks. Now that I actually have some first-hand experience managing my own classroom, I have lots of thoughts on the matter, which I will share in a forthcoming node. The results of April 18, 2008 will feature prominently, of course. It's been a blast, it's given me some good money earned under my own terms (isn't it nice to earn money in a way that seems consistent with your core ethical beliefs?), and I have learned a lot.

But it's time to move on...

Don't get me wrong. Teaching is great, and I may do it again for a living, hopefully at the university level, but high school is also a very rewarding experience. It's just that I have not completed my goal to be a full mathematician, and until I am one, I will not be fulfilled. So I want to move on, finish my MSc, and go on to my PhD.

Things, those wonderful things, are moving right along in that direction. I have been lucky enough to, get this, find a professor at UNAM who wrote precisely the majority of the articles I've been basing my MSc research on, and he's quite happy to guide my work to its completion. So far, because of my day job, I haven't been able to focus completely on finishing the thesis, but in two more weeks I give my students their finals, I'll be again free to work day and night on completing what needs to be completed for my thesis, and I fully expect to get everything done by September.

Work on my thesis, which right now consists mostly of about a paltry 7,000 lines of C++ code, was stalled for a long time and my code was accumulating bit rot. Now that I've started talking to my new advisor, I've taken up my code again, and have been cleaning it up, and it's looking better than ever. Not only that, but a couple of wonderful things have recently happened with my code. First, my new advisor asked me, unprompted, how I felt about releasing my code under the GPL. He wants me to develop my code so that it can be shared with other researchers worldwide under free software principles so that as a scientific community we can reduce duplicate efforts. He also wants me to work with other students of his who also have code similar to mine so that we can all combine it and release a kickass free library for everyone. I almost swooned when hearing this.

My code is still not clean enough to be distributed, but remembering the words of great geeks ("release early, release often"), I have already begun distributing my code anyways to anyone who has asked, cautioning them that it's still not very clean. So far, two people have asked. One of them is a Yucatec Mayan, another student of my advisor (looks like he and another student will be the beta-testers of our team), and the other is an Italian who asked in a mailing list online for code like mine, so I gave him a copy. That means not only that I now have two users (yeah, baby!) but also, the Italian has been sending me patches.

Alright! I'm living the dream. Let's build the code together.

Where to now?

My goals are clear: get a PhD, travel around the world, and never leave school again.

Finishing my MSc is of course a prerequisite for this. So I'll focus on that first. But then comes the big choice: where to go for a PhD? So far, my two biggest choices are Norway and Israel. I would love to go to Russia, but they don't have money to offer, or at least I can't find any. It used to be that if you were willing to tolerate a little communist brainwashing, then Mother Russia would take you no matter where you came from, but since that whole shindig has fallen through, they now seem to expect for you to pay your own way.

So! Vikings or the promised land! Which one? I don't know. I'll send applications to both and see how it works out. Both of those places seem to be friendly to foreigners as far as money goes, so I'm hopeful. And what will I study? I am a bit torn, to tell the truth.

My MSc has been about applied mathematics. As I've discovered, apparently this means 10% mathematics and 90% coding. Not that I mind that too much, but I miss being able to work without a computer. I miss taking a book, some ideas, sitting under a tree somewhere and working out some pure, pristine, untainted mathematics. Particularly, I find number theory alluring. So far, I have been working mostly with functional analysis and numerical analysis. These two are have a very different flavour than number theory, almost diametrically opposite (of course, this is always a lie, since all fields of mathematics have connections between each other, but as a first-order approximation, it's a true statement).

So I'm pondering now, Norway or Israel, and number theory or more computery stuff? As far as location, that largely depends on factors mostly beyond my control, depending on how my applications go (by the way, the school I'm looking at in Israel wants me to take the GRE, ugh, how very un-international). I have found interesting people in both places that do both of the things I want to do, so I do have some choice. If I decide to stick to numerical analysis, there is a person in Israel who does *exactly* what I would want to work on: numerical models related to geophysical fluid dynamics (e.g. physical oceanography and atmospheric dynamics, weather prediction), and both places also have a good dosage of number theory (those guys are everywhere).

Number theory would be the more difficult choice, but also very seductive choice. Number theory has always seemed to me like the hardest branch of mathematics. The most famous open problems in mathematics (e.g. the Riemann hypothesis) are problems in number theory, and that's no coincidence. I would have to do a lot of catching up in order to get my number theory up to a level where I can write a PhD thesis about it. I'm not sure if advisors would take for a PhD in number theory given the gaps I have right now. I will still not discard this option, since working in number theory is still a dream I must pursue. Also, although I said earlier that I wanted number theory because I wanted to work on something that was away from computers, the truth is that a lot of experimentation in number theory takes place with computers, so I could easily integrate them with whatever else I wanted to do in that field.

One big problem with doing number theory, and part of the reason why I moved away from pure to more applied mathematics, is that number theory is much more lonely enterprise than applied mathematics. When people right now ask me what do I do, I tell them, well, I'm working with some mathematical equations for modelling wave motion with the eventual goal of applying this to weather prediction. Then I show them my glorious animation of this. Of course I can't go into specifics with lay people, but at least I can give them a rough explanation of what I do. Also, there many more people in the world I can interface with when doing numerical analysis, and this includes most scientists. It's easier to be a social butterfly when doing applied mathematics, and I am very social.

Number theory is more austere, more isolationist. The biggest modern celebrity in number theory, Andrew Wiles, achieved his solution by locking himself up in his attic for many years and not discussing his ideas with anyone except one person he trusted, and only after he had spend long sleepless nights alone for many years working on the problem. This may be an extreme characterisation, but certainly not too fringe as far as number theorists in general goes. That solitude was one of the things I dreaded most about doing applied mathematics forever.

So these are my ponderings, and I'm feeling very lucky that I am again in a position to make this kind of choices. Exciting times ahoy!

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