I'm writing this on the iPad, just to see what it's like. But this has more to do with one application I'd love to see on the iPad: Mathematica.

I'm a big fan of Mathematica. I don't know why people still use calculators when they can have the full computational power of another computer algebra system instead. Take 3D plotting as an example. It's a lot nicer to have a color, manipulable plot that refreshes instantly, as opposed to some anemic gray mesh on tiny low resolution graphing calculator.

Though I suppose I forego Mathematica for a calculator, or simply a pencil and paper, from time to time, mostly because lugging my laptop to class is something for a chore, and I find having a computer distracting.

Which is why I had hoped Wolfram Research would release a Mathematica application for the iPad. (I feel like the iPhone's screen is too small to support the full Mathematica interface.) I would gladly pay over $100 for that application. To have Mathematica's amazing computational power at my fingertips would improve my life immeasurably. Some would point to Wolfram Alpha, available via the web or a purpose-built application for the iPhone and iPad, as a potential substitute. But Wolfram Alpha, while powerful, isn't quite the same. I still haven't figured out how to factor polynomials in finite fields with Wolfram Alpha, but it's easy to do with Mathematica.

But it occurred to me that we'll likely never see Mathematica for the iPhone OS. For Apple prohibits developers from executing arbitrary code in third-party applications, which is exactly how the Mathematica interface works. Mathematica is not just a program — it's a programming language as well.

Hopefully, given that the iPad is closer to a general purpose computer than the iPhone, Apple will ease up slightly on their restrictions. Perhaps more on this tomorrow when they take the wraps off iPhone OS.