If everything goes well, SymPy should be quite well tested when the summer is over and GSoC projects will improve it in the areas: geometry, graphing, concrete mathematics, linear algebra and polynomial equations (and stuff).
For me SymPy starts to be usable enough so that I can actually calculate something interesting. I started with the Schwarzschild solution to the Einstein's equations of the general relativity. So I start with a diagonal metric tensor, and calculate the Ricci tensor using SymPy and this works remarkably well and I get the correct differential equations. Now I am trying to make the SymPy's dsolve() to solve them. And then I would like to make pictures like this one using the graphing module. The code is in examples/relativity.py
My other application is the Quantum Field Theory, where I am trying to calculate some simple cross sections, however, SymPy is pretty slow on that, but when we optimize the polynomials stuff, it should work just fine. The code is in examples/qft.py
Being able to use symbolic manipulation in the Python language allows me to be really productive. And also it's fun, because it's a pleasure, like any other programming in Python. Programming in Maple is not a pleasure for me at all.
So over the summer, I'll try to make SymPy calculate the above things because that will show, if SymPy is usable, or not. Besides that, I want to polish the web page, and documentation and installation especially. And get it to Debian and Ubuntu.
Is any of you using something else than Debian/Ubuntu/Windows? If so, would you be willing to create a package for your distribution? :)