We can lick gravity, but sometimes the paperwork is overwhelming. — Wernher von Braun Because having a worst case algorithm of n^2 is tractable, while solving

We can lick gravity, but sometimes the paperwork is overwhelming. — Wernher von Braun Because having a worst case algorithm of n^2 is tractable, while solving for n^1000000 or bigger is not so much. The numbers are as shockingly big as in thermodynamics. And for real problems, it's not just one matrix, but thousands, all interlocked. And for some reason, the most common cases involve extremely sparse matrices. Numerical methods can only scratch the surface. On the bright side, we can't even imagine the true difficultly level. Sure computers can model the easy text book examples, but when it comes to modeling the real world, our current best mathematical capabilities don't even get off the paper.