[dekhn]

I wasn't very good at solving integrals in grad school, so I bought Mathematica because I had the impression it could solve them. What I found was interesting. First, for all the integrals I dealt with, computers can't solve them using the rule systems that exist. Instead, you need a Physics Grad Student who knows how to solve integrals. Mathmeatica will just take your integral and spit out a more complicated one.

However, Mathematica is really good for symbolic algebra! I wrote a Python-Mathematica bridge many, many years ago, and learned that not only could it decompose numeric matrices, it could do it for matrices with symbols. Mind=blown.