Programming Mathematics?

Adam asks: "I'm an undergraduate math and CS major, and as such, I would like to write some programs that do basic math, from finding perfect numbers to solving basic algebraic equations--just for fun. However, I only have experience with Java, and BigInteger and BigDecimal suck pretty hard as far as writing equations with them is concerned. So, to all you mathematicians and math lovers, what languages do you program mathematics in, and why?"