Personally, I'd say you should always check important calculations in some "by hand" way; just because you think you programmed the software right, doesn't mean the results come out.

Special rounding and age calculation rules are common (leap day); implicit conversions can be problematic... and who else remembers the Pentium floating point bug?

The ability to deliberately try to break the system in every reasonable way... over and over and over again... is invaluable in a tester.