“The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?”, 2014-11 (; backlinks):
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it.
As an example, we show how we have detected an error of Mathematica computing determinants of matrices of integer numbers: not only it computes the determinants wrongly, but also it produces different results if one evaluates the same determinant twice. [reported 2013-10-07, not fixed as of 2014-06-29..]
…We have been using Mathematica as a tool in our mathematical research. All our computations with Mathematica have been symbolic, involving only integers (large integers, about 10 thousand digits long) and polynomials (with degree 60 at most), so no numerical rounding or instability can arise in them, and we completely trusted the results generated by Mathematica. However, we have obtained completely erroneous results. Perhaps someone may think that this was an esoteric error, without real relevance, because large integers do not appear in real life. This is not the case, because large integers are commonly used, for instance, in cryptography, where everything should work without serious errors. We have also briefly pointed out some other wrong computations that are clear to any mathematician. How then can we trust in computer algebra systems?